Given's Rotation SVD example

Time bar (total: 7.4s)

analyze606.0ms (8.2%)

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: 371.0ms
...c/correct-round.rkt:119:19: 114.0ms (30.7% of total)
ival-mult: 83.0ms (22.4% of total)
ival-sqrt: 43.0ms (11.6% of total)
ival-div: 36.0ms (9.7% of total)
ival-fabs: 31.0ms (8.4% of total)
ival-add: 30.0ms (8.1% of total)
ival-<: 27.0ms (7.3% of total)
ival-and: 4.0ms (1.1% of total)
const: 4.0ms (1.1% of total)
backward-pass: 1.0ms (0.3% of total)

sample2.4s (32.8%)

Results
997.0ms6186×0valid
608.0ms1222×2valid
227.0ms650×1valid
166.0ms198×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.5s
ival-mult: 519.0ms (33.6% of total)
...c/correct-round.rkt:119:19: 305.0ms (19.7% of total)
ival-sqrt: 213.0ms (13.8% of total)
ival-add: 154.0ms (10% of total)
ival-div: 120.0ms (7.8% of total)
ival-<: 83.0ms (5.4% of total)
backward-pass: 65.0ms (4.2% of total)
ival-fabs: 60.0ms (3.9% of total)
const: 16.0ms (1% of total)
ival-and: 11.0ms (0.7% of total)
Bogosity

preprocess134.0ms (1.8%)

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
042102
110698
222292
351092
4109192
5208792
6344992
7462292
8533392
9589992
10618492
11633792
12639592
13639992
01416
13016
24015
34515
44715
54815
04815
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 (fmsub x x (* (* p p) -4))) -1/2))
(sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x)))))))
(sqrt (fnmsub (* x -1/2) (rsqrt (fmsub x x (* (* p p) -4))) -1/2))
(sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x))))))))
(sqrt (fnmsub (* 1/2 x) (rsqrt (fmsub x x (* (* p p) -4))) -1/2))
(neg (sqrt (* 1/2 (+ 1 (/ x (sqrt (+ (* (* 4 (neg p)) (neg p)) (* x x))))))))
(neg (sqrt (fnmsub (* x -1/2) (rsqrt (fmsub x x (* (* p p) -4))) -1/2)))
(neg (sqrt (* 1/2 (+ 1 (/ (neg x) (sqrt (+ (* (* 4 p) p) (* (neg x) (neg x)))))))))
(neg (sqrt (fnmsub (* 1/2 x) (rsqrt (fmsub x x (* (* p p) -4))) -1/2)))
(sqrt (* 1/2 (+ 1 (/ p (sqrt (+ (* (* 4 x) x) (* p p)))))))
(sqrt (fnmsub (* p -1/2) (rsqrt (fmsub p p (* x (* x -4)))) -1/2))
Symmetry

(abs p)

explain173.0ms (2.4%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
530-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
320-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
281(5.388852821180543e-214 -1.582114622956378e+109)2(9.369262580210603e-167 -4.24030267807187e-7)(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
54.0ms374×0valid
32.0ms72×2valid
14.0ms46×1valid
11.0ms20×3valid
Compiler

Compiled 213 to 44 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-mult: 24.0ms (40% of total)
ival-sqrt: 12.0ms (20% of total)
ival-add: 9.0ms (15% of total)
backward-pass: 8.0ms (13.3% of total)
ival-div: 6.0ms (10% of total)
const: 2.0ms (3.3% 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
▶78.7%
(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
01379
12277
23277
33977
44477
54677
04677
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 p (*.f64 #s(literal 4 binary64) 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 p (*.f64 #s(literal 4 binary64) 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 p (*.f64 #s(literal 4 binary64) 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 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 p (*.f64 #s(literal 4 binary64) p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)

localize88.0ms (1.2%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 4 binary64) (*.f64 p p))
✓accuracy90.2%
(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))))))
✓accuracy88.7%
(+.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)))))
✓accuracy80.9%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Results
26.0ms22×1valid
24.0ms187×0valid
14.0ms36×2valid
6.0ms11×3valid
Compiler

Compiled 87 to 14 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-mult: 31.0ms (65.4% of total)
ival-sqrt: 6.0ms (12.7% of total)
ival-add: 4.0ms (8.4% of total)
ival-div: 3.0ms (6.3% of total)
backward-pass: 3.0ms (6.3% of total)
const: 1.0ms (2.1% of total)

series17.0ms (0.2%)

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
x
@inf
(+ 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
@0
(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))))

rewrite270.0ms (3.7%)

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
01361
16259
252359
3764359
0850259
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 x (*.f64 #s(literal 1/4 binary64) x)) (+.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 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1/4 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 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 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 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 #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 x (*.f64 #s(literal 1/4 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) (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 x (*.f64 #s(literal 1/4 binary64) x)) (+.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 x (*.f64 #s(literal 1/4 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 #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 x (*.f64 #s(literal 1/4 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 #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 x (*.f64 #s(literal 1/4 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 #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 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 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 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 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 (*.f64 #s(literal 1/4 binary64) x)) (+.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 x (*.f64 #s(literal 1/4 binary64) x)) (+.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 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) x)) (+.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)))))))))
(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 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 x (*.f64 #s(literal 1/4 binary64) x)) (+.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 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 x x) (*.f64 x x))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 x x) (*.f64 x x)) (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))))) (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 #s(literal 64 binary64) (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 (*.f64 x 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 (*.f64 x 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 (*.f64 x 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 (*.f64 x 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)

simplify311.0ms (4.2%)

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
112091990
243371951
085551951
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 #s(literal 1/8 binary64) (/.f64 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 #s(literal 1/2 binary64) x) (/.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)))) (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 #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)))) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 (+.f64 (+.f64 (*.f64 #s(literal -16 binary64) (pow.f64 p #s(literal 6 binary64))) (*.f64 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p))))) (*.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 #s(literal 1/2 binary64) (*.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 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) 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 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) p))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.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)) (*.f64 p p)) #s(literal -1/64 binary64)))) (*.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 (neg.f64 (+.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (/.f64 #s(literal -12 binary64) (*.f64 x x))) (/.f64 #s(literal 1/8 binary64) p)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.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)) (*.f64 p p)) #s(literal -1/64 binary64))) (*.f64 p (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))))) (+.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 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.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)) (*.f64 p p)) #s(literal -1/64 binary64))) (/.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) (*.f64 p p))) #s(literal -1/8 binary64))) (*.f64 p (pow.f64 x #s(literal 6 binary64)))))))) p) 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 (*.f64 (*.f64 p p) #s(literal 11/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.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 (*.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 #s(literal 1/8 binary64) (/.f64 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 (sqrt.f64 #s(literal 1/2 binary64)) (+.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 #s(literal 1/2 binary64) (/.f64 (+.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 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 1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) p) (/.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 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 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal 1/32 binary64) (*.f64 p (*.f64 p p))))))))
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 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p))))) (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 #s(literal 1/4 binary64) (*.f64 #s(literal -12 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) 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 (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -12 binary64) (/.f64 (*.f64 (*.f64 p p) (*.f64 p p)) x))) x) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal 16 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 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.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 #s(literal 2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.f64 #s(literal 64 binary64) (pow.f64 p #s(literal 6 binary64)))))) (+.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 p p) (*.f64 p p)) (/.f64 #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 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.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 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) (*.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 #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 (*.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 (*.f64 (*.f64 x x) #s(literal 3/512 binary64)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal 1/32 binary64) (*.f64 p (*.f64 p 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))))
(*.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 #s(literal -1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p))))) (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 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 p p) (*.f64 x x)) (/.f64 (*.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal -12 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))))
(- (+ (* 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 -12 binary64)) #s(literal 1/4 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) (*.f64 #s(literal -12 binary64) (*.f64 p p)))) (*.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 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (*.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 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) (*.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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.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 #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 (*.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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.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 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal -3/256 binary64) (*.f64 x x))) (*.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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.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 #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 (*.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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.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 (*.f64 x x) (*.f64 x x)) (*.f64 #s(literal -3/256 binary64) (*.f64 x x))) (*.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 p (*.f64 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 #s(literal 2 binary64) (+.f64 (+.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 p (+.f64 #s(literal -2 binary64) (neg.f64 (+.f64 (+.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))
(+ (* 1/4 (/ (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 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64))))))
(+ (* 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 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)) (/.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 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x)) (/.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 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 p (*.f64 p #s(literal 4 binary64)))

eval37.0ms (0.5%)

Compiler

Compiled 9954 to 1199 computations (88% saved)

prune38.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2926298
Fresh000
Picked011
Done000
Total2927299
Accuracy
100.0%
Counts
299 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶29.2%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
53.0%
(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)))))))
▶53.0%
(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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
✓78.7%
(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))))))
▶47.9%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
▶52.1%
(sqrt.f64 #s(literal 1/2 binary64))
▶37.2%
#s(literal 1 binary64)
Compiler

Compiled 171 to 123 computations (28.1% saved)

simplify83.0ms (1.1%)

Algorithm
1×egg-herbie
Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 #s(literal 1/4 binary64) p)
✓cost-diff0
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 p x)
✓cost-diff0
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓cost-diff128
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64))))))
✓cost-diff128
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))
✓cost-diff128
(+.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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64))))))))
✓cost-diff128
(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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
Rules
1952×fma-define
1138×fma-lowering-fma.f32
1138×fma-lowering-fma.f64
756×sum3-define
642×*-lowering-*.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
029247
160236
2143218
3378206
4799206
51014206
61101206
71123206
81338206
93063206
103418206
113463206
123464206
03464206
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))
1/2
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))
(* 1/2 x)
x
(+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))
(* p 2)
p
2
(* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))
(* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))
(+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))
(/ 1/4 p)
1/4
(* (/ (/ (/ (* x x) p) p) p) -1/64)
(/ (/ (/ (* x x) p) p) p)
(/ (/ (* x x) p) p)
(/ (* x x) p)
(* x x)
-1/64
1
(- 0 (/ p x))
0
(/ p x)
p
x
(sqrt 1/2)
1/2
(sqrt (+ 1/2 (* x (/ 1/4 p))))
(+ 1/2 (* x (/ 1/4 p)))
1/2
(* x (/ 1/4 p))
x
(/ 1/4 p)
1/4
p
Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)))))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)))))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))
(*.f64 (/.f64 (*.f64 x x) p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))))
(* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))
(*.f64 (/.f64 x p) (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))))
(+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
1/4
#s(literal 1/4 binary64)
(* (/ (/ (/ (* x x) p) p) p) -1/64)
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p)))
(/ (/ (/ (* x x) p) p) p)
(/.f64 (*.f64 x x) (*.f64 p (*.f64 p p)))
(/ (/ (* x x) p) p)
(/.f64 (*.f64 x x) (*.f64 p p))
(/ (* x x) p)
(/.f64 (*.f64 x x) p)
(* x x)
(*.f64 x x)
-1/64
#s(literal -1/64 binary64)
1
#s(literal 1 binary64)
(- 0 (/ p x))
(/.f64 (/.f64 p #s(literal -1 binary64)) x)
0
#s(literal 0 binary64)
(/ p x)
(/.f64 p x)
p
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 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 p)
(/.f64 #s(literal 1/4 binary64) p)
1/4
#s(literal 1/4 binary64)
p

localize140.0ms (1.9%)

Localize:

Found 11 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 #s(literal 1/4 binary64) p)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p)))
✓accuracy99.7%
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
✓accuracy97.7%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓accuracy99.8%
(/.f64 (*.f64 x x) p)
✓accuracy99.6%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))
✓accuracy98.7%
(*.f64 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))
✓accuracy96.9%
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64))))
Results
72.0ms187×0valid
27.0ms69×0invalid
Compiler

Compiled 255 to 30 computations (88.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 42.0ms
ival-mult: 15.0ms (36% of total)
ival-div: 14.0ms (33.6% of total)
ival-add: 5.0ms (12% of total)
ival-sqrt: 5.0ms (12% of total)
ival-sub: 1.0ms (2.4% of total)
const: 1.0ms (2.4% of total)
backward-pass: 0.0ms (0% of total)

series37.0ms (0.5%)

Counts
14 → 300
Calls
Call 1
Inputs
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))>
#<alt (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))>
#<alt (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))>
#<alt (- 0 (/ p x))>
#<alt (/ p x)>
#<alt (sqrt 1/2)>
#<alt (sqrt (+ 1/2 (* x (/ 1/4 p))))>
#<alt (+ 1/2 (* x (/ 1/4 p)))>
#<alt (* x (/ 1/4 p))>
#<alt (/ 1/4 p)>
#<alt (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))>
#<alt (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))>
#<alt (/ (* x x) 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 (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (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) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))>
#<alt (+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))>
#<alt (+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))>
#<alt 1/2>
#<alt (+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))>
#<alt (+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))>
#<alt (+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))>
#<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 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (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 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 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) (- (* 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) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (/ (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))) (pow x 4)))) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* -1 (/ (+ (* 32 (pow p 3)) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -8192 (pow p 7)) (* -4096 (pow p 7))) (pow x 4))) (* 32 (pow p 3))) (* -512 (/ (pow p 5) (pow x 2)))) (pow x 3)))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* -65536 (pow p 9)) (* 16 (* (pow p 2) (+ (* -8192 (pow p 7)) (* -4096 (pow p 7)))))) (pow x 6))) (* 32 (pow p 3))) (+ (* -8192 (/ (pow p 7) (pow x 4))) (+ (* -4096 (/ (pow p 7) (pow x 4))) (* -512 (/ (pow p 5) (pow x 2)))))) (pow x 3)))>
#<alt (* -32 (/ (pow p 3) (pow x 3)))>
#<alt (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)>
#<alt (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))))) (* 1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 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 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p))>
#<alt (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))))) (* -1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))>
#<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))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* 2 p)>
#<alt (* -1 (* p (- (* -1/4 (/ (pow x 2) (pow p 2))) 2)))>
#<alt (* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))>
#<alt (* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 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) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<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 (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 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (* 1/4 (/ x p))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))>
#<alt (* -1/64 (/ (pow x 3) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))>
#<alt (* 1/4 (/ x p))>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)>
#<alt (* 1/4 (/ x p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))>
#<alt (* -1/64 (/ (pow x 4) (pow p 3)))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)>
#<alt (* 1/4 (/ (pow x 2) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
#<alt (/ (pow x 2) p)>
Calls

75 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))
2.0ms
p
@-inf
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))
1.0ms
p
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))
1.0ms
x
@inf
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))
1.0ms
x
@-inf
(sqrt (+ 1/2 (* x (/ 1/4 p))))

rewrite324.0ms (4.4%)

Algorithm
1×batch-egg-rewrite
Rules
3382×/-lowering-/.f32
3382×/-lowering-/.f64
3312×*-lowering-*.f32
3312×*-lowering-*.f64
1768×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028178
1158162
21571156
08134156
Stop Event
1×iter limit
1×node limit
Counts
14 → 373
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))))
(/ (* 1/2 x) (+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))))
(+ (* p 2) (* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))))
(- 0 (/ p x))
(/ p x)
(sqrt 1/2)
(sqrt (+ 1/2 (* x (/ 1/4 p))))
(+ 1/2 (* x (/ 1/4 p)))
(* x (/ 1/4 p))
(/ 1/4 p)
(* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64)))
(* x (* x (+ (/ 1/4 p) (* (/ (/ (/ (* x x) p) p) p) -1/64))))
(/ (* x x) p)
Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))) #s(literal 1/2 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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))))))
(/.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 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))) #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) 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) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))))))))))
(/.f64 (sqrt.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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) 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) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))))) (sqrt.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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))) #s(literal 1/2 binary64)) (/.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (sqrt.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 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) 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) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))))) (sqrt.f64 (+.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))))))))
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(/.f64 (neg.f64 (*.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)))) (*.f64 p p)) x)) (neg.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))) p)))
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))) x)
(+.f64 (*.f64 x (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) (*.f64 x (*.f64 (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 #s(literal -1/64 binary64) x))))
(+.f64 (*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p)) (*.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))
(+.f64 (*.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p)))
(+.f64 (*.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) x) (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 #s(literal -1/64 binary64) x)) x))
(+.f64 (*.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x)) (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (*.f64 x x)))
(+.f64 (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (*.f64 x x)) (*.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x)))
(fma.f64 x (/.f64 x (/.f64 p #s(literal 1/4 binary64))) (*.f64 x (*.f64 (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 #s(literal -1/64 binary64) x))))
(fma.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x) (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (*.f64 x x)))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))
(fma.f64 (*.f64 x x) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p)))
(fma.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (*.f64 x x) (*.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x)))
(fma.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) x (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p (*.f64 p p))) (*.f64 #s(literal -1/64 binary64) x)) x))
(/.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 (/.f64 #s(literal -1/262144 binary64) (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (*.f64 p (*.f64 p p))))) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)) #s(literal 1/4 binary64)) p))))
(/.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)))) (*.f64 p p))) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))) p))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 (/.f64 #s(literal -1/262144 binary64) (*.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (*.f64 p (*.f64 p p)))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)) (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)) #s(literal 1/4 binary64)) p)))))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) (/.f64 (-.f64 #s(literal 1/16 binary64) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p)))) (*.f64 p p)))) (neg.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p p))) p)))
(*.f64 x (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))))
(*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))))
(*.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p))) (*.f64 x x))
(*.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (*.f64 x x) (*.f64 p p)) (/.f64 #s(literal -1/64 binary64) p)))) x)
(exp.f64 (*.f64 (log.f64 (/.f64 p (*.f64 x x))) #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) p)))
(/.f64 (*.f64 x x) p)
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) p))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 p (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) p)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 0 binary64) p)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p))))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) p))
(pow.f64 (/.f64 p (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 p (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 x p))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) p))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) p))
(*.f64 (/.f64 x p) x)
(*.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 x x))
(*.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)))

simplify324.0ms (4.4%)

Algorithm
1×egg-herbie
Rules
5292×*-lowering-*.f32
5292×*-lowering-*.f64
2424×/-lowering-/.f32
2424×/-lowering-/.f64
1986×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
05533639
116433568
255963512
080143512
Stop Event
1×iter limit
1×node limit
Counts
300 → 300
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)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (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)))))
(+ (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 (/ (+ (* -1/2 (/ (- (* 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)))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
(+ 1/2 (* -1 (/ (- (* 1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 4))) (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3)))) (pow x 3))))
1/2
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+ 1/2 (* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3))))))
(+ 1/2 (* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3))))))
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 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (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 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))
(+ 1/2 (* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) 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) (+ (* -1/1024 (/ (pow x 2) (pow p 7))) (* 3/512 (/ 1 (pow p 5))))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p))))
(* -32 (/ (pow p 3) (pow x 3)))
(/ (+ (* -512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))
(/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))) (pow x 4)))) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3))
(/ (- (+ (* -32 (pow p 3)) (* -1 (/ (+ (* 16 (* (pow p 2) (+ (* 4096 (pow p 7)) (* 8192 (pow p 7))))) (* 65536 (pow p 9))) (pow x 6)))) (+ (* 512 (/ (pow p 5) (pow x 2))) (+ (* 4096 (/ (pow p 7) (pow x 4))) (* 8192 (/ (pow p 7) (pow x 4)))))) (pow x 3))
(* -32 (/ (pow p 3) (pow x 3)))
(* -1 (/ (+ (* 32 (pow p 3)) (* 512 (/ (pow p 5) (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ (* -1 (/ (+ (* -8192 (pow p 7)) (* -4096 (pow p 7))) (pow x 4))) (* 32 (pow p 3))) (* -512 (/ (pow p 5) (pow x 2)))) (pow x 3)))
(* -1 (/ (- (+ (* -1 (/ (+ (* -65536 (pow p 9)) (* 16 (* (pow p 2) (+ (* -8192 (pow p 7)) (* -4096 (pow p 7)))))) (pow x 6))) (* 32 (pow p 3))) (+ (* -8192 (/ (pow p 7) (pow x 4))) (+ (* -4096 (/ (pow p 7) (pow x 4))) (* -512 (/ (pow p 5) (pow x 2)))))) (pow x 3)))
(* -32 (/ (pow p 3) (pow x 3)))
(* (pow p 3) (- (* -512 (/ (pow p 2) (pow x 5))) (* 32 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* (pow p 2) (- (* -12288 (/ (pow p 2) (pow x 7))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))
(* (pow p 3) (- (* (pow p 2) (- (* (pow p 2) (- (* -262144 (/ (pow p 2) (pow x 9))) (* 12288 (/ 1 (pow x 7))))) (* 512 (/ 1 (pow x 5))))) (* 32 (/ 1 (pow x 3)))))
(* 1/4 (/ x p))
(/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)
(/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))))) (* 1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* -1/128 (pow x 5)) (* -1/256 (pow x 5))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)))) p)
(* 1/4 (/ x p))
(* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2))))) p))
(* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (* (pow x 2) (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))))) (* -1/2048 (pow x 7))) (pow p 6))) (+ (* -1/2 (/ (+ (* 1/256 (pow x 5)) (* 1/128 (pow x 5))) (pow p 4))) (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))))) p))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* (pow p 2) (+ (* 1/4 (pow x 2)) (* 2 (pow p 2))))) (pow p 3))
(* 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))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* 2 p)
(* -1 (* p (- (* -1/4 (/ (pow x 2) (pow p 2))) 2)))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 2)))
(* -1 (* p (- (+ (* -1/4 (/ (pow x 2) (pow p 2))) (* 1/64 (/ (pow x 4) (pow p 4)))) 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) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (+ (* 2 (/ p (pow x 4))) (/ 1/4 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -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)
(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 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(* 1/4 (/ x p))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* x (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 3) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(* 1/4 (/ x p))
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(* 1/4 (/ x p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(* 1/4 (/ (pow x 2) p))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(* 1/4 (/ (pow x 2) p))
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(* 1/4 (/ (pow x 2) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 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) p)
(/ (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 #s(literal -1/64 binary64) (/.f64 (/.f64 x (*.f64 p p)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.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) (*.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))))) (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)))))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x))))) (/.f64 (*.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 5 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))))
(+ (sqrt 1/2) (+ (* -256 (/ (pow p 5) (* (pow x 5) (sqrt 1/2)))) (+ (* -128 (/ (pow p 6) (* (pow x 6) (pow (sqrt 1/2) 3)))) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (+.f64 (/.f64 (*.f64 #s(literal -256 binary64) (pow.f64 p #s(literal 5 binary64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))) (*.f64 #s(literal -256 binary64) (/.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x))))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2))))) (pow x 3))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal 256 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x)))) (*.f64 x (*.f64 x x))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 16 (/ (pow p 3) (sqrt 1/2))) (+ (* 128 (/ (pow p 6) (* (pow x 3) (pow (sqrt 1/2) 3)))) (* 256 (/ (pow p 5) (* (pow x 2) (sqrt 1/2)))))) (pow x 3))))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (+.f64 (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 16 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal 256 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x)))) (*.f64 #s(literal 256 binary64) (/.f64 (/.f64 (pow.f64 p #s(literal 6 binary64)) (*.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 x (*.f64 x x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* -16 (/ (pow p 3) (* (pow x 3) (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x)))))
(+ (sqrt 1/2) (* (pow p 3) (- (* -256 (/ (pow p 2) (* (pow x 5) (sqrt 1/2)))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 p (*.f64 p p)) (-.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -256 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (/.f64 #s(literal 16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 x (*.f64 x x))))))
(+ (sqrt 1/2) (* (pow p 3) (- (* (pow p 2) (- (* -128 (/ p (* (pow x 6) (pow (sqrt 1/2) 3)))) (* 256 (/ 1 (* (pow x 5) (sqrt 1/2)))))) (* 16 (/ 1 (* (pow x 3) (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (*.f64 p (*.f64 p p)) (+.f64 (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 #s(literal -256 binary64) (/.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -256 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 x #s(literal 5 binary64)))))) (/.f64 #s(literal -16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.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 #s(literal -1/64 binary64) (/.f64 (/.f64 x (*.f64 p p)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.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 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (*.f64 #s(literal -1/64 binary64) (/.f64 (/.f64 x (*.f64 p p)) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))))) (*.f64 (/.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 (*.f64 p p))) (/.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 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) p)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 #s(literal 1/64 binary64) (/.f64 (/.f64 (*.f64 x x) p) (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 x #s(literal -1/8 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) p) (/.f64 (+.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal 1/32 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal 1/2 binary64)))) (*.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 #s(literal 1/4 binary64) (/.f64 x 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))))))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -32 binary64)) (*.f64 x (*.f64 x x))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (* -32 (/ (pow p 3) (pow x 3)))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -32 binary64)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -512 binary64)) (pow.f64 x #s(literal 5 binary64)))))
(+ 1/2 (+ (* -512 (/ (pow p 5) (pow x 5))) (+ (* -32 (/ (pow p 3) (pow x 3))) (* -1/2 (/ (+ (* 8192 (pow p 7)) (* 16384 (pow p 7))) (pow x 7))))))
(+.f64 (+.f64 (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -32 binary64)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 p #s(literal 7 binary64)) #s(literal 24576 binary64))) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 p #s(literal 5 binary64)) #s(literal -512 binary64)) (pow.f64 x #s(literal 5 binary64)))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -32 (/ (pow p 3) (pow x 3))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal -32 binary64)) (*.f64 x (*.f64 x x))))
(+ 1/2 (* -1 (/ (- (* 512 (/ (pow p 5) (pow x 2))) (* -32 (pow p 3))) (pow x 3))))
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(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(*.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(*.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/64 (/ 1 (pow p 3))) (* 1/4 (/ 1 (* p (pow x 2)))))))
(*.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p)))) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 x x))))
(* -1/64 (/ (pow x 3) (pow p 3)))
(/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 x (*.f64 (*.f64 p p) #s(literal 1/4 binary64)))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 x (*.f64 (*.f64 p p) #s(literal 1/4 binary64)))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 3)) (* 1/4 (* (pow p 2) x))) (pow p 3))
(/.f64 (+.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 x (*.f64 (*.f64 p p) #s(literal 1/4 binary64)))) (*.f64 p (*.f64 p p)))
(* 1/4 (/ x p))
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 p p))) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 p p))) p)
(/ (+ (* -1/64 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 (*.f64 x (*.f64 (*.f64 x x) #s(literal -1/64 binary64))) (*.f64 p p))) p)
(* 1/4 (/ x p))
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 x) (* 1/64 (/ (pow x 3) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(*.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)))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(*.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)))))
(* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(*.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)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p)))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* (pow x 4) (- (* 1/4 (/ 1 (* p (pow x 2)))) (* 1/64 (/ 1 (pow p 3)))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x (*.f64 x p))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p)))))
(* -1/64 (/ (pow x 4) (pow p 3)))
(/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (*.f64 p (*.f64 p p)))
(/ (+ (* -1/64 (pow x 4)) (* 1/4 (* (pow p 2) (pow x 2)))) (pow p 3))
(/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p (*.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (*.f64 p (*.f64 p p)))
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p p))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p p))) p)
(/ (+ (* -1/64 (/ (pow x 4) (pow p 2))) (* 1/4 (pow x 2))) p)
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (*.f64 p p))) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(* -1 (/ (+ (* -1/4 (pow x 2)) (* 1/64 (/ (pow x 4) (pow p 2)))) p))
(/.f64 (+.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/64 binary64)) (*.f64 p p))) (-.f64 #s(literal 0 binary64) p))
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)
(/ (pow x 2) p)
(/.f64 (*.f64 x x) p)

eval94.0ms (1.3%)

Compiler

Compiled 21567 to 2413 computations (88.8% saved)

prune71.0ms (1%)

Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New6993702
Fresh101
Picked145
Done011
Total7018709
Accuracy
100.0%
Counts
709 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)))))
✓53.0%
(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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
✓78.7%
(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))))))
✓47.9%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
▶47.8%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓52.1%
(sqrt.f64 #s(literal 1/2 binary64))
▶29.2%
(neg.f64 (/.f64 p x))
✓37.2%
#s(literal 1 binary64)
Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify18.0ms (0.2%)

Algorithm
1×egg-herbie
Localize:

Found 10 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 (*.f64 (*.f64 x x) #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 (*.f64 (*.f64 x x) #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 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)))))
✓cost-diff0
(/.f64 #s(literal 1/4 binary64) p)
✓cost-diff0
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
✓cost-diff128
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x)))
✓cost-diff128
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓cost-diff-64
(neg.f64 (/.f64 p x))
✓cost-diff0
(/.f64 p x)
Rules
196×sum3-define
190×fma-define
124×fma-lowering-fma.f32
124×fma-lowering-fma.f64
108×+-lowering-+.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
021128
148126
277126
3107120
4141120
5161120
6177120
7236120
8465120
9517120
10529120
11530120
0530120
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(neg (/ p x))
(/ p x)
p
x
(sqrt (* x (+ (/ 1/4 p) (/ 1/2 x))))
(* x (+ (/ 1/4 p) (/ 1/2 x)))
x
(+ (/ 1/4 p) (/ 1/2 x))
(/ 1/4 p)
1/4
p
(/ 1/2 x)
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 x) 1/4)
(* x x)
1/4
Outputs
(neg (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(/ p x)
(/.f64 p x)
p
x
(sqrt (* x (+ (/ 1/4 p) (/ 1/2 x))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(* x (+ (/ 1/4 p) (/ 1/2 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
x
(+ (/ 1/4 p) (/ 1/2 x))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
1/4
#s(literal 1/4 binary64)
p
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
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 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (/ (* (* x x) 1/4) p))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (+ (* p 2) (/ (* (* x x) 1/4) p)))
(/.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(+ (* p 2) (/ (* (* x x) 1/4) p))
(+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(/ (* (* x x) 1/4) p)
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(* (* x x) 1/4)
(*.f64 #s(literal 1/4 binary64) (*.f64 x x))
(* x x)
(*.f64 x x)
1/4
#s(literal 1/4 binary64)

localize83.0ms (1.1%)

Localize:

Found 10 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 1/2 binary64) x)
✓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 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)))))
✓accuracy99.8%
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
✓accuracy95.3%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)))
✓accuracy100.0%
(/.f64 #s(literal 1/4 binary64) p)
✓accuracy100.0%
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
✓accuracy99.8%
(*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x)))
✓accuracy97.7%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(neg.f64 (/.f64 p x))
Results
44.0ms187×0valid
13.0ms69×0invalid
Compiler

Compiled 135 to 22 computations (83.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 32.0ms
ival-div: 12.0ms (38% of total)
ival-mult: 10.0ms (31.7% of total)
ival-add: 4.0ms (12.7% of total)
ival-sqrt: 4.0ms (12.7% of total)
const: 1.0ms (3.2% of total)
ival-neg: 1.0ms (3.2% of total)
backward-pass: 0.0ms (0% of total)

series43.0ms (0.6%)

Counts
11 → 240
Calls
Call 1
Inputs
#<alt (/ p x)>
#<alt (neg (/ p x))>
#<alt (sqrt (* x (+ (/ 1/4 p) (/ 1/2 x))))>
#<alt (* x (+ (/ 1/4 p) (/ 1/2 x)))>
#<alt (+ (/ 1/4 p) (/ 1/2 x))>
#<alt (/ 1/4 p)>
#<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 (/ (* (* x x) 1/4) p)>
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 (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 (* -1/2 (* (sqrt (/ x p)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 5) (pow x 7))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))))>
#<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 p)>
#<alt (/ (+ 1/4 (* 1/2 (/ p x))) p)>
#<alt (/ (+ 1/4 (* 1/2 (/ p x))) p)>
#<alt (/ (+ 1/4 (* 1/2 (/ p x))) p)>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/4 (/ x p))) x)>
#<alt (/ (+ 1/2 (* 1/4 (/ x p))) x)>
#<alt (/ (+ 1/2 (* 1/4 (/ x p))) x)>
#<alt (/ 1/4 p)>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (/ 1/4 p)>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<alt (/ 1/4 p)>
#<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 (* 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

60 calls:

TimeVariablePointExpression
25.0ms
x
@-inf
(sqrt (* x (+ (/ 1/4 p) (/ 1/2 x))))
5.0ms
x
@-inf
(* x (+ (/ 1/4 p) (/ 1/2 x)))
2.0ms
p
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (/ (* (* x x) 1/4) p)))))
1.0ms
x
@inf
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (/ (* (* x x) 1/4) p)))))
0.0ms
x
@-inf
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (/ (* (* x x) 1/4) p)))))

rewrite318.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
4422×*-lowering-*.f32
4422×*-lowering-*.f64
3710×/-lowering-/.f32
3710×/-lowering-/.f64
2254×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02193
112891
2125185
0824385
Stop Event
1×iter limit
1×node limit
Counts
11 → 440
Calls
Call 1
Inputs
(/ p x)
(neg (/ p x))
(sqrt (* x (+ (/ 1/4 p) (/ 1/2 x))))
(* x (+ (/ 1/4 p) (/ 1/2 x)))
(+ (/ 1/4 p) (/ 1/2 x))
(/ 1/4 p)
(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)
(/ (* (* x x) 1/4) p)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 x p)) #s(literal -1 binary64)))
(-.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)))
(/.f64 p x)
(/.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x p))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x p) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x p))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x p)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x p) #s(literal 1 binary64))))
(/.f64 (*.f64 p #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (*.f64 p #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(pow.f64 (/.f64 x p) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x p) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 #s(literal 1 binary64) (/.f64 p 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 #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) (neg.f64 (-.f64 #s(literal 0 binary64) x))) (/.f64 p (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (*.f64 #s(literal 0 binary64) (/.f64 p x))))) (/.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (*.f64 #s(literal 0 binary64) (/.f64 p x))))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 #s(literal 0 binary64) (/.f64 p x))) (/.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (+.f64 #s(literal 0 binary64) (/.f64 p x))))
(neg.f64 (/.f64 p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) p) x)
(/.f64 (-.f64 #s(literal 0 binary64) p) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x p)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) x) p))
(/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) p)))
(/.f64 #s(literal -1 binary64) (/.f64 x p))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (/.f64 x p))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) p)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (-.f64 #s(literal 0 binary64) p))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p)) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) 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 p x)) (*.f64 #s(literal 0 binary64) (/.f64 p x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 p x) (/.f64 p x))) (+.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 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p))) (neg.f64 (-.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))))) (neg.f64 (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (*.f64 #s(literal 0 binary64) (/.f64 p x))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 p x) (/.f64 p x)))) (neg.f64 (+.f64 #s(literal 0 binary64) (/.f64 p x))))
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(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64))) (*.f64 p #s(literal 2 binary64))) (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))))))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))))) (-.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))))
(*.f64 (/.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1/2 binary64) (-.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) p)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 (*.f64 p (*.f64 p p)) #s(literal 8 binary64)) (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64))) (*.f64 p #s(literal 2 binary64))) (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))))))
(*.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 (*.f64 x x) (*.f64 x x))))) (/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))))))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(exp.f64 (*.f64 (log.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) p)) (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) p)))
(neg.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 x x) p)))
(neg.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) p))
(/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) p)
(/.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) p))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal 1 binary64))))
(/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64)) p)
(/.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) p)))
(/.f64 (neg.f64 (*.f64 x x)) (neg.f64 (/.f64 p #s(literal 1/4 binary64))))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64)) (/.f64 p #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) p))
(/.f64 (neg.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) p))))
(/.f64 (neg.f64 (*.f64 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (/.f64 p #s(literal 1/4 binary64))))
(pow.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 p (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 x (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(*.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) p)))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 x x))
(*.f64 (*.f64 x x) (/.f64 #s(literal 1/4 binary64) p))
(*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (*.f64 (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) p)))
(*.f64 #s(literal -1/4 binary64) (/.f64 (neg.f64 (*.f64 x x)) p))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (/.f64 p #s(literal 1/4 binary64))))
(*.f64 (/.f64 x p) (/.f64 x #s(literal 4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) p) (*.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/4 binary64) (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(*.f64 (/.f64 (*.f64 x x) p) #s(literal 1/4 binary64))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (neg.f64 (*.f64 x #s(literal 1/4 binary64))) p))
(*.f64 (/.f64 (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1/4 binary64) p))
(*.f64 (/.f64 (neg.f64 (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/4 binary64) p))

simplify277.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
5162×*-lowering-*.f32
5162×*-lowering-*.f64
2972×+-lowering-+.f64
2972×+-lowering-+.f32
1978×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04312482
112922358
243172302
082672302
Stop Event
1×iter limit
1×node limit
Counts
240 → 240
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))
(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))))))))
(* -1/2 (* (sqrt (/ x p)) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 5) (pow x 7))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))))
(* 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 p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/ 1/2 x)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(/ 1/2 x)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/ 1/4 p)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(/ 1/4 p)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(/ 1/4 p)
(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)))))
(+ (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 (/ (+ (* -1/2 (/ (- (* 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) (- (* 1/256 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
1/2
(+ 1/2 (* 2 (/ p x)))
(+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (* 2 (/ p x))))
(+ 1/2 (+ (* -16 (/ (pow p 3) (pow x 3))) (+ (* 2 (/ p x)) (* 128 (/ (pow p 5) (pow x 5))))))
1/2
(+ 1/2 (* 2 (/ p x)))
(+ 1/2 (* -1 (/ (- (* 16 (/ (pow p 3) (pow x 2))) (* 2 p)) x)))
(+ 1/2 (* -1 (/ (- (* -128 (/ (pow p 5) (pow x 4))) (+ (* -16 (/ (pow p 3) (pow x 2))) (* 2 p))) x)))
1/2
(+ 1/2 (* 2 (/ p x)))
(+ 1/2 (* p (+ (* -16 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ 1/2 (* p (+ (* (pow p 2) (- (* 128 (/ (pow p 2) (pow x 5))) (* 16 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))
(+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (+ (* 1/256 (/ (pow x 5) (pow p 5))) (* 1/4 (/ x p)))))
1/2
(+ 1/2 (* 1/4 (/ x p)))
(+ 1/2 (* -1 (/ (+ (* -1/4 x) (* 1/32 (/ (pow x 3) (pow p 2)))) p)))
(+ 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))
(* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p))))
(* 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)
(* 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
(/ 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))
(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 #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (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 p (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (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)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal 1/1024 binary64) (/.f64 (/.f64 x (*.f64 p p)) p)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/128 binary64) (*.f64 p (*.f64 p (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))))))))
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(* x (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3))))))
(*.f64 x (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x))) (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x)))))))
(* x (+ (* -1/4 (sqrt (/ (pow p 3) (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (* p x)))) (* 1/2 (sqrt (/ p (pow x 3)))))))
(*.f64 x (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x))) (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 x #s(literal 5 binary64)))))))
(* 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))))))))
(*.f64 x (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x))) (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x)))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 7 binary64))))))))
(* -1/2 (* (sqrt (/ x p)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (+.f64 (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x)))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2)))))))
(*.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x))) #s(literal -1/2 binary64)) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 3) (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/4 (* (sqrt (/ (pow p 5) (pow x 7))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (* p x))) (pow (sqrt -1) 2))))))))
(*.f64 (+.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x))) #s(literal -1/2 binary64))) (*.f64 #s(literal 1/4 binary64) (+.f64 (sqrt.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (sqrt (/ x p)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 x p)))
(/ (+ (* 1/2 (sqrt (* p x))) (* 1/2 (sqrt (/ (pow p 3) x)))) p)
(/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (*.f64 p x)) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) x)))) p)
(/ (+ (* 1/2 (sqrt (* p x))) (* (pow p 2) (+ (* -1/4 (sqrt (/ p (pow x 3)))) (* 1/2 (sqrt (/ 1 (* p x))))))) p)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 p x))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x)))) (*.f64 (sqrt.f64 (/.f64 p (*.f64 x (*.f64 x x)))) #s(literal -1/4 binary64))))) 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)
(/.f64 (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 p x))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x)))) (*.f64 (*.f64 p p) (+.f64 (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (*.f64 p p))) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (pow.f64 x #s(literal 5 binary64))))))))))) 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 #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (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 p (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (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)))))))
(+.f64 (+.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 p (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 (*.f64 #s(literal 1/1024 binary64) (*.f64 x (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 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 #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3))))) 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 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1/64 binary64)) p)) 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)))
(-.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 -1/64 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 (*.f64 #s(literal 1/1024 binary64) (*.f64 x x)) x) (*.f64 p (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 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 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* x (+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (/.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) (* 1/2 p)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))) p)
(/ (+ (* 1/4 x) (* 1/2 p)) p)
(/.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))) 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 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) 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 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(+ 1/2 (* 1/4 (/ x p)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 p #s(literal 1/2 binary64)) x)) p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 p #s(literal 1/2 binary64)) x)) p)
(/ (+ 1/4 (* 1/2 (/ p x))) p)
(/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 p #s(literal 1/2 binary64)) x)) p)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) x)
(/ (+ 1/2 (* 1/4 (/ x p))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)) x)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(+ (* 1/4 (/ 1 p)) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) p)
(/ 1/4 p)
(/.f64 #s(literal 1/4 binary64) 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 #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (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 p (sqrt.f64 #s(literal 1/2 binary64)))))))
(+ (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 p (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (+.f64 (*.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 (+.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 p (*.f64 p (*.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) (/ p (* x (sqrt 1/2))))
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(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))
(* 1/4 (/ (pow x 2) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p))

eval81.0ms (1.1%)

Compiler

Compiled 13936 to 2201 computations (84.2% saved)

prune88.0ms (1.2%)

Pruning

8 alts after pruning (0 fresh and 8 done)

PrunedKeptTotal
New6800680
Fresh000
Picked033
Done055
Total6808688
Accuracy
100.0%
Counts
688 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓53.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)))))
✓53.0%
(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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
✓78.7%
(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))))))
✓47.9%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x (/.f64 #s(literal 1/4 binary64) p))))
✓47.8%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓52.1%
(sqrt.f64 #s(literal 1/2 binary64))
✓29.2%
(neg.f64 (/.f64 p x))
✓37.2%
#s(literal 1 binary64)
Compiler

Compiled 238 to 137 computations (42.4% saved)

regimes29.0ms (0.4%)

Counts
11 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(sqrt.f64 #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 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
(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) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) 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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 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))))))
Outputs
(neg.f64 (/.f64 p x))
(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)))))))
Calls

7 calls:

6.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
4.0ms
p
4.0ms
x
4.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
3.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Results
AccuracySegmentsBranch
78.7%1p
83.0%2x
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))))
78.7%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes11.0ms (0.1%)

Counts
9 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(sqrt.f64 #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 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
(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) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) 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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))
Calls

2 calls:

7.0ms
x
3.0ms
p
Results
AccuracySegmentsBranch
73.6%3p
67.4%3x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

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

1 calls:

3.0ms
p
Results
AccuracySegmentsBranch
73.5%3p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0%)

Counts
6 → 3
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(sqrt.f64 #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 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
Outputs
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 1/2 binary64))
Calls

1 calls:

3.0ms
p
Results
AccuracySegmentsBranch
72.9%3p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0.1%)

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

2 calls:

2.0ms
x
2.0ms
p
Results
AccuracySegmentsBranch
59.2%2x
40.6%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:

2.0ms
p
1.0ms
x
Results
AccuracySegmentsBranch
37.2%1p
37.2%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.0
-0.07456799018574271
Compiler

Compiled 24 to 18 computations (25% saved)

bsearch61.0ms (0.8%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
22.0ms
1.7527351103926464e-22
3.8100165790344107e-20
33.0ms
8.719017118125952e-274
3.205739303661766e-269
Results
21.0ms66×2valid
13.0ms139×0valid
7.0ms20×1valid
6.0ms15×3valid
Compiler

Compiled 371 to 272 computations (26.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 34.0ms
ival-mult: 15.0ms (43.6% of total)
ival-sqrt: 7.0ms (20.3% of total)
ival-add: 6.0ms (17.4% of total)
ival-div: 4.0ms (11.6% of total)
backward-pass: 3.0ms (8.7% of total)
const: 1.0ms (2.9% of total)

bsearch64.0ms (0.9%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
21.0ms
1.7527351103926464e-22
3.8100165790344107e-20
35.0ms
8.719017118125952e-274
3.205739303661766e-269
Results
19.0ms65×2valid
17.0ms135×0valid
8.0ms20×3valid
4.0ms20×1valid
Compiler

Compiled 287 to 223 computations (22.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 16.0ms (44.5% of total)
ival-sqrt: 7.0ms (19.5% of total)
ival-add: 6.0ms (16.7% of total)
ival-div: 4.0ms (11.1% of total)
backward-pass: 3.0ms (8.3% of total)
const: 1.0ms (2.8% of total)

bsearch72.0ms (1%)

Algorithm
2×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
18.0ms
1.7527351103926464e-22
3.8100165790344107e-20
48.0ms
8.719017118125952e-274
3.205739303661766e-269
Results
22.0ms151×0valid
15.0ms51×2valid
9.0ms22×3valid
3.0ms16×1valid
Compiler

Compiled 175 to 153 computations (12.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 37.0ms
ival-mult: 19.0ms (51.8% of total)
ival-sqrt: 7.0ms (19.1% of total)
ival-add: 4.0ms (10.9% of total)
ival-div: 3.0ms (8.2% of total)
backward-pass: 2.0ms (5.5% of total)
const: 1.0ms (2.7% of total)

bsearch44.0ms (0.6%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
41.0ms
-1.8771134091480853e-148
-3.4211627585472513e-150
Results
30.0ms77×0valid
5.0ms27×1valid
2.0ms8×2valid
Compiler

Compiled 101 to 81 computations (19.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 4.0ms (38.6% of total)
ival-sqrt: 2.0ms (19.3% of total)
ival-add: 2.0ms (19.3% of total)
ival-div: 1.0ms (9.7% of total)
backward-pass: 1.0ms (9.7% of total)
const: 0.0ms (0% of total)

simplify15.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
26×*-commutative_binary64
20×+-commutative_binary64
6×sub-neg_binary64
6×neg-sub0_binary64
6×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064135
190135
296135
3101135
4103135
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 binary64)) (neg.f64 (/.f64 p x)) (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))))))))
(if (<=.f64 p #s(literal 5353260870520019/297403381695556612559612499629980112026252040331878891811154371863188131432080874709033662899231270117959744758038594610090917049108981141558166116220478925156594168089491974788537281966859547374047839156470287441213549741375576017631419788069731616602409021090828782564753069762936832 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 4253529586511731/1329227995784915872903807060280344576 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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))))
(if (<=.f64 p #s(literal 7004444445693749/76135265714062492815260799905274908678720522324960996303655519196976161646612703925512617702203205150197694658057880220183274764571899172238890525752442604840088107030909945545865544183516044127756246824056393584950668733792147460513643465745851293850216709399252168336576785859311828992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 5316911983139663/21267647932558653966460912964485513216 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 8283516909689999/4872657005699999540176691193937594155438113428797503763433953228606474345383213051232807532941005129612652458115704334091729584932601547023288993648156326709765638849978236514935394827745026824176399796739609189436842798962697437472873181807734482806413869401552138773540914294995957055488 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 7656353255721115/10633823966279326983230456482242756608 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -3224821407928563/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656 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 binary64)) (neg.f64 (/.f64 p x)) (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))))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 #s(literal 4 binary64) p)) (*.f64 x x)))) #s(literal 1 binary64)))))
(if (<=.f64 p #s(literal 5353260870520019/297403381695556612559612499629980112026252040331878891811154371863188131432080874709033662899231270117959744758038594610090917049108981141558166116220478925156594168089491974788537281966859547374047839156470287441213549741375576017631419788069731616602409021090828782564753069762936832 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 4253529586511731/1329227995784915872903807060280344576 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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))))
(if (<=.f64 p #s(literal 5353260870520019/297403381695556612559612499629980112026252040331878891811154371863188131432080874709033662899231270117959744758038594610090917049108981141558166116220478925156594168089491974788537281966859547374047839156470287441213549741375576017631419788069731616602409021090828782564753069762936832 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) p) x) (if (<=.f64 p #s(literal 4253529586511731/1329227995784915872903807060280344576 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 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.f64 (/.f64 (*.f64 x x) p) p) p) #s(literal -1/64 binary64)))))))))))
(if (<=.f64 p #s(literal 7004444445693749/76135265714062492815260799905274908678720522324960996303655519196976161646612703925512617702203205150197694658057880220183274764571899172238890525752442604840088107030909945545865544183516044127756246824056393584950668733792147460513643465745851293850216709399252168336576785859311828992 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 5316911983139663/21267647932558653966460912964485513216 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)))))))))
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#s(literal 1 binary64)

soundness880.0ms (11.9%)

Rules
6082×*-lowering-*.f32
6082×*-lowering-*.f64
3762×+-lowering-+.f64
3762×+-lowering-+.f32
3382×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028178
1158162
21571156
08134156
03812053
112091990
243371951
085551951
01416
13016
24015
34515
44715
54815
04815
Stop Event
1×done
1×iter limit
1×saturated
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 495 to 314 computations (36.6% saved)

preprocess95.0ms (1.3%)

Compiler

Compiled 432 to 222 computations (48.6% saved)

end0.0ms (0%)

Profiling

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