Given's Rotation SVD example

Time bar (total: 11.7s)

analyze617.0ms (5.3%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%48.6%51.4%0%0%0%0
0%0%48.6%51.4%0%0%0%1
0%0%48.6%51.4%0%0%0%2
0%0%48.6%51.4%0%0%0%3
0%0%48.6%51.4%0%0%0%4
31.3%15.2%33.4%51.4%0%0%0%5
34.4%16.7%31.9%51.4%0%0%0%6
51.6%25.1%23.6%51.4%0%0%0%7
53.1%25.8%22.8%51.4%0%0%0%8
62.5%30.4%18.2%51.4%0%0%0%9
63.7%31%17.7%51.4%0%0%0%10
68.6%33.3%15.3%51.4%0%0%0%11
69.2%33.7%15%51.4%0%0%0%12
Compiler

Compiled 28 to 20 computations (28.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 351.0ms
...c/correct-round.rkt:119:19: 115.0ms (32.7% of total)
ival-mult: 85.0ms (24.2% of total)
ival-sqrt: 49.0ms (13.9% of total)
ival-add: 32.0ms (9.1% of total)
ival-div: 21.0ms (6% of total)
ival-fabs: 20.0ms (5.7% of total)
ival-<: 18.0ms (5.1% of total)
ival-and: 6.0ms (1.7% of total)
const: 3.0ms (0.9% of total)
backward-pass: 1.0ms (0.3% of total)

sample2.7s (23.5%)

Results
1.3s6177×0valid
544.0ms1206×2valid
293.0ms686×1valid
91.0ms187×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.7s
...c/correct-round.rkt:119:19: 563.0ms (32.8% of total)
ival-mult: 371.0ms (21.6% of total)
ival-sqrt: 209.0ms (12.2% of total)
ival-add: 149.0ms (8.7% of total)
ival-<: 137.0ms (8% of total)
ival-div: 103.0ms (6% of total)
backward-pass: 92.0ms (5.4% of total)
ival-fabs: 63.0ms (3.7% of total)
ival-and: 16.0ms (0.9% of total)
const: 15.0ms (0.9% of total)
Bogosity

preprocess124.0ms (1.1%)

Algorithm
2×egg-herbie
Rules
2100×fnmadd-define
1558×fma-define
1450×fnmsub-define
1444×fmsub-define
1054×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04296
110986
222680
351380
4109680
5209180
6345480
7462780
8534080
9590880
10619380
11634680
12640480
13640880
01415
13114
24213
34713
44913
55013
05013
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
Call 2
Inputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
Outputs
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))
(sqrt (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(sqrt (fnmsub (* 1/2 x) (rsqrt (fma 4 (square p) (square x))) -1/2))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (fnmsub (* x -1/2) (rsqrt (fma 4 (square p) (square x))) -1/2)))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(neg (sqrt (fnmsub (* 1/2 x) (rsqrt (fma 4 (square p) (square x))) -1/2)))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
(sqrt (fnmsub (* p -1/2) (rsqrt (fma 4 (square x) (square p))) -1/2))
Symmetry

(abs p)

explain207.0ms (1.8%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
640-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
310-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
270-2(2.163996381858955e-23 -4.969679070780381e+134)(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
00-0-x
00-0-#s(literal 1/2 binary64)
00-0-(*.f64 #s(literal 4 binary64) p)
00-0-(*.f64 (*.f64 #s(literal 4 binary64) p) p)
00-0-(+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))
00-0-p
00-0-(*.f64 x x)
00-0-#s(literal 4 binary64)
00-0-(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
00-0-#s(literal 1 binary64)
00-0-(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
Results
72.0ms394×0valid
44.0ms78×2valid
12.0ms32×1valid
6.0ms8×3valid
Compiler

Compiled 213 to 44 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 61.0ms
ival-mult: 20.0ms (32.9% of total)
ival-sqrt: 18.0ms (29.6% of total)
ival-add: 9.0ms (14.8% of total)
backward-pass: 7.0ms (11.5% of total)
ival-div: 6.0ms (9.9% of total)
const: 1.0ms (1.6% of total)

eval0.0ms (0%)

Compiler

Compiled 19 to 13 computations (31.6% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶79.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
Rules
32×*-lowering-*.f32
32×*-lowering-*.f64
18×fma-lowering-fma.f32
18×fma-define
18×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01366
12464
23464
34164
44664
54864
04864
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
1/2
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(* 1/2 x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
(* 4 (* p p))
4
(* p p)
p
(* x x)
Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)

localize104.0ms (0.9%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(*.f64 #s(literal 4 binary64) (*.f64 p p))
✓accuracy90.5%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
✓accuracy89.2%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓accuracy76.7%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Results
51.0ms196×0valid
23.0ms39×2valid
8.0ms17×1valid
3.0ms4×3valid
Compiler

Compiled 87 to 14 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-mult: 30.0ms (65.5% of total)
ival-sqrt: 5.0ms (10.9% of total)
ival-add: 4.0ms (8.7% of total)
ival-div: 3.0ms (6.6% of total)
backward-pass: 3.0ms (6.6% of total)
const: 1.0ms (2.2% of total)

series16.0ms (0.1%)

Counts
6 → 120
Calls
Call 1
Inputs
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))>
#<alt (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))>
#<alt (* 1/2 x)>
#<alt (sqrt (+ (* 4 (* p p)) (* x x)))>
#<alt (* 4 (* p p))>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (/ (pow p 2) (pow x 2)))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* -1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
#<alt (* 4 (pow p 2))>
Calls

30 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
1.0ms
p
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
1.0ms
x
@inf
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
1.0ms
p
@inf
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
1.0ms
x
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))

rewrite256.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
4058×*-lowering-*.f32
4058×*-lowering-*.f64
2612×/-lowering-/.f32
2612×/-lowering-/.f64
1718×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01352
16450
252850
3767650
0868250
Stop Event
1×iter limit
1×node limit
Counts
6 → 178
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(* 1/2 x)
(sqrt (+ (* 4 (* p p)) (* x x)))
(* 4 (* p p))
Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))) #s(literal -1/8 binary64))) (sqrt.f64 (+.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal -1/4 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal -1/4 binary64))) (sqrt.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(+.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (neg.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(-.f64 (/.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1/2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (neg.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))) (+.f64 (neg.f64 (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal -1/4 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x (*.f64 #s(literal -1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(neg.f64 (/.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))))
(neg.f64 (/.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal 1 binary64)))
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(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (*.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))) (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal -16 binary64) (*.f64 p (*.f64 p (*.f64 p p)))))) (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (neg.f64 (sqrt.f64 (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(*.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64))))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
(*.f64 p (*.f64 #s(literal 4 binary64) p))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(*.f64 (*.f64 #s(literal 4 binary64) p) p)

simplify314.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
6082×*-lowering-*.f32
6082×*-lowering-*.f64
3762×+-lowering-+.f64
3762×+-lowering-+.f32
1706×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03812053
112091828
243411780
085651780
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 1/4 (/ x p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (/ (pow p 2) (pow x 2)))) 1/2)
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* -1/4 (/ x p))
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
(* 4 (pow p 2))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 x (-.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 p (*.f64 p p))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/128 binary64) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (*.f64 (*.f64 x x) (*.f64 x x))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (+.f64 (+.f64 (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))))) (pow.f64 x #s(literal 6 binary64))))) #s(literal 1 binary64)))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (*.f64 p p)))) (*.f64 p (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (+.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (*.f64 p p))) (*.f64 p (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (+.f64 (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)))))) (*.f64 (/.f64 #s(literal -1/8 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) #s(literal -1/64 binary64)) (*.f64 p p)))) p))) (*.f64 p (pow.f64 x #s(literal 6 binary64))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 11/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) p) (/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 p p))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal -1/8 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 (*.f64 x x) p) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (+.f64 (*.f64 p p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 1/4 binary64)) #s(literal -12 binary64)) (*.f64 x x))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (+.f64 (*.f64 p p) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (/.f64 (+.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 (*.f64 p p) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (+.f64 (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64))))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -10 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (/.f64 #s(literal -3/256 binary64) (pow.f64 p #s(literal 5 binary64)))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/4 binary64)) p))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)))) (*.f64 (*.f64 p p) (*.f64 p p)))) p))
(* 1/4 (/ x p))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p)))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64)))))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x (*.f64 x (+.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -5/4096 binary64)) (pow.f64 p #s(literal 7 binary64))) (/.f64 #s(literal 3/512 binary64) (pow.f64 p #s(literal 5 binary64))))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (*.f64 p p) (*.f64 x x))) (/.f64 (+.f64 (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))) (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)))) (pow.f64 x #s(literal 6 binary64)))))
-1/2
#s(literal -1/2 binary64)
(- (/ (pow p 2) (pow x 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(+.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 1/4 binary64)) #s(literal -12 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64)))
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (/ (pow p 2) (pow x 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 1/4 binary64)) #s(literal -12 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 6 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -10 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal -1 binary64) (*.f64 x x)))))
(* 1/4 (/ x p))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)))) (*.f64 (*.f64 p p) (*.f64 p p)))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (+.f64 (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) p)
(* -1/4 (/ x p))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) p)
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(/.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64)))) (*.f64 (*.f64 p p) (*.f64 p p)))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (+.f64 (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) p))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ x (* 2 (/ (pow p 2) x)))
(+.f64 x (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -2 binary64)) (*.f64 x (*.f64 x x))) (/.f64 #s(literal 2 binary64) x))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(+.f64 x (*.f64 p (*.f64 p (+.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x)))))))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 p (+.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))
(* -2 p)
(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p)) (-.f64 #s(literal 0 binary64) p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))))) (-.f64 #s(literal 0 binary64) p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) p) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -2 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))

eval39.0ms (0.3%)

Compiler

Compiled 9951 to 1186 computations (88.1% saved)

prune40.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2908298
Fresh000
Picked011
Done000
Total2909299
Accuracy
100.0%
Counts
299 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
17.4%
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
▶78.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
25.5%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
▶26.3%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
▶58.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓79.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
53.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
▶57.4%
(sqrt.f64 #s(literal 1/2 binary64))
▶36.1%
#s(literal 1 binary64)
Compiler

Compiled 229 to 161 computations (29.7% saved)

simplify19.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 p p)
✓cost-diff0
(*.f64 (*.f64 p p) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
✓cost-diff128
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
Rules
170×*-lowering-*.f32
170×*-lowering-*.f64
78×fma-define
70×fma-lowering-fma.f32
70×fma-lowering-fma.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
031207
169200
2120200
3171198
4208198
5220198
6221198
0221198
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
1
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
1/2
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(* 1/2 x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
(* 4 (* p p))
4
(* p p)
p
(* x x)
1
(+ 1 (/ (* (* p p) -1/2) (* x x)))
1
(/ (* (* p p) -1/2) (* x x))
(* (* p p) -1/2)
(* p p)
p
-1/2
(* x x)
x
(sqrt 1/2)
1/2
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))
1/2
(/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))
(* 1/2 x)
x
(+ (* p 2) (* x (* x (/ 1/4 p))))
(* p 2)
p
2
(* x (* x (/ 1/4 p)))
(* x (/ 1/4 p))
(/ 1/4 p)
1/4
Outputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (/ (* (* p p) -1/2) (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x)))
1
#s(literal 1 binary64)
(/ (* (* p p) -1/2) (* x x))
(/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x))
(* (* p p) -1/2)
(*.f64 p (*.f64 p #s(literal -1/2 binary64)))
(* p p)
(*.f64 p p)
p
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ (* p 2) (* x (* x (/ 1/4 p))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(* x (* x (/ 1/4 p)))
(/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)
(* x (/ 1/4 p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
1/4
#s(literal 1/4 binary64)

localize226.0ms (1.9%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓accuracy99.7%
(*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓accuracy99.6%
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓accuracy92.3%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(*.f64 x x)
✓accuracy100.0%
(*.f64 p p)
✓accuracy100.0%
(*.f64 (*.f64 p p) #s(literal -1/2 binary64))
✓accuracy87.4%
(/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))
✓accuracy99.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
✓accuracy90.1%
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
✓accuracy89.2%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓accuracy76.7%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Results
97.0ms197×0valid
48.0ms33×2valid
23.0ms22×1valid
9.0ms4×3valid
Compiler

Compiled 255 to 32 computations (87.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 73.0ms
ival-mult: 20.0ms (27.2% of total)
ival-sqrt: 17.0ms (23.1% of total)
ival-div: 13.0ms (17.7% of total)
backward-pass: 13.0ms (17.7% of total)
ival-add: 8.0ms (10.9% of total)
const: 1.0ms (1.4% of total)

series40.0ms (0.3%)

Counts
17 → 336
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))>
#<alt (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))>
#<alt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))>
#<alt (+ 1 (/ (* (* p p) -1/2) (* x x)))>
#<alt (/ (* (* p p) -1/2) (* x x))>
#<alt (* (* p p) -1/2)>
#<alt (* p p)>
#<alt (sqrt 1/2)>
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))>
#<alt (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))>
#<alt (* 1/2 x)>
#<alt (sqrt (+ (* 4 (* p p)) (* x x)))>
#<alt (* x x)>
#<alt (* x (/ 1/4 p))>
#<alt (* x (* x (/ 1/4 p)))>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (* 1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (pow p 2) (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 6))) (* 1/2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 49/16 (/ (pow p 2) (pow x 6))) (* 9/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* p (sqrt 2))))) p)) (* -1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))>
#<alt (+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))>
#<alt (/ (pow x 2) (pow p 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))>
#<alt (- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))>
#<alt 2>
#<alt (+ 2 (/ x p))>
#<alt (+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (* -1/2 (pow p 2))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- (* -16 (pow p 3)) (* -1 (/ (pow p 3) (pow (sqrt 1/2) 4)))) (* (pow x 3) (sqrt 1/2)))) (/ p (* x (sqrt 1/2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* 1/2 (/ (pow p 2) (* x (pow (sqrt 1/2) 3))))) x)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* -1 (/ (+ (* -1/2 (/ (pow p 2) (pow (sqrt 1/2) 3))) (* 1/2 (/ (+ (* -16 (pow p 3)) (/ (pow p 3) (pow (sqrt 1/2) 4))) (* x (sqrt 1/2))))) x))) x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* p (+ (* -1/2 (/ p (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* p (+ (* p (- (* 1/2 (/ (* p (- (/ 1 (* (pow x 3) (pow (sqrt 1/2) 4))) (* 16 (/ 1 (pow x 3))))) (sqrt 1/2))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (/ 1 (* x (sqrt 1/2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (* 2 (/ p x))))>
#<alt (+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (+ (* 2 (/ p x)) (* 128 (/ (pow p 5) (pow x 5))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* -1 (/ (- (* 16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)))>
#<alt (+ 1/2 (* -1 (/ (- (* -128 (/ (pow p 5) (pow x 4))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p))) x)))>
#<alt 1/2>
#<alt (+ 1/2 (* 2 (/ p x)))>
#<alt (+ 1/2 (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ 1/2 (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (+ (* 1/256 (/ (pow x 5) (pow p 5))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 7))) (* 1/256 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* 2 (/ p x))>
#<alt (/ (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)>
#<alt (/ (- (+ (* 2 p) (* 128 (/ (pow p 5) (pow x 4)))) (* 16 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1024 (/ (pow p 7) (pow x 6))) (* 2 p)) (+ (* -128 (/ (pow p 5) (pow x 4))) (* 16 (/ (pow p 3) (pow x 2))))) x)>
#<alt (* 2 (/ p x))>
#<alt (* -1 (/ (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -128 (/ (pow p 5) (pow x 4))) (* -2 p)) (* -16 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (- (+ (* -2 p) (* 1024 (/ (pow p 7) (pow x 6)))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 128 (/ (pow p 5) (pow x 4))))) x))>
#<alt (* 2 (/ p x))>
#<alt (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -1024 (/ (pow p 2) (pow x 7))) (* 128 (/ 1 (pow x 5))))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* -1/2048 (/ (pow x 7) (pow p 6))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x)))) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* 1/2048 (/ (pow x 7) (pow p 6))) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
Calls

84 calls:

TimeVariablePointExpression
7.0ms
x
@0
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
3.0ms
x
@-inf
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
3.0ms
p
@inf
(+ 1 (/ (* (* p p) -1/2) (* x x)))
1.0ms
x
@inf
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
1.0ms
p
@inf
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))

rewrite334.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
4242×*-lowering-*.f32
4242×*-lowering-*.f64
2494×+-lowering-+.f64
2494×+-lowering-+.f32
2314×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
031148
1180139
21571129
08737129
Stop Event
1×iter limit
1×node limit
Counts
17 → 343
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+ 1 (/ (* (* p p) -1/2) (* x x)))
(/ (* (* p p) -1/2) (* x x))
(* (* p p) -1/2)
(* p p)
(sqrt 1/2)
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p))))))
(/ (* 1/2 x) (+ (* p 2) (* x (* x (/ 1/4 p)))))
(* 1/2 x)
(sqrt (+ (* 4 (* p p)) (* x x)))
(* x x)
(* x (/ 1/4 p))
(* x (* x (/ 1/4 p)))
Outputs
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))) (sqrt.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal -1 binary64))))
(fabs.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (+.f64 #s(literal -1/2 binary64) (neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
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(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x)))) (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))))) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x))))))
(*.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(neg.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x))))
(/.f64 (*.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
(/.f64 (neg.f64 (*.f64 x #s(literal -1/2 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(pow.f64 (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(*.f64 #s(literal 1/2 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(*.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(*.f64 x (/.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(*.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))
(*.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1 binary64)))
(*.f64 (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))) #s(literal 1/2 binary64))
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (/.f64 (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))))) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) (-.f64 (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))) (*.f64 p #s(literal 2 binary64))))))
(*.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) p)) (*.f64 x (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))))) (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
(exp.f64 (*.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(hypot.f64 x (*.f64 p #s(literal 2 binary64)))
(hypot.f64 (*.f64 p #s(literal 2 binary64)) x)
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))) (+.f64 (*.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))))))
(/.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(/.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 p p) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p))) #s(literal 64 binary64)) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (sqrt.f64 (neg.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))
(*.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))) #s(literal 1/2 binary64)))
(*.f64 (hypot.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x #s(literal 1/4 binary64))))
(/.f64 x (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(/.f64 (neg.f64 (*.f64 x #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) p))
(/.f64 (*.f64 x #s(literal 1 binary64)) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) p))
(/.f64 (*.f64 #s(literal 1 binary64) x) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 #s(literal -1/4 binary64) x) (-.f64 #s(literal 0 binary64) p))
(pow.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) p) x))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) x)
(*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))
(/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)
(/.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) p))
(/.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) x) p)
(*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x))
(*.f64 (*.f64 x (/.f64 #s(literal 1/4 binary64) p)) x)
(*.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))

simplify370.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
6052×*-lowering-*.f32
6052×*-lowering-*.f64
4106×+-lowering-+.f64
4106×+-lowering-+.f32
1656×fma-lowering-fma.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07985170
126254506
082814506
Stop Event
1×iter limit
1×node limit
Counts
336 → 336
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
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1
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
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(* -1 (/ x p))
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(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))
1
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(sqrt 2)
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(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))
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2
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1
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(- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(/ (pow x 2) (pow p 2))
(* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))
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(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (/ x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))
1/2
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(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
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(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
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(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
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(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(* -1/2 (pow p 2))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- (* -16 (pow p 3)) (* -1 (/ (pow p 3) (pow (sqrt 1/2) 4)))) (* (pow x 3) (sqrt 1/2)))) (/ p (* x (sqrt 1/2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* 1/2 (/ (pow p 2) (* x (pow (sqrt 1/2) 3))))) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* -1 (/ (+ (* -1/2 (/ (pow p 2) (pow (sqrt 1/2) 3))) (* 1/2 (/ (+ (* -16 (pow p 3)) (/ (pow p 3) (pow (sqrt 1/2) 4))) (* x (sqrt 1/2))))) x))) x)))
(sqrt 1/2)
(+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))
(+ (sqrt 1/2) (* p (+ (* -1/2 (/ p (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ 1 (* x (sqrt 1/2))))))
(+ (sqrt 1/2) (* p (+ (* p (- (* 1/2 (/ (* p (- (/ 1 (* (pow x 3) (pow (sqrt 1/2) 4))) (* 16 (/ 1 (pow x 3))))) (sqrt 1/2))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))))) (/ 1 (* x (sqrt 1/2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
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(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* 1/32 (pow x 3)) (* 1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
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(+ 1/2 (* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1/2
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(+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (+ (* 2 (/ p x)) (* 128 (/ (pow p 5) (pow x 5))))))
1/2
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1/2
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1/2
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1/2
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(+ 1/2 (* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p)))
(* 1/4 (/ x p))
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(* x (+ (* (pow x 2) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -1/2048 (/ (pow x 2) (pow p 7))) (* 1/256 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* 2 (/ p x))
(/ (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)
(/ (- (+ (* 2 p) (* 128 (/ (pow p 5) (pow x 4)))) (* 16 (/ (pow p 3) (pow x 2)))) x)
(/ (- (+ (* -1024 (/ (pow p 7) (pow x 6))) (* 2 p)) (+ (* -128 (/ (pow p 5) (pow x 4))) (* 16 (/ (pow p 3) (pow x 2))))) x)
(* 2 (/ p x))
(* -1 (/ (+ (* -2 p) (* 16 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (- (+ (* -128 (/ (pow p 5) (pow x 4))) (* -2 p)) (* -16 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (- (+ (* -2 p) (* 1024 (/ (pow p 7) (pow x 6)))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 128 (/ (pow p 5) (pow x 4))))) x))
(* 2 (/ p x))
(* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x))))
(* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))
(* p (+ (* (pow p 2) (- (* (pow p 2) (+ (* -1024 (/ (pow p 2) (pow x 7))) (* 128 (/ 1 (pow x 5))))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x))) p)
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (+ (* -1/2048 (/ (pow x 7) (pow p 6))) (+ (* 1/256 (/ (pow x 5) (pow p 4))) (* 1/4 x)))) p)
(* 1/4 (/ x p))
(* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (* 1/32 (/ (pow x 3) (pow p 2))))) p))
(* -1 (/ (+ (* -1/4 x) (+ (* -1/256 (/ (pow x 5) (pow p 4))) (+ (* 1/2048 (/ (pow x 7) (pow p 6))) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
(* 1/4 (/ (pow x 2) p))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) x) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 #s(literal 1/512 binary64) (*.f64 (*.f64 p p) (*.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/128 binary64) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) p) p) #s(literal 2 binary64)) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))))) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (+.f64 p (*.f64 (/.f64 #s(literal 1/8 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 p (*.f64 (/.f64 #s(literal 1/8 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 x x)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 p p)))) (*.f64 p (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (+.f64 p (+.f64 (*.f64 (/.f64 #s(literal 1/8 binary64) p) (/.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) (*.f64 p (*.f64 p #s(literal 2 binary64)))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 p (*.f64 p #s(literal 2 binary64)))) (*.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 8 binary64)))))) (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) (*.f64 #s(literal -12 binary64) (-.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 p p)))))) (*.f64 p p))) (*.f64 p (pow.f64 x #s(literal 6 binary64)))) (/.f64 (-.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)))) (*.f64 #s(literal 16 binary64) (pow.f64 p #s(literal 6 binary64)))) (/.f64 (*.f64 #s(literal 1/64 binary64) (pow.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64)) #s(literal 2 binary64))) (*.f64 p p))) (*.f64 p (pow.f64 x #s(literal 4 binary64)))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal -1/2 binary64))) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal 11/8 binary64) (*.f64 p p)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal -69/16 binary64) (*.f64 p p)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (/.f64 (*.f64 #s(literal -1/128 binary64) (*.f64 x x)) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (/.f64 (*.f64 #s(literal -1/128 binary64) (*.f64 x x)) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (*.f64 p p))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) #s(literal -1/8 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/128 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (*.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/32 binary64))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))) (*.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (*.f64 p (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (*.f64 x (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 p p)) (/.f64 #s(literal -1/4 binary64) (*.f64 p (*.f64 p #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 p (sqrt.f64 #s(literal 2 binary64))))) x)))
(+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 p p)) (/.f64 #s(literal -1/4 binary64) (*.f64 p (*.f64 p #s(literal 2 binary64))))) p)) (/.f64 #s(literal 1/8 binary64) (*.f64 p (*.f64 p p)))))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 p p)) (/.f64 #s(literal -1/4 binary64) (*.f64 p (*.f64 p #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 #s(literal -1/2 binary64) (*.f64 p (sqrt.f64 #s(literal 2 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (* 1/2 (/ (pow p 2) (pow x 2)))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x)) (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))))
(+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (pow p 2) (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 6))) (* 1/2 (/ (pow p 2) (pow x 2))))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64)))))) (+.f64 (*.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) p) p) (+.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) p) p) #s(literal 2 binary64)) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 p (*.f64 p (-.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (pow.f64 p #s(literal 4 binary64)))))))) (pow.f64 x #s(literal 6 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 x x))))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* -1 (* x (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))
(-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 p #s(literal 4 binary64))) #s(literal -12 binary64)) (*.f64 x (*.f64 x (*.f64 p (*.f64 p p))))) (/.f64 #s(literal 1 binary64) p))))
(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))
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1
#s(literal 1 binary64)
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(sqrt 2)
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(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))
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2
#s(literal 2 binary64)
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1
#s(literal 1 binary64)
(+ 1 (/ (pow p 2) (pow x 2)))
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(/ (pow x 2) (pow p 2))
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1
#s(literal 1 binary64)
(+ 1 (/ (pow p 2) (pow x 2)))
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2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
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2
#s(literal 2 binary64)
(+ 2 (/ x p))
(+.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
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(+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))
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1/2
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(*.f64 p #s(literal -2 binary64))
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p)))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p)) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (*.f64 p p)) (+.f64 (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64))) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (neg.f64 p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 #s(literal -1/64 binary64) (*.f64 x x)) (*.f64 p (*.f64 p p))))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(*.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 (*.f64 p (*.f64 p #s(literal 2 binary64))) (*.f64 x x)) (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)

eval95.0ms (0.8%)

Compiler

Compiled 17288 to 2260 computations (86.9% saved)

prune95.0ms (0.8%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New7254729
Fresh123
Picked145
Done101
Total72810738
Accuracy
100.0%
Counts
738 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶17.4%
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
54.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
▶56.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
▶25.5%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓26.3%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
▶53.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
▶79.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
✓58.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓57.4%
(sqrt.f64 #s(literal 1/2 binary64))
✓36.1%
#s(literal 1 binary64)
Compiler

Compiled 184 to 134 computations (27.2% saved)

simplify252.0ms (2.2%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 x #s(literal 1/4 binary64))
✓cost-diff0
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff128
(*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)))
✓cost-diff384
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))
✓cost-diff384
(+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p))))
✓cost-diff512
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
✓cost-diff0
(/.f64 p x)
✓cost-diff0
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓cost-diff0
(*.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
Rules
5864×*-lowering-*.f32
5864×*-lowering-*.f64
2958×/-lowering-/.f32
2958×/-lowering-/.f64
1632×distribute-rgt-neg-in
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
036164
188152
2241152
3966147
42448144
53482143
08335143
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
1/2
(/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(* 1/2 x)
x
(sqrt (+ (* x x) (* (* p 2) (* p 2))))
(* p 2)
p
2
(- 0 (/ p x))
0
(/ p x)
p
x
(/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))
(+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p))))
p
(/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))
(* 1/8 (* (* (* p p) (* p p)) -12))
1/8
(* (* (* p p) (* p p)) -12)
(* (* p p) (* p p))
(* p p)
-12
(* x (* x p))
x
(* x p)
(- 0 x)
0
(/ 1 (sqrt 2))
1
(sqrt 2)
2
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(+ 1/2 (/ (* x 1/4) p))
1/2
(/ (* x 1/4) p)
(* x 1/4)
x
1/4
p
Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* x x) (* (* p 2) (* p 2))))
(hypot.f64 x (*.f64 p #s(literal 2 binary64)))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(- 0 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
0
#s(literal 0 binary64)
(/ p x)
(/.f64 p x)
p
x
(/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))
(/.f64 (*.f64 p (-.f64 #s(literal -1 binary64) (*.f64 p (/.f64 (*.f64 p (/.f64 #s(literal -3/2 binary64) x)) x)))) x)
(+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p))))
(*.f64 p (+.f64 #s(literal 1 binary64) (*.f64 p (/.f64 (*.f64 p (/.f64 #s(literal -3/2 binary64) x)) x))))
p
(/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))
(/.f64 (*.f64 #s(literal -3/2 binary64) (*.f64 p (/.f64 (*.f64 p p) x))) x)
(* 1/8 (* (* (* p p) (* p p)) -12))
(*.f64 p (*.f64 (*.f64 p (*.f64 p p)) #s(literal -3/2 binary64)))
1/8
#s(literal 1/8 binary64)
(* (* (* p p) (* p p)) -12)
(*.f64 p (*.f64 (*.f64 p p) (*.f64 p #s(literal -12 binary64))))
(* (* p p) (* p p))
(*.f64 p (*.f64 p (*.f64 p p)))
(* p p)
(*.f64 p p)
-12
#s(literal -12 binary64)
(* x (* x p))
(*.f64 x (*.f64 x p))
x
(* x p)
(*.f64 x p)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(+ 1/2 (/ (* x 1/4) p))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
1/2
#s(literal 1/2 binary64)
(/ (* x 1/4) p)
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
x
1/4
#s(literal 1/4 binary64)
p

localize417.0ms (3.6%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
✓accuracy100.0%
(*.f64 x #s(literal 1/4 binary64))
✓accuracy96.6%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy98.8%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy99.8%
(*.f64 (*.f64 p p) (*.f64 p p))
✓accuracy99.7%
(*.f64 x (*.f64 x p))
✓accuracy97.7%
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
✓accuracy74.8%
(/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
✓accuracy100.0%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
Results
302.0ms196×0valid
24.0ms60×0invalid
Compiler

Compiled 201 to 34 computations (83.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 64.0ms
ival-div: 23.0ms (35.9% of total)
ival-mult: 17.0ms (26.5% of total)
ival-sqrt: 7.0ms (10.9% of total)
compiled-spec: 7.0ms (10.9% of total)
ival-add: 6.0ms (9.4% of total)
ival-sub: 2.0ms (3.1% of total)
const: 1.0ms (1.6% of total)
backward-pass: 0.0ms (0% of total)

series29.0ms (0.2%)

Counts
18 → 336
Calls
Call 1
Inputs
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))>
#<alt (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))>
#<alt (* 1/2 x)>
#<alt (- 0 (/ p x))>
#<alt (/ p x)>
#<alt (/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))>
#<alt (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p))))>
#<alt (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))>
#<alt (* 1/8 (* (* (* p p) (* p p)) -12))>
#<alt (/ 1 (sqrt 2))>
#<alt (sqrt 2)>
#<alt (sqrt (+ 1/2 (/ (* x 1/4) p)))>
#<alt (+ 1/2 (/ (* x 1/4) p))>
#<alt (/ (* x 1/4) p)>
#<alt (* x 1/4)>
#<alt (* x (* x p))>
#<alt (* (* p p) (* p p))>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt -1/2>
#<alt (- (/ (pow p 2) (pow x 2)) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)>
#<alt (- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (/ (pow p 2) (pow x 2)))) 1/2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)>
#<alt (* -1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (* -1 (/ p x))>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt p>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt (/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt p>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (+ p (* -3/2 (/ (pow p 3) (pow x 2))))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (* -3/2 (pow p 4))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))>
#<alt (* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))>
#<alt (* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))>
#<alt (* 1/2 (sqrt (/ x p)))>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)>
#<alt (/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt (/ (+ (* 1/4 x) (* 1/2 p)) p)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 (/ x p))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (* p (pow x 2))>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
#<alt (pow p 4)>
Calls

84 calls:

TimeVariablePointExpression
5.0ms
x
@inf
(/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))
2.0ms
x
@-inf
(- 0 (/ p x))
2.0ms
p
@0
(sqrt (+ 1/2 (/ (* x 1/4) p)))
2.0ms
x
@inf
(+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p))))
1.0ms
x
@0
(/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))

rewrite356.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
3326×*-lowering-*.f32
3326×*-lowering-*.f64
3106×/-lowering-/.f32
3106×/-lowering-/.f64
1634×pow-lowering-pow.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036126
1205114
21871114
08343114
Stop Event
1×iter limit
1×node limit
Counts
18 → 428
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2))))))
(/ (* 1/2 x) (sqrt (+ (* x x) (* (* p 2) (* p 2)))))
(* 1/2 x)
(- 0 (/ p x))
(/ p x)
(/ (+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))) (- 0 x))
(+ p (/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p))))
(/ (* 1/8 (* (* (* p p) (* p p)) -12)) (* x (* x p)))
(* 1/8 (* (* (* p p) (* p p)) -12))
(/ 1 (sqrt 2))
(sqrt 2)
(sqrt (+ 1/2 (/ (* x 1/4) p)))
(+ 1/2 (/ (* x 1/4) p))
(/ (* x 1/4) p)
(* x 1/4)
(* x (* x p))
(* (* p p) (* p p))
Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 1/4 binary64))) (sqrt.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))
(+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))) (/.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 x (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/2 binary64))
(fma.f64 (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64))))) (-.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))))
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(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)))
(*.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 x #s(literal 1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) x)
(*.f64 x #s(literal 1/4 binary64))
(*.f64 #s(literal 1/4 binary64) x)
(*.f64 x (*.f64 x p))
(*.f64 (*.f64 x x) p)
(*.f64 p (*.f64 x x))
(*.f64 (*.f64 x p) x)
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 p)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 p) #s(literal 4 binary64)))
(exp.f64 (+.f64 (*.f64 #s(literal 2 binary64) (log.f64 p)) (*.f64 #s(literal 2 binary64) (log.f64 p))))
(pow.f64 p #s(literal 4 binary64))
(pow.f64 (*.f64 p p) #s(literal 2 binary64))
(pow.f64 (*.f64 p (*.f64 p (*.f64 p p))) #s(literal 1 binary64))
(*.f64 p (*.f64 p (*.f64 p p)))
(*.f64 (*.f64 p p) (*.f64 p p))
(*.f64 (*.f64 p (*.f64 p p)) p)

simplify523.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
6422×*-lowering-*.f32
6422×*-lowering-*.f64
2812×+-lowering-+.f64
2812×+-lowering-+.f32
2008×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04653632
114243289
249583231
087353231
Stop Event
1×iter limit
1×node limit
Counts
336 → 336
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(/ (pow p 2) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
1
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* -1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(* 1/4 (/ x p))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* x (+ (* (pow x 2) (- (* (pow x 2) (+ (* -5/4096 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+ 1/2 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
-1/2
(- (/ (pow p 2) (pow x 2)) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (/ (pow p 2) (pow x 2))) 1/2)
(- (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))) (/ (pow p 2) (pow x 2)))) 1/2)
1/2
(+ 1/2 (* -1 (/ (pow p 2) (pow x 2))))
(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
(/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* -1/4 (/ x p))
(* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p))
(* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/2 (/ (* x (+ (* 1/256 (pow x 6)) (* 1/8 (* (pow x 2) (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4))))))) (pow p 6))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
p
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* p (+ 1 (* -3/2 (/ (pow p 2) (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -1 (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2)))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
(/ (+ (* -3/2 (pow p 3)) (* p (pow x 2))) (pow x 2))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
p
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(+ p (* -3/2 (/ (pow p 3) (pow x 2))))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (/ (pow p 3) (pow x 2)))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(* -3/2 (pow p 4))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/1024 (/ x (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/2 (sqrt (/ x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/4 (sqrt (/ (pow p 5) (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))))
(* -1 (* (sqrt (/ x p)) (* (sqrt -1) (sqrt -1/4))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ (pow p 3) (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/4) 3)))) (+ (* 1/128 (* (sqrt (/ (pow p 5) (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/4) 5)))) (+ (* 1/4 (* (sqrt (/ p (pow x 3))) (/ (sqrt -1) (sqrt -1/4)))) (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (sqrt -1/4))))))))
(* 1/2 (sqrt (/ x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* (pow p 2) (+ (* -1/4 (sqrt (/ 1 (* (pow p 3) (pow x 3))))) (* 1/4 (sqrt (/ 1 (* p (pow x 5)))))))))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/1024 (/ (pow x 3) (* (pow p 3) (pow (sqrt 1/2) 5)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3))) (* 1/1024 (/ (pow x 3) (* p (pow (sqrt 1/2) 5))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(* 1/4 (/ x p))
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 (/ x p))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(* p (pow x 2))
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
(pow p 4)
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 (/.f64 #s(literal 1/512 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (*.f64 p (*.f64 p p))) (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))))) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1/128 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (*.f64 p p)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (pow.f64 x #s(literal 4 binary64))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 p (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))))))) (pow.f64 x #s(literal 6 binary64))))))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(/.f64 (+.f64 p (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (+.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (*.f64 (/.f64 #s(literal -1/64 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) p))))) (*.f64 p (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
(/.f64 (+.f64 p (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p))) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (+.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (*.f64 (/.f64 #s(literal -1/64 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) p)))) (*.f64 p (pow.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (+.f64 (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)))))) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (+.f64 (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64)) (*.f64 (/.f64 #s(literal -1/64 binary64) p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64)) p))))) #s(literal -1/8 binary64)) (*.f64 p p))) (*.f64 p (pow.f64 x #s(literal 6 binary64)))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 11/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(+.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -69/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 11/8 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (*.f64 p p)))) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) p) #s(literal -1/8 binary64)))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 (*.f64 x x) p) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) x) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 #s(literal -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) p)) p))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal -1/32 binary64) (*.f64 p (*.f64 p p))) (/.f64 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))
(+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 p p) (*.f64 x x))))
(+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))
(+.f64 (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (*.f64 p p) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64))) (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 6 binary64))))
(/ (pow p 2) (pow x 2))
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))
(/.f64 (+.f64 (*.f64 p p) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/4 binary64)) (*.f64 x x))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))
(/.f64 (+.f64 (*.f64 p p) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x)) (/.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 x x))
(/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))
(/.f64 (+.f64 (+.f64 (*.f64 p p) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p (*.f64 p (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 binary64))) (pow.f64 x #s(literal 4 binary64)))) (*.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))) (*.f64 #s(literal 2 binary64) (*.f64 p p))) (+.f64 (*.f64 #s(literal -256 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p)))) (*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 (*.f64 p p) (*.f64 p p))) #s(literal 144 binary64))))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 x x))))) (*.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -10 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 3 binary64) (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal -1 binary64) (*.f64 x x))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))))
(+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/32 binary64)) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) p))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)))) (pow.f64 p #s(literal 5 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/4 binary64)) p))
(+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) p))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))
(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p)) (*.f64 x #s(literal 1/4 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 x (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/256 binary64)))) (*.f64 (*.f64 p p) (*.f64 p p)))) p))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
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(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* 1/4 x)
(*.f64 x #s(literal 1/4 binary64))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(* p (pow x 2))
(*.f64 x (*.f64 x p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))
(pow p 4)
(*.f64 (*.f64 p p) (*.f64 p p))

eval93.0ms (0.8%)

Compiler

Compiled 16212 to 1778 computations (89% saved)

prune228.0ms (2%)

Pruning

11 alts after pruning (4 fresh and 7 done)

PrunedKeptTotal
New7613764
Fresh011
Picked235
Done044
Total76311774
Accuracy
100.0%
Counts
774 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶25.3%
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
▶54.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓56.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓26.3%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
▶25.4%
(*.f64 p (/.f64 #s(literal -1 binary64) x))
✓53.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓79.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
✓58.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓57.4%
(sqrt.f64 #s(literal 1/2 binary64))
▶25.5%
(neg.f64 (/.f64 p x))
✓36.1%
#s(literal 1 binary64)
Compiler

Compiled 110 to 81 computations (26.4% saved)

simplify468.0ms (4%)

Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 p (*.f64 p p))
✓cost-diff0
(*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x)))
✓cost-diff0
(-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p)
✓cost-diff0
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓cost-diff0
(/.f64 #s(literal -1 binary64) x)
✓cost-diff0
(*.f64 p (/.f64 #s(literal -1 binary64) x))
✓cost-diff-64
(neg.f64 (/.f64 p x))
✓cost-diff0
(/.f64 p x)
Rules
2746×*-lowering-*.f32
2746×*-lowering-*.f64
1996×fnmsub-define
1386×/-lowering-/.f32
1386×/-lowering-/.f64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02185
15385
210285
322985
451285
5101884
6214584
7535184
8784584
0803784
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(neg (/ p x))
(/ p x)
p
x
(* p (/ -1 x))
p
(/ -1 x)
-1
x
(/ 1 (sqrt (- 2 (/ x p))))
1
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
2
(/ x p)
x
p
(/ (- (* (* p (* p p)) (/ 3/2 (* x x))) p) x)
(- (* (* p (* p p)) (/ 3/2 (* x x))) p)
(* (* p (* p p)) (/ 3/2 (* x x)))
(* p (* p p))
p
(* p p)
(/ 3/2 (* x x))
3/2
(* x x)
x
Outputs
(neg (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ p x)
(/.f64 p x)
p
x
(* p (/ -1 x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
p
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
-1
#s(literal -1 binary64)
x
(/ 1 (sqrt (- 2 (/ x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
1
#s(literal 1 binary64)
(sqrt (- 2 (/ x p)))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
(- 2 (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(/ x p)
(/.f64 x p)
x
p
(/ (- (* (* p (* p p)) (/ 3/2 (* x x))) p) x)
(*.f64 p (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 3/2 binary64))) (*.f64 x x))) x))
(- (* (* p (* p p)) (/ 3/2 (* x x))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 p (*.f64 p #s(literal 3/2 binary64))) (*.f64 x x))))
(* (* p (* p p)) (/ 3/2 (* x x)))
(/.f64 (*.f64 p (*.f64 p (*.f64 p #s(literal 3/2 binary64)))) (*.f64 x x))
(* p (* p p))
(*.f64 p (*.f64 p p))
p
(* p p)
(*.f64 p p)
(/ 3/2 (* x x))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
3/2
#s(literal 3/2 binary64)
(* x x)
(*.f64 x x)
x

localize125.0ms (1.1%)

Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓accuracy99.9%
(*.f64 p (*.f64 p p))
✓accuracy99.7%
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
✓accuracy97.7%
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
✓accuracy91.9%
(*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x)))
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓accuracy99.1%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓accuracy98.5%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓accuracy100.0%
(/.f64 #s(literal -1 binary64) x)
✓accuracy99.7%
(*.f64 p (/.f64 #s(literal -1 binary64) x))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(neg.f64 (/.f64 p x))
Results
73.0ms193×0valid
16.0ms63×0invalid
Compiler

Compiled 107 to 22 computations (79.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-sqrt: 21.0ms (46.1% of total)
ival-div: 12.0ms (26.3% of total)
ival-mult: 8.0ms (17.6% of total)
ival-sub: 3.0ms (6.6% of total)
const: 1.0ms (2.2% of total)
ival-neg: 1.0ms (2.2% of total)
backward-pass: 0.0ms (0% of total)

series18.0ms (0.2%)

Counts
13 → 276
Calls
Call 1
Inputs
#<alt (/ p x)>
#<alt (neg (/ p x))>
#<alt (* p (/ -1 x))>
#<alt (/ -1 x)>
#<alt (/ 1 (sqrt (- 2 (/ x p))))>
#<alt (sqrt (- 2 (/ x p)))>
#<alt (- 2 (/ x p))>
#<alt (/ x p)>
#<alt (/ (- (* (* p (* p p)) (/ 3/2 (* x x))) p) x)>
#<alt (- (* (* p (* p p)) (/ 3/2 (* x x))) p)>
#<alt (* (* p (* p p)) (/ 3/2 (* x x)))>
#<alt (* p (* p p))>
#<alt (/ 3/2 (* x x))>
Outputs
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (/ p x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ p x))>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (/ -1 x)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))>
#<alt (* -1 (* (sqrt (/ x p)) (sqrt -1)))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (* -1 (/ x p))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (/ x p))>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (* -1 (/ p x))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))>
#<alt (* -1 (/ p x))>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))>
#<alt (* -1 p)>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))>
#<alt (/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))>
#<alt (* -1 p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (* -1 p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (- (* 3/2 (/ (pow p 3) (pow x 2))) p)>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (* 3/2 (/ (pow p 3) (pow x 2)))>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (pow p 3)>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
#<alt (/ 3/2 (pow x 2))>
Calls

69 calls:

TimeVariablePointExpression
2.0ms
x
@0
(/ (- (* (* p (* p p)) (/ 3/2 (* x x))) p) x)
1.0ms
x
@inf
(/ 1 (sqrt (- 2 (/ x p))))
1.0ms
p
@0
(/ 1 (sqrt (- 2 (/ x p))))
1.0ms
x
@inf
(sqrt (- 2 (/ x p)))
1.0ms
x
@-inf
(/ 1 (sqrt (- 2 (/ x p))))

rewrite623.0ms (5.3%)

Algorithm
1×batch-egg-rewrite
Rules
5124×*-lowering-*.f32
5124×*-lowering-*.f64
3666×/-lowering-/.f32
3666×/-lowering-/.f64
1134×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02169
111469
277369
0863569
Stop Event
1×iter limit
1×node limit
Counts
13 → 667
Calls
Call 1
Inputs
(/ p x)
(neg (/ p x))
(* p (/ -1 x))
(/ -1 x)
(/ 1 (sqrt (- 2 (/ x p))))
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
(/ x p)
(/ (- (* (* p (* p p)) (/ 3/2 (* x x))) p) x)
(- (* (* p (* p p)) (/ 3/2 (* x x))) p)
(* (* p (* p p)) (/ 3/2 (* x x)))
(* p (* p p))
(/ 3/2 (* x x))
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 p x))
(exp.f64 (*.f64 (log.f64 (/.f64 x p)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64)))
(/.f64 p x)
(/.f64 (/.f64 p x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) p))
(/.f64 #s(literal 1 binary64) (/.f64 x p))
(/.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) p))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (neg.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))) (/.f64 p x))
(/.f64 (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) p))
(pow.f64 (/.f64 p x) #s(literal 1 binary64))
(pow.f64 (/.f64 x p) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) p))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 p x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) p)
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) p) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) p) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) p)
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) p)
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))) (/.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 p x)) (/.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (/.f64 p x)))
(neg.f64 (/.f64 p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 p x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 x p))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) p))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))))
(/.f64 (-.f64 #s(literal 0 binary64) p) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) p))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 p x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (/.f64 p #s(literal -1 binary64)) x)
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x))))))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) p)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p x) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) p))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 p #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 x p))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) p)) (/.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))) (/.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 p x)) (/.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (/.f64 p x)))
(neg.f64 (/.f64 p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 p x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 x p))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) p))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))))
(/.f64 (-.f64 #s(literal 0 binary64) p) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) p))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 p x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (/.f64 p #s(literal -1 binary64)) x)
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x))))))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) p)) x)
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p x) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 (/.f64 #s(literal -1 binary64) x) p)
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 0 binary64) p))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 p #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 x p))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) p) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) p)) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x))
(neg.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) x)
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
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(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) #s(literal -3/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 3/2 binary64) x)))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/.f64 #s(literal -3/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 2/3 binary64))
(/.f64 (/.f64 #s(literal 3/2 binary64) x) x)
(/.f64 (/.f64 #s(literal -3/2 binary64) x) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 3/2 binary64) x) #s(literal 1 binary64)) x)
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -3/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 3/2 binary64) x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal -3/2 binary64) x) #s(literal -1 binary64)) x)
(pow.f64 (/.f64 x (/.f64 #s(literal 3/2 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/2 binary64) (*.f64 x x)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 3/2 binary64) (*.f64 x x)))
(*.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal -3/2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 3/2 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64))
(*.f64 (/.f64 #s(literal 3/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -3/2 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal -3/2 binary64))
(*.f64 (pow.f64 (/.f64 x (/.f64 #s(literal 3/2 binary64) x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x (/.f64 #s(literal 3/2 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 (/.f64 #s(literal 3/2 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))

simplify502.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
6010×*-lowering-*.f32
6010×*-lowering-*.f64
2866×+-lowering-+.f64
2866×+-lowering-+.f32
2840×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03702669
111062413
238902333
084682333
Stop Event
1×iter limit
1×node limit
Counts
276 → 276
Calls
Call 1
Inputs
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(/ p x)
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(* -1 (/ p x))
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(/ -1 x)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(* (sqrt (/ x p)) (sqrt -1))
(* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))
(* -1 (* (sqrt (/ x p)) (sqrt -1)))
(* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))
(* (sqrt (/ x p)) (sqrt -1))
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(* -1 (/ x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* -1 (/ x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (/ x p))
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(* -1 (/ p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(* -1 (/ p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(* -1 (/ p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(* -1 p)
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(* -1 p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(* -1 p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(* 3/2 (/ (pow p 3) (pow x 2)))
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(pow p 3)
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
(/ 3/2 (pow x 2))
Outputs
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(/ p x)
(/.f64 p x)
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ p x))
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(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))
(+.f64 (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 p p)) (/.f64 #s(literal -1/2 binary64) (*.f64 p (sqrt.f64 #s(literal 2 binary64)))))) (+.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/16 binary64))) (*.f64 p (*.f64 p p))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 p (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (+.f64 (*.f64 #s(literal 1/16 binary64) (/.f64 (/.f64 (*.f64 x x) p) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) p))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -1/16 binary64) (+.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x (*.f64 x x)) (*.f64 p (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))))) p)) p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(* p (- (* 3/2 (/ (pow p 2) (pow x 3))) (/ 1 x)))
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(* 3/2 (/ (pow p 3) (pow x 3)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x)))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 3))) (/ 1 (* (pow p 2) x))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x)))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* -1 (* (pow p 3) (- (/ 1 (* (pow p 2) x)) (* 3/2 (/ 1 (pow x 3))))))
(*.f64 (*.f64 p p) (*.f64 p (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 p p)) x))))
(* 3/2 (/ (pow p 3) (pow x 3)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x (*.f64 x x)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 3))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x (*.f64 x x)))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(/ (+ (* -1 p) (* 3/2 (/ (pow p 3) (pow x 2)))) x)
(/.f64 (*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x)))) x)
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -3/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -3/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ p (* -3/2 (/ (pow p 3) (pow x 2)))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -3/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 p)
(-.f64 #s(literal 0 binary64) p)
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(* p (- (* 3/2 (/ (pow p 2) (pow x 2))) 1))
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* (pow p 3) (- (* 3/2 (/ 1 (pow x 2))) (/ 1 (pow p 2))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* -1 (* (pow p 3) (- (/ 1 (pow p 2)) (* 3/2 (/ 1 (pow x 2))))))
(*.f64 (*.f64 p (*.f64 p p)) (+.f64 (/.f64 #s(literal 3/2 binary64) (*.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 p p))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x x))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x x))
(/ (+ (* -1 (* p (pow x 2))) (* 3/2 (pow p 3))) (pow x 2))
(/.f64 (*.f64 p (-.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))) (*.f64 x x))
(* -1 p)
(-.f64 #s(literal 0 binary64) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(* -1 p)
(-.f64 #s(literal 0 binary64) p)
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(- (* 3/2 (/ (pow p 3) (pow x 2))) p)
(*.f64 p (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 3/2 binary64)) (*.f64 x x))))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(* 3/2 (/ (pow p 3) (pow x 2)))
(/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 3/2 binary64)) (*.f64 x x))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(pow p 3)
(*.f64 p (*.f64 p p))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))
(/ 3/2 (pow x 2))
(/.f64 #s(literal 3/2 binary64) (*.f64 x x))

eval126.0ms (1.1%)

Compiler

Compiled 25351 to 2258 computations (91.1% saved)

prune121.0ms (1%)

Pruning

12 alts after pruning (1 fresh and 11 done)

PrunedKeptTotal
New9421943
Fresh000
Picked044
Done077
Total94212954
Accuracy
100.0%
Counts
954 → 12
Alt Table
Click to see full alt table
StatusAccuracyProgram
54.9%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓25.3%
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
✓54.0%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓56.6%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓26.3%
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
✓25.4%
(*.f64 p (/.f64 #s(literal -1 binary64) x))
✓53.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
✓79.4%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
✓58.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
✓57.4%
(sqrt.f64 #s(literal 1/2 binary64))
✓25.5%
(neg.f64 (/.f64 p x))
✓36.1%
#s(literal 1 binary64)
Compiler

Compiled 307 to 169 computations (45% saved)

regimes58.0ms (0.5%)

Counts
18 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
Outputs
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64))))))
Calls

7 calls:

17.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
15.0ms
x
6.0ms
p
5.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
5.0ms
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
Results
AccuracySegmentsBranch
81.5%2p
86.9%4x
100.0%2(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
100.0%2(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))))
100.0%2(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
100.0%2(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
79.4%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes13.0ms (0.1%)

Counts
14 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
Outputs
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))
Calls

2 calls:

7.0ms
p
5.0ms
x
Results
AccuracySegmentsBranch
77.3%3p
71.9%5x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts
13 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
Outputs
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
Calls

1 calls:

4.0ms
p
Results
AccuracySegmentsBranch
77.2%3p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts
7 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x)
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64))) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) x))
Outputs
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
Calls

2 calls:

3.0ms
x
3.0ms
p
Results
AccuracySegmentsBranch
54.7%2x
39.5%2p
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(literal 1 binary64)
Outputs
#s(literal 1 binary64)
Calls

2 calls:

1.0ms
x
1.0ms
p
Results
AccuracySegmentsBranch
36.1%1p
36.1%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch38.0ms (0.3%)

Algorithm
1×left-value
Steps
TimeLeftRight
37.0ms
-0.9999999994721974
-0.014391827010503193
Compiler

Compiled 24 to 18 computations (25% saved)

bsearch47.0ms (0.4%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
28.0ms
2.0042633860204706e-13
1.6615902666236577e-12
16.0ms
1.456224942265874e-263
2.1715341733313224e-263
Results
24.0ms113×0valid
10.0ms33×2valid
2.0ms6×3valid
2.0ms8×1valid
Compiler

Compiled 218 to 168 computations (22.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 29.0ms
ival-add: 15.0ms (51.2% of total)
ival-mult: 6.0ms (20.5% of total)
ival-sqrt: 4.0ms (13.7% of total)
ival-div: 2.0ms (6.8% of total)
backward-pass: 2.0ms (6.8% of total)
const: 0.0ms (0% of total)

bsearch43.0ms (0.4%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
16.0ms
2.0042633860204706e-13
1.6615902666236577e-12
16.0ms
1.456224942265874e-263
2.1715341733313224e-263
Results
11.0ms115×0valid
10.0ms28×2valid
3.0ms6×3valid
2.0ms11×1valid
Compiler

Compiled 122 to 108 computations (11.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 18.0ms
ival-mult: 6.0ms (34.3% of total)
ival-sqrt: 5.0ms (28.6% of total)
ival-div: 2.0ms (11.4% of total)
backward-pass: 2.0ms (11.4% of total)
ival-add: 2.0ms (11.4% of total)
const: 0.0ms (0% of total)

bsearch29.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
26.0ms
-5.426268330617951e-145
-3.717989232420226e-150
Results
9.0ms100×0valid
7.0ms22×2valid
4.0ms22×1valid
Compiler

Compiled 123 to 99 computations (19.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 13.0ms
ival-mult: 5.0ms (37.9% of total)
ival-sqrt: 3.0ms (22.7% of total)
ival-div: 2.0ms (15.2% of total)
ival-add: 2.0ms (15.2% of total)
backward-pass: 1.0ms (7.6% of total)
const: 0.0ms (0% of total)

simplify13.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
22×*-commutative_binary64
16×+-commutative_binary64
8×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05498
17798
28498
38998
49198
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(if (<=.f64 p #s(literal 1169957112783595/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 8120886657712095/39614081257132168796771975168 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 8962580548839177/567251933470833993071770667324028228809837418235547813055332893110634100784456014078204465673887768016738404766156377048665842149942362101665813667717893457711399398974403333260607303556174368618102720559063506014277553065062667880308951927318061097340410272771508755807405604864 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 1436010445571041/4951760157141521099596496896 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -3455165794209175/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656 binary64)) (neg.f64 (/.f64 p x)) #s(literal 1 binary64))
#s(literal 1 binary64)
Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -1/2 binary64)) (/.f64 (-.f64 (*.f64 (*.f64 p (*.f64 p p)) (/.f64 #s(literal 3/2 binary64) (*.f64 x x))) p) x) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (hypot.f64 x (*.f64 p #s(literal 2 binary64)))))))
(if (<=.f64 p #s(literal 1169957112783595/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 8120886657712095/39614081257132168796771975168 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 1169957112783595/70906491683854249133971333415503528601229677279443476631916611638829262598057001759775558209235971002092300595769547131083230268742795262708226708464736682213924924871800416657575912944521796077262840069882938251784694133132833485038618990914757637167551284096438594475925700608 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 8120886657712095/39614081257132168796771975168 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))))))))
(if (<=.f64 p #s(literal 8962580548839177/567251933470833993071770667324028228809837418235547813055332893110634100784456014078204465673887768016738404766156377048665842149942362101665813667717893457711399398974403333260607303556174368618102720559063506014277553065062667880308951927318061097340410272771508755807405604864 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 1436010445571041/4951760157141521099596496896 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 p #s(literal 8962580548839177/567251933470833993071770667324028228809837418235547813055332893110634100784456014078204465673887768016738404766156377048665842149942362101665813667717893457711399398974403333260607303556174368618102720559063506014277553065062667880308951927318061097340410272771508755807405604864 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 1436010445571041/4951760157141521099596496896 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -3455165794209175/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656 binary64)) (neg.f64 (/.f64 p x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -3455165794209175/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.8s (15.5%)

Rules
6422×*-lowering-*.f32
6422×*-lowering-*.f64
6082×*-lowering-*.f32
6082×*-lowering-*.f64
4242×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01415
13114
24213
34713
44913
55013
05013
031148
1180139
21571129
08737129
04653632
114243289
249583231
087353231
036126
1205114
21871114
08343114
03812053
112091828
243411780
085651780
01352
16450
252850
3767650
0868250
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×saturated
Compiler

Compiled 407 to 271 computations (33.4% saved)

preprocess71.0ms (0.6%)

Compiler

Compiled 364 to 216 computations (40.7% saved)

end0.0ms (0%)

Profiling

Loading profile data...