Given's Rotation SVD example

Time bar (total: 9.7s)

analyze684.0ms (7.1%)

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: 460.0ms
...c/correct-round.rkt:119:19: 118.0ms (25.6% of total)
ival-mult: 102.0ms (22.2% of total)
ival-sqrt: 102.0ms (22.2% of total)
ival-<: 47.0ms (10.2% of total)
ival-add: 31.0ms (6.7% of total)
ival-div: 29.0ms (6.3% of total)
ival-fabs: 22.0ms (4.8% of total)
ival-and: 4.0ms (0.9% of total)
const: 4.0ms (0.9% of total)
backward-pass: 1.0ms (0.2% of total)

sample2.5s (25.6%)

Results
1.2s6284×0valid
496.0ms1172×2valid
195.0ms623×1valid
94.0ms177×3valid
Precisions
Click to see histograms. Total time spent on operations: 1.6s
ival-mult: 484.0ms (29.4% of total)
ival-sqrt: 371.0ms (22.6% of total)
...c/correct-round.rkt:119:19: 288.0ms (17.5% of total)
ival-add: 160.0ms (9.7% of total)
ival-div: 100.0ms (6.1% of total)
backward-pass: 80.0ms (4.9% of total)
ival-<: 77.0ms (4.7% of total)
ival-fabs: 58.0ms (3.5% of total)
const: 15.0ms (0.9% of total)
ival-and: 11.0ms (0.7% of total)
Bogosity

preprocess127.0ms (1.3%)

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)

explain304.0ms (3.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
550-0-(sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))
340-0-(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
230-0-(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
103.0ms12×3valid
71.0ms386×0valid
52.0ms68×2valid
14.0ms46×1valid
Compiler

Compiled 213 to 44 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 193.0ms
ival-mult: 134.0ms (69.4% of total)
ival-div: 33.0ms (17.1% of total)
ival-sqrt: 12.0ms (6.2% of total)
ival-add: 8.0ms (4.1% of total)
backward-pass: 5.0ms (2.6% of total)
const: 1.0ms (0.5% of total)

eval0.0ms (0%)

Compiler

Compiled 19 to 13 computations (31.6% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶79.3%
(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)

localize70.0ms (0.7%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
✓accuracy92.1%
(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))))))
✓accuracy87.5%
(+.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)))))
✓accuracy79.9%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Results
25.0ms193×0valid
14.0ms35×2valid
6.0ms22×1valid
3.0ms6×3valid
Compiler

Compiled 87 to 14 computations (83.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 26.0ms
ival-mult: 11.0ms (41.9% of total)
ival-sqrt: 6.0ms (22.8% of total)
ival-add: 4.0ms (15.2% of total)
ival-div: 3.0ms (11.4% of total)
backward-pass: 3.0ms (11.4% of total)
const: 1.0ms (3.8% of total)

series22.0ms (0.2%)

Counts
6 → 132
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)) (* x x))>
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 (pow x 2)>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
Calls

33 calls:

TimeVariablePointExpression
7.0ms
p
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
2.0ms
x
@-inf
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
1.0ms
x
@inf
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
1.0ms
p
@inf
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
1.0ms
x
@0
(sqrt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))

rewrite330.0ms (3.4%)

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
01364
16262
252362
3764362
0850262
Stop Event
1×iter limit
1×node limit
Counts
6 → 255
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)) (* x x))
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)))))))
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(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))))
(*.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)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))
(*.f64 (*.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 1/4 binary64))) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal 1/4 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal -1 binary64)) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 (/.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x)))) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(*.f64 (/.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 (*.f64 #s(literal 4096 binary64) (*.f64 (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 p p) (*.f64 p (*.f64 p (*.f64 p p)))))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))))))) (+.f64 (*.f64 #s(literal 256 binary64) (*.f64 (*.f64 p (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (-.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64))))))))
(*.f64 (/.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 (*.f64 #s(literal 256 binary64) (*.f64 (*.f64 p (*.f64 p (*.f64 p p))) (*.f64 p (*.f64 p (*.f64 p p))))) (*.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal -4 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 (/.f64 (-.f64 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (*.f64 x x))) (-.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 (*.f64 p (*.f64 p (*.f64 (*.f64 p p) #s(literal 16 binary64)))) (*.f64 (*.f64 x x) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))

simplify413.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
6406×*-lowering-*.f32
6406×*-lowering-*.f64
3798×+-lowering-+.f64
3798×+-lowering-+.f32
1768×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03872233
112342164
244242125
087992125
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
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))))))))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 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 (*.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)))))))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) 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 -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)) (+.f64 #s(literal 1 binary64) (/.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 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) 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 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (*.f64 (*.f64 p p) (*.f64 p p)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))))) (pow.f64 x #s(literal 6 binary64))))))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
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1/2
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1
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1
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1/2
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1/2
#s(literal 1/2 binary64)
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1/2
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(+ 1/2 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (/.f64 (*.f64 (*.f64 p p) #s(literal 3 binary64)) (*.f64 (*.f64 x x) (*.f64 x x))))))
(+ 1/2 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 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 #s(literal 1/4 binary64) (/.f64 x 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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p)) (+.f64 (*.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 x x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) p)
(* -1/4 (/ x p))
(*.f64 #s(literal -1/4 binary64) (/.f64 x 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 #s(literal -1/32 binary64) (*.f64 x (*.f64 x x))) (*.f64 p p)) (+.f64 (*.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 (neg.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 x (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 (*.f64 p p) (*.f64 p p))) (/.f64 (+.f64 (*.f64 #s(literal 1/256 binary64) (pow.f64 x #s(literal 7 binary64))) (*.f64 (*.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -3/256 binary64))) (*.f64 #s(literal 1/8 binary64) x))) (pow.f64 p #s(literal 6 binary64)))))) (+.f64 (/.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)
(*.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 (/.f64 (*.f64 p p) x) x) #s(literal -2 binary64)) 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 (*.f64 p p) (+.f64 (/.f64 #s(literal 2 binary64) x) (*.f64 (*.f64 p p) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) x)) (/.f64 #s(literal -2 binary64) (*.f64 x (*.f64 x x))))))))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(*.f64 p (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p)))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(*.f64 p (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (+.f64 #s(literal 2 binary64) (/.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 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x 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 #s(literal 1/4 binary64) (/.f64 x 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 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))))) (-.f64 #s(literal 0 binary64) p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/64 binary64)) (*.f64 (*.f64 p p) (*.f64 p p))) (+.f64 (/.f64 (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))) p) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 (*.f64 (*.f64 x x) #s(literal -1/64 binary64)) (*.f64 p (*.f64 p p))))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (*.f64 x x) (+.f64 (/.f64 (*.f64 #s(literal 1/512 binary64) (*.f64 x x)) (pow.f64 p #s(literal 5 binary64))) (/.f64 #s(literal -1/64 binary64) (*.f64 p (*.f64 p p))))))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(*.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.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 #s(literal 2 binary64) (/.f64 (/.f64 (*.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 x (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))) #s(literal -1 binary64)))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(*.f64 x (+.f64 #s(literal -1 binary64) (neg.f64 (+.f64 (*.f64 #s(literal 2 binary64) (/.f64 (/.f64 (*.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)))))))
(* -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 #s(literal 2 binary64) (/.f64 (/.f64 (*.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))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (*.f64 x x) (*.f64 p p))))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))))

eval64.0ms (0.7%)

Compiler

Compiled 14803 to 1717 computations (88.4% saved)

prune48.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3798387
Fresh000
Picked101
Done000
Total3808388
Accuracy
100.0%
Counts
388 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶78.6%
(/.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))))))))
26.8%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
▶48.9%
(+.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))))
▶29.8%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
54.1%
(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 #s(literal 1/4 binary64) (/.f64 x p)))))))
▶49.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
53.0%
(sqrt.f64 #s(literal 1/2 binary64))
▶38.8%
#s(literal 1 binary64)
Compiler

Compiled 186 to 136 computations (26.9% saved)

simplify32.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))
✓cost-diff0
(*.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(+.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))))
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓cost-diff0
(/.f64 (*.f64 p p) x)
✓cost-diff0
(/.f64 (/.f64 (*.f64 p p) x) x)
✓cost-diff0
(*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
✓cost-diff128
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
Rules
166×*-lowering-*.f32
166×*-lowering-*.f64
80×/-lowering-/.f32
80×/-lowering-/.f64
76×fma-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032216
164208
2112208
3161208
4211208
5232208
0232208
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
1
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
1/2
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(* 1/2 x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
(* 4 (* p p))
4
(* p p)
p
(* x x)
1
(+ 1 (* -1/2 (/ (/ (* p p) x) x)))
1
(* -1/2 (/ (/ (* p p) x) x))
-1/2
(/ (/ (* p p) x) x)
(/ (* p p) x)
(* p p)
p
x
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(+ 1/2 (* 1/4 (/ x p)))
1/2
(* 1/4 (/ x p))
1/4
(/ x p)
x
p
(+ (sqrt 1/2) (* 1/8 (/ x (* (sqrt 1/2) p))))
(sqrt 1/2)
1/2
(* 1/8 (/ x (* (sqrt 1/2) p)))
1/8
(/ x (* (sqrt 1/2) p))
x
(* (sqrt 1/2) p)
p
Outputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
1
#s(literal 1 binary64)
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(sqrt (+ (* 4 (* p p)) (* x x)))
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
(+ (* 4 (* p p)) (* x x))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
(* 4 (* p p))
(*.f64 #s(literal 4 binary64) (*.f64 p p))
4
#s(literal 4 binary64)
(* p p)
(*.f64 p p)
p
(* x x)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (/ (* p p) x) x)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p (*.f64 p (/.f64 #s(literal -1/2 binary64) x))) x))
1
#s(literal 1 binary64)
(* -1/2 (/ (/ (* p p) x) x))
(/.f64 (*.f64 p (*.f64 p (/.f64 #s(literal -1/2 binary64) x))) x)
-1/2
#s(literal -1/2 binary64)
(/ (/ (* p p) x) x)
(/.f64 (*.f64 p p) (*.f64 x x))
(/ (* p p) x)
(/.f64 (*.f64 p p) x)
(* p p)
(*.f64 p p)
p
x
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(sqrt.f64 (+.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)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
1/4
#s(literal 1/4 binary64)
(/ x p)
(/.f64 x p)
x
p
(+ (sqrt 1/2) (* 1/8 (/ x (* (sqrt 1/2) p))))
(+.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)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 1/8 (/ x (* (sqrt 1/2) p)))
(/.f64 (*.f64 x #s(literal 1/8 binary64)) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))
1/8
#s(literal 1/8 binary64)
(/ x (* (sqrt 1/2) p))
(/.f64 x (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))
x
(* (sqrt 1/2) p)
(*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))
p

localize141.0ms (1.4%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 1/8 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
✓accuracy100.0%
(+.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))))
✓accuracy99.7%
(/.f64 x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p))
✓accuracy99.5%
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
✓accuracy100.0%
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
✓accuracy95.5%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓accuracy100.0%
(*.f64 p p)
✓accuracy100.0%
(*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x))
✓accuracy97.0%
(/.f64 (*.f64 p p) x)
✓accuracy95.5%
(/.f64 (/.f64 (*.f64 p p) x) x)
✓accuracy100.0%
(/.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))))))
✓accuracy100.0%
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))
✓accuracy99.3%
(/.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))))))))
✓accuracy79.9%
(sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))
Results
59.0ms193×0valid
19.0ms63×0invalid
Compiler

Compiled 231 to 33 computations (85.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-mult: 14.0ms (32.8% of total)
ival-div: 12.0ms (28.1% of total)
ival-add: 8.0ms (18.8% of total)
ival-sqrt: 8.0ms (18.8% of total)
const: 1.0ms (2.3% of total)
backward-pass: 0.0ms (0% of total)

series41.0ms (0.4%)

Counts
20 → 432
Calls
Call 1
Inputs
#<alt (/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))>
#<alt (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))>
#<alt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))>
#<alt (+ 1 (* -1/2 (/ (/ (* p p) x) x)))>
#<alt (* -1/2 (/ (/ (* p p) x) x))>
#<alt (/ (/ (* p p) x) x)>
#<alt (/ (* p p) x)>
#<alt (sqrt (+ 1/2 (* 1/4 (/ x p))))>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ x p))>
#<alt (/ x p)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* (sqrt 1/2) p))))>
#<alt (sqrt 1/2)>
#<alt (* 1/8 (/ x (* (sqrt 1/2) p)))>
#<alt (/ x (* (sqrt 1/2) p))>
#<alt (sqrt (+ (* 4 (* p p)) (* x x)))>
#<alt (+ (* 4 (* p p)) (* x x))>
#<alt (* p p)>
#<alt (* (sqrt 1/2) p)>
Outputs
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))>
#<alt (* -1 (/ p x))>
#<alt (* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))>
#<alt (* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (* 1/2 (/ (pow p 2) (pow x 2)))))>
#<alt (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (pow p 2) (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 6))) (* 1/2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 49/16 (/ (pow p 2) (pow x 6))) (* 9/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* p (sqrt 2))))) p)) (* -1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))>
#<alt (+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))>
#<alt (/ (pow x 2) (pow p 2))>
#<alt (* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))>
#<alt (* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))>
#<alt 1>
#<alt (+ 1 (/ (pow p 2) (pow x 2)))>
#<alt (+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))>
#<alt (- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))>
#<alt 2>
#<alt (+ 2 (/ x p))>
#<alt (+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))>
#<alt (+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ 1/2 (* x (+ (* (pow x 2) (- (* 3/512 (/ (pow x 2) (pow p 5))) (* 1/32 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4)))))>
#<alt (+ 1 (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))) (* -1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 6))))))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (pow p 2)) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2))) (pow x 2))>
#<alt (/ (+ (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow x 6))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 2))) (+ (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow x 4))) (pow p 2)))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* (pow p 2) (- (* 3 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))>
#<alt (+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -10 (/ (pow p 2) (pow x 6))) (* 3 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/4 (/ x p)))>
#<alt (+ 1/2 (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p))))>
#<alt (+ 1/2 (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 5))) (+ (* -1/32 (/ (pow x 3) (pow p 3))) (* 1/4 (/ x p)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 (/ x p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x)) p)))>
#<alt (+ 1/2 (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1/64 (pow x 4)) (* 1/256 (pow x 4)))) (pow p 4))) (+ (* -1/32 (/ (pow x 3) (pow p 2))) (* 1/4 x))) p)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt (/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (* -1/2 (/ (pow p 2) (pow x 2)))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) (pow x 2))>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) x)>
#<alt (/ (pow p 2) 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 (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (* 1/8 (/ x (* p (sqrt 1/2))))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt (/ x (* p (sqrt 1/2)))>
#<alt x>
#<alt (+ x (* 2 (/ (pow p 2) x)))>
#<alt (+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))>
#<alt (+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))>
#<alt (* 2 p)>
#<alt (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -2 p)>
#<alt (* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))>
#<alt (* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))>
#<alt (* 2 p)>
#<alt (+ (* 1/4 (/ (pow x 2) p)) (* 2 p))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))>
#<alt (+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))>
#<alt (pow x 2)>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))>
#<alt (* 4 (pow p 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (+ (* 4 (pow p 2)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (pow p 2)>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
#<alt (* p (sqrt 1/2))>
Calls

108 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(* 1/4 (/ x p))
2.0ms
p
@inf
(+ 1 (* -1/2 (/ (/ (* p p) x) x)))
2.0ms
x
@-inf
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
2.0ms
x
@inf
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
1.0ms
x
@-inf
(sqrt (+ 1/2 (* 1/4 (/ x p))))

rewrite327.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
3782×/-lowering-/.f32
3782×/-lowering-/.f64
3382×*-lowering-*.f32
3382×*-lowering-*.f64
1690×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032171
1177161
21425155
08266155
Stop Event
1×iter limit
1×node limit
Counts
20 → 643
Calls
Call 1
Inputs
(/ 1 (sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))))
(sqrt (/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))))
(/ 1 (+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x))))))
(+ 1/2 (/ (* 1/2 x) (sqrt (+ (* 4 (* p p)) (* x x)))))
(+ 1 (* -1/2 (/ (/ (* p p) x) x)))
(* -1/2 (/ (/ (* p p) x) x))
(/ (/ (* p p) x) x)
(/ (* p p) x)
(sqrt (+ 1/2 (* 1/4 (/ x p))))
(+ 1/2 (* 1/4 (/ x p)))
(* 1/4 (/ x p))
(/ x p)
(+ (sqrt 1/2) (* 1/8 (/ x (* (sqrt 1/2) p))))
(sqrt 1/2)
(* 1/8 (/ x (* (sqrt 1/2) p)))
(/ x (* (sqrt 1/2) p))
(sqrt (+ (* 4 (* p p)) (* x x)))
(+ (* 4 (* p p)) (* x x))
(* p p)
(* (sqrt 1/2) p)
Outputs
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal -1 binary64)))
(exp.f64 (*.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)))
(exp.f64 (*.f64 (log.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 -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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))))))
(neg.f64 (/.f64 #s(literal -1 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 -1/2 binary64))))
(/.f64 #s(literal 1 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 -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 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 -1/2 binary64))))))
(/.f64 (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)))))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (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 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.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 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 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))))))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (neg.f64 (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))))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 1/4 binary64))) (sqrt.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (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 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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 -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (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)))))) #s(literal 1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 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 -1/2 binary64))))
(*.f64 (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)))))) #s(literal 1 binary64))
(*.f64 (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)))))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (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 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.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 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))))))
(*.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 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1/2 binary64) (/.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 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 #s(literal 1/4 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
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(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(/.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (*.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)) (*.f64 x (*.f64 x (*.f64 x x))))) (*.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))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))))) (neg.f64 (neg.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))))) (neg.f64 (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))))) (neg.f64 (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (+.f64 (*.f64 (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (*.f64 (/.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) (/.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.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 binary64))
(pow.f64 (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))) #s(literal -1 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 1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.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))) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))))
(*.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x (*.f64 x (*.f64 x x))) (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 p p) (*.f64 #s(literal 4 binary64) (*.f64 x x)))))))
(*.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))
(*.f64 (neg.f64 (+.f64 (*.f64 #s(literal 64 binary64) (*.f64 (*.f64 p (*.f64 p p)) (*.f64 p (*.f64 p p)))) (*.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 (*.f64 x x) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p))))))))
(*.f64 (neg.f64 (-.f64 (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x)))))
(*.f64 (-.f64 (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 #s(literal 16 binary64) (*.f64 (*.f64 p p) (*.f64 p p)))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (*.f64 #s(literal 4 binary64) (*.f64 p p)))))
(exp.f64 (*.f64 (log.f64 p) #s(literal 2 binary64)))
(pow.f64 p #s(literal 2 binary64))
(pow.f64 (*.f64 p p) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 p)) #s(literal 2 binary64))
(*.f64 p p)
(*.f64 (exp.f64 (log.f64 p)) (exp.f64 (log.f64 p)))
(*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)

simplify391.0ms (4%)

Algorithm
1×egg-herbie
Rules
6258×*-lowering-*.f32
6258×*-lowering-*.f64
3742×+-lowering-+.f64
3742×+-lowering-+.f32
2140×/-lowering-/.f32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07215562
123525312
083935312
Stop Event
1×iter limit
1×node limit
Counts
432 → 432
Calls
Call 1
Inputs
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4)))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(* -1 (/ p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4)))))) x))
(* -1 (/ (+ p (+ (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2)))) (+ (* 1/2 (/ (- (* 1/4 (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))))))) (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2))))) (pow p 2)))) (* p (pow x 6)))) (* 1/2 (/ (- (* 1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 2)))) (* p (pow x 4))))))) x))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (- (* 11/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (- (* (pow p 2) (+ (* -69/16 (/ (pow p 2) (pow x 6))) (* 11/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/128 (/ (pow x 2) (* (pow p 2) (pow (sqrt 1/2) 3)))) (+ (* 1/8 (/ x (* p (sqrt 1/2)))) (* 1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* (pow p 3) (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* 1/128 (/ (pow x 2) (* p (pow (sqrt 1/2) 3)))) (* 1/8 (/ x (sqrt 1/2)))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (- (* -1/32 (pow x 3)) (* -1/512 (/ (pow x 3) (pow (sqrt 1/2) 4)))) (* p (sqrt 1/2)))) (* -1/128 (/ (pow x 2) (pow (sqrt 1/2) 3)))) p)) (* 1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* 1/2 (/ (* x (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2)))))) (sqrt 2))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (+ (* -1/2 (/ (* x (+ (* -1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (* p (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow p 3))))) (sqrt 2))) (* 1/2 (/ (- (* 1/2 (/ 1 (pow p 2))) (* 1/4 (/ 1 (* (pow p 2) (pow (sqrt 2) 2))))) (sqrt 2))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
1
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (* 1/2 (/ (pow p 2) (pow x 2)))))
(+ 1 (+ (* -1/2 (/ (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))) (pow x 4))) (+ (* -1/2 (/ (+ (* -1/2 (* (pow p 2) (+ (* -1 (pow p 4)) (+ (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))))))) (pow x 6))) (* 1/2 (/ (pow p 2) (pow x 2))))))
(* -1 (/ x p))
(* -1 (* x (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))
(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p)))))
(* -1 (* x (+ (* -1/2 (/ (* p (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (+ (* 1/8 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow p 2))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))))) (pow x 6))) (+ (* -1/2 (/ (* p (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (+ (* 1/64 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))))) (pow x 4))) (+ (* -1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 3) (pow x 2)))) (/ 1 p))))))
1
(+ 1 (* 1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* (pow p 2) (+ (* -9/8 (/ (pow p 2) (pow x 4))) (* 1/2 (/ 1 (pow x 2))))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 49/16 (/ (pow p 2) (pow x 6))) (* 9/8 (/ 1 (pow x 4))))) (* 1/2 (/ 1 (pow x 2))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2))))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* (pow p 2) (sqrt 2)))) (* -1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* (pow p 3) (sqrt 2)))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* -1 (/ (+ (* -1/2 (/ x (sqrt 2))) (* 1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (* p (sqrt 2))))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2)))) (sqrt 2))) (* 1/2 (/ (+ (* -1/8 (pow x 3)) (+ (* 1/4 (pow x 3)) (* 1/2 (/ (* x (+ (* -1/2 (pow x 2)) (* 1/4 (/ (pow x 2) (pow (sqrt 2) 2))))) (pow (sqrt 2) 2))))) (* p (sqrt 2))))) p)) (* -1/2 (/ x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
(+ 2 (* x (- (* x (+ (* -1/8 (/ x (pow p 3))) (* 1/2 (/ 1 (pow p 2))))) (/ 1 p))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(- (+ 1 (* -1 (/ (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (pow x 4)))) (* -1 (/ (pow p 2) (pow x 2))))
(- (+ 1 (* -1 (/ (+ (* -1/4 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (+ (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* (pow p 2) (+ (* -1 (pow p 4)) (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))))))) (pow x 6)))) (+ (* -1 (/ (pow p 2) (pow x 2))) (+ (* -1 (/ (pow p 4) (pow x 4))) (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (pow x 4))))))
(/ (pow x 2) (pow p 2))
(* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4)))) (pow x 4))) (/ 1 (pow p 2))) (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2))))))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1/4 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (pow p 6))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (pow p 4))))) (pow p 2))) (+ (* -1/16 (/ (* (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (pow p 6))) (* 1/4 (/ (+ (* -256 (pow p 8)) (+ (* 1/4 (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2)) (* 2 (* (pow p 2) (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))))))) (pow p 4))))) (pow x 6))) (/ 1 (pow p 2))) (+ (* -1/16 (/ (pow (+ (* -16 (pow p 4)) (* 4 (pow p 4))) 2) (* (pow p 6) (pow x 4)))) (+ (* 1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (* 1/4 (/ (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6))) (* (pow p 4) (pow x 4))))))))
1
(+ 1 (/ (pow p 2) (pow x 2)))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
2
(+ 2 (* -1 (/ x p)))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
(- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
2
(+ 2 (/ x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
(+ 2 (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (/ (pow x 3) p)) (* 1/4 (/ (pow x 3) p))) (* -1/2 (pow x 2))) p)) x) p)))
1/2
(+ 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
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow p 2) (- (/ 1 (pow p 2)) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 (pow p 2)) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
1
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(+ 1 (* -1/2 (/ (pow p 2) (pow x 2))))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(* -1/2 (/ (pow p 2) (pow x 2)))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) (pow x 2))
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) x)
(/ (pow p 2) 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))
(/ 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)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))
(* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))
(* x (+ (* 1/8 (/ 1 (* p (sqrt 1/2)))) (/ (sqrt 1/2) x)))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(/ (+ (* 1/8 (/ x (sqrt 1/2))) (* p (sqrt 1/2))) p)
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(* 1/8 (/ x (* p (sqrt 1/2))))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
(/ x (* p (sqrt 1/2)))
x
(+ x (* 2 (/ (pow p 2) x)))
(+ x (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 3))) (* 2 (/ 1 x)))))
(+ x (* (pow p 2) (+ (* (pow p 2) (- (* 4 (/ (pow p 2) (pow x 5))) (* 2 (/ 1 (pow x 3))))) (* 2 (/ 1 x)))))
(* 2 p)
(* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2)))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2))))))
(* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -2 p)
(* -1 (* p (+ 2 (* 1/4 (/ (pow x 2) (pow p 2))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(* 2 p)
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+ (* 2 p) (* (pow x 2) (+ (* (pow x 2) (- (* 1/512 (/ (pow x 2) (pow p 5))) (* 1/64 (/ 1 (pow p 3))))) (* 1/4 (/ 1 p)))))
x
(* x (+ 1 (* 2 (/ (pow p 2) (pow x 2)))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2))))))
(* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 2 (/ (pow p 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (* 2 (/ (pow p 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -2 (/ (pow p 4) (pow x 4))) (+ (* 2 (/ (pow p 2) (pow x 2))) (* 4 (/ (pow p 6) (pow x 6))))))))
(pow x 2)
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(* 4 (pow p 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(+ (* 4 (pow p 2)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(pow p 2)
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
(* p (sqrt 1/2))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) p))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) x) (*.f64 p (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/2 (/ (* x (- (* 1/512 (/ 1 (* (pow p 3) (pow (sqrt 1/2) 4)))) (* 1/32 (/ 1 (pow p 3))))) (sqrt 1/2))) (* 1/128 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 3)))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)) (*.f64 x (+.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (/.f64 (/.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 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))))))
(+ 1 (+ (* -1/2 (/ (pow p 2) (pow x 2))) (+ (* 1/2 (/ (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4))) (pow x 4))) (* 1/2 (/ (- (* -1/4 (+ (* 2 (* (pow p 2) (+ (* -16 (pow p 4)) (* 4 (pow p 4))))) (* 64 (pow p 6)))) (* -1/2 (* (pow p 2) (- (* -1/4 (+ (* -16 (pow p 4)) (* 4 (pow p 4)))) (* 1/4 (pow p 4)))))) (pow x 6))))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (*.f64 p p) #s(literal -1/2 binary64)) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) (/.f64 (+.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64))) (*.f64 (pow.f64 p #s(literal 6 binary64)) #s(literal -16 binary64))) (*.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 p p) (+.f64 (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -1/4 binary64) (pow.f64 p #s(literal 4 binary64))))))) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(* -1 (/ (+ p (* 1/8 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* p (pow x 2))))) x))
(/.f64 (+.f64 p (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 p #s(literal 4 binary64)) #s(literal -12 binary64))) (*.f64 p (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
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1
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(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (* p (sqrt 2)))))
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2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* x (- (* 1/2 (/ x (pow p 2))) (/ 1 p))))
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1
#s(literal 1 binary64)
(+ 1 (/ (pow p 2) (pow x 2)))
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(/ (pow x 2) (pow p 2))
(/.f64 (/.f64 (*.f64 x x) p) p)
(* (pow x 2) (+ (* -1/4 (/ (+ (* -16 (pow p 4)) (* 4 (pow p 4))) (* (pow p 4) (pow x 2)))) (/ 1 (pow p 2))))
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1
#s(literal 1 binary64)
(+ 1 (/ (pow p 2) (pow x 2)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 p p) (*.f64 x x)))
(+ 1 (* (pow p 2) (+ (* -2 (/ (pow p 2) (pow x 4))) (/ 1 (pow x 2)))))
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(+ 1 (* (pow p 2) (+ (* (pow p 2) (- (* 5 (/ (pow p 2) (pow x 6))) (* 2 (/ 1 (pow x 4))))) (/ 1 (pow x 2)))))
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2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(- (+ 2 (* 1/2 (/ (pow x 2) (pow p 2)))) (/ x p))
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(- (+ 2 (* -1 (/ (+ (* -1/8 (pow x 3)) (* 1/4 (pow x 3))) (pow p 3)))) (+ (* -1/2 (/ (pow x 2) (pow p 2))) (/ x p)))
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2
#s(literal 2 binary64)
(+ 2 (/ x p))
(+.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ (- (* -1/2 (/ (pow x 2) p)) x) p)))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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(+ 1/2 (* x (+ (* -1/32 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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(/ (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))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow p 2) (pow x 2))))
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1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/4 (/ x p)))
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1/2
#s(literal 1/2 binary64)
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(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (* 1/4 (/ (pow x 2) (pow p 2)))))))
(*.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p)) p)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))) (neg.f64 p))
(* -1 (* p (+ 2 (+ (* -1/64 (/ (pow x 4) (pow p 4))) (+ (* 1/512 (/ (pow x 6) (pow p 6))) (* 1/4 (/ (pow x 2) (pow p 2))))))))
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p)) p)) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/64 binary64)) (pow.f64 p #s(literal 4 binary64)))) (/.f64 (*.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 p #s(literal 6 binary64)))) (neg.f64 p))
(* 2 p)
(*.f64 p #s(literal 2 binary64))
(+ (* 1/4 (/ (pow x 2) p)) (* 2 p))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 x x) p)))
(+ (* 2 p) (* (pow x 2) (+ (* -1/64 (/ (pow x 2) (pow p 3))) (* 1/4 (/ 1 p)))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 (*.f64 x x) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (*.f64 (/.f64 (/.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 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(* 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 #s(literal 2 binary64) (*.f64 p p)) x) x) (+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 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 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 (*.f64 #s(literal 2 binary64) (*.f64 p p)) x) x) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.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 #s(literal 2 binary64) (*.f64 p p)) x) x) (+.f64 (/.f64 (*.f64 #s(literal 4 binary64) (pow.f64 p #s(literal 6 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (*.f64 #s(literal -2 binary64) (pow.f64 p #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(pow x 2)
(*.f64 x x)
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* (pow p 2) (+ 4 (/ (pow x 2) (pow p 2))))
(*.f64 (*.f64 p p) (+.f64 #s(literal 4 binary64) (/.f64 (/.f64 (*.f64 x x) p) p)))
(* 4 (pow p 2))
(*.f64 (*.f64 p p) #s(literal 4 binary64))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(+ (* 4 (pow p 2)) (pow x 2))
(+.f64 (*.f64 x x) (*.f64 (*.f64 p p) #s(literal 4 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(* (pow x 2) (+ 1 (* 4 (/ (pow p 2) (pow x 2)))))
(*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 p p) #s(literal 4 binary64)) (*.f64 x x))))
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(pow p 2)
(*.f64 p p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)
(* p (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)

eval144.0ms (1.5%)

Compiler

Compiled 24777 to 3383 computations (86.3% saved)

prune116.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New109731100
Fresh033
Picked235
Done000
Total109991108
Accuracy
100.0%
Counts
1108 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶50.7%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
▶52.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
▶26.8%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓29.8%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
▶54.1%
(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 #s(literal 1/4 binary64) (/.f64 x p)))))))
✓49.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
48.9%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
▶53.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓38.8%
#s(literal 1 binary64)
Compiler

Compiled 144 to 112 computations (22.2% saved)

simplify26.0ms (0.3%)

Algorithm
1×egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓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-diff0
(*.f64 #s(literal 1/2 binary64) x)
✓cost-diff0
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))
✓cost-diff0
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
Rules
284×sum3-define
250×fma-define
126×fma-lowering-fma.f32
126×fma-lowering-fma.f64
120×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
024126
146124
281124
3114124
4148124
5181124
6222124
7259124
8379124
9606124
10640124
11651124
12652124
0652124
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p))))))
1/2
(/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))
(* 1/2 x)
x
(+ (* p 2) (* x (* 1/4 (/ x p))))
(* p 2)
p
2
(* x (* 1/4 (/ x p)))
(* 1/4 (/ x p))
1/4
(/ x p)
(- 0 (/ p x))
0
(/ p x)
p
x
(sqrt 1/2)
1/2
(/ 1 (sqrt 2))
1
(sqrt 2)
2
(/ 1 (sqrt (- 2 (/ x p))))
1
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
2
(/ x p)
x
p
Outputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p))))))
(+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))))
1/2
#s(literal 1/2 binary64)
(/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
x
(+ (* p 2) (* x (* 1/4 (/ x p))))
(+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p)))
(* p 2)
(*.f64 p #s(literal 2 binary64))
p
2
#s(literal 2 binary64)
(* x (* 1/4 (/ x p)))
(*.f64 x (/.f64 (*.f64 x #s(literal 1/4 binary64)) p))
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
1/4
#s(literal 1/4 binary64)
(/ x p)
(/.f64 x p)
(- 0 (/ p x))
(-.f64 #s(literal 0 binary64) (/.f64 p 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)
(/ 1 (sqrt 2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
1
#s(literal 1 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1 (sqrt (- 2 (/ x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
1
#s(literal 1 binary64)
(sqrt (- 2 (/ x p)))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
(- 2 (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(/ x p)
(/.f64 x p)
x
p

localize90.0ms (0.9%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓accuracy99.2%
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
✓accuracy96.6%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy98.9%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(/.f64 p x)
✓accuracy100.0%
(-.f64 #s(literal 0 binary64) (/.f64 p x))
✓accuracy100.0%
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
✓accuracy99.8%
(*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))
✓accuracy96.0%
(/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 p #s(literal 2 binary64)) (*.f64 x (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))
Results
43.0ms184×0valid
16.0ms72×0invalid
Compiler

Compiled 138 to 25 computations (81.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 30.0ms
ival-div: 10.0ms (33.5% of total)
ival-mult: 7.0ms (23.4% of total)
ival-sqrt: 7.0ms (23.4% of total)
ival-add: 3.0ms (10% of total)
ival-sub: 2.0ms (6.7% of total)
const: 1.0ms (3.3% of total)
backward-pass: 0.0ms (0% of total)

series28.0ms (0.3%)

Counts
15 → 276
Calls
Call 1
Inputs
#<alt (sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))))>
#<alt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p))))))>
#<alt (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))>
#<alt (* 1/2 x)>
#<alt (- 0 (/ p x))>
#<alt (/ p x)>
#<alt (sqrt 1/2)>
#<alt (/ 1 (sqrt 2))>
#<alt (sqrt 2)>
#<alt (/ 1 (sqrt (- 2 (/ x p))))>
#<alt (sqrt (- 2 (/ x p)))>
#<alt (- 2 (/ x p))>
#<alt (/ x p)>
#<alt (* x (* 1/4 (/ x p)))>
#<alt (* 1/4 (/ 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) (/ 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 (/ 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 (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))>
#<alt (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))>
#<alt (* -1 (* (sqrt (/ x p)) (sqrt -1)))>
#<alt (* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))>
#<alt (* (sqrt (/ x p)) (sqrt -1))>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)>
#<alt (/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))>
#<alt (+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt (+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (* -1 (/ x p))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (/ x p))>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (* 1/4 (/ (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))>
#<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))>
Calls

69 calls:

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

rewrite309.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
3676×*-lowering-*.f32
3676×*-lowering-*.f64
3228×/-lowering-/.f32
3228×/-lowering-/.f64
1642×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02495
113393
2110693
0847093
Stop Event
1×iter limit
1×node limit
Counts
15 → 441
Calls
Call 1
Inputs
(sqrt (+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))))
(+ 1/2 (/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p))))))
(/ (* 1/2 x) (+ (* p 2) (* x (* 1/4 (/ x p)))))
(* 1/2 x)
(- 0 (/ p x))
(/ p x)
(sqrt 1/2)
(/ 1 (sqrt 2))
(sqrt 2)
(/ 1 (sqrt (- 2 (/ x p))))
(sqrt (- 2 (/ x p)))
(- 2 (/ x p))
(/ x p)
(* x (* 1/4 (/ x p)))
(* 1/4 (/ x p))
Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64)))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 (+.f64 (/.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64)))) #s(literal -1/2 binary64)) (/.f64 (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64))) (*.f64 x #s(literal -1/2 binary64)))))) (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 (*.f64 x #s(literal 1/4 binary64))) p)) (*.f64 (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)) (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 (/.f64 x (/.f64 p x)) #s(literal -1/4 binary64)) (*.f64 p #s(literal -2 binary64)))))) (sqrt.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 #s(literal -1/4 binary64) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)))) (/.f64 x (+.f64 (*.f64 p #s(literal 2 binary64)) (/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p))))))))
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(-.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))
(-.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))))
(fma.f64 x (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p)) #s(literal 2 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 x p) #s(literal 2 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) p) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p)))))
(/.f64 (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x))))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(/.f64 (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p)))) (+.f64 #s(literal 2 binary64) (/.f64 x p)))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))))
(/.f64 (-.f64 (*.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))))) (*.f64 (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))
(/.f64 (-.f64 (*.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 x p)) (/.f64 x (/.f64 p (/.f64 x p))))) (*.f64 (+.f64 #s(literal 2 binary64) (/.f64 x p)) (+.f64 #s(literal 2 binary64) (/.f64 x p))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x))))) #s(literal 8 binary64)) (+.f64 (/.f64 x (/.f64 p (/.f64 x p))) (-.f64 #s(literal 4 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))) (+.f64 (*.f64 (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))) (*.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (+.f64 (*.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (*.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(/.f64 (-.f64 (/.f64 x (/.f64 p (/.f64 x p))) #s(literal 4 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))) (*.f64 (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))) (+.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (*.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (+.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p)))
(*.f64 (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))
(*.f64 (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x p) (/.f64 p (/.f64 x (/.f64 p x)))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(exp.f64 (*.f64 (log.f64 (/.f64 p x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 x p)
(/.f64 (/.f64 x p) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 p x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) p))
(/.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 x p) #s(literal 1 binary64))
(pow.f64 (/.f64 p x) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) p))
(*.f64 x (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p))))
(*.f64 (/.f64 x p) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 x p))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) p))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p)))
(*.f64 (/.f64 #s(literal 1 binary64) p) x)
(*.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) p) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) p) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) p))
(*.f64 (pow.f64 (/.f64 p x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 p x) #s(literal -1/2 binary64)))
(/.f64 x (/.f64 p (*.f64 x #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p x) (*.f64 x #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 (*.f64 x #s(literal 1/4 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 p x))
(/.f64 (*.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) x) p)
(/.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) p)
(/.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) p))
(/.f64 (neg.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) x)) (-.f64 #s(literal 0 binary64) p))
(/.f64 (neg.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) p))
(/.f64 (neg.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x))) p)
(*.f64 x (/.f64 #s(literal 1/4 binary64) (/.f64 p x)))
(*.f64 #s(literal 1/4 binary64) (/.f64 x (/.f64 p x)))
(*.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x p) x))
(*.f64 (/.f64 x p) (*.f64 x #s(literal 1/4 binary64)))
(*.f64 (/.f64 x p) (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 p x)) x)
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 x p))
(*.f64 (/.f64 x (/.f64 p x)) #s(literal 1/4 binary64))
(*.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) x) (/.f64 #s(literal 1 binary64) p))
(*.f64 (*.f64 x (*.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) p))
(*.f64 (*.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) p))
(*.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 x p))
(*.f64 (/.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(*.f64 (/.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1/4 binary64) p))
(*.f64 (/.f64 x (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) p)))
(*.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 0 binary64) p)) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 x p))
(*.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) p)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -1 binary64) p))
(*.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 #s(literal 1/4 binary64) (/.f64 p x))
(/.f64 #s(literal 1 binary64) (/.f64 p (*.f64 x #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p x) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64)))))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(/.f64 (*.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) p))
(/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (/.f64 p x)))
(/.f64 (neg.f64 (*.f64 x #s(literal -1/4 binary64))) p)
(pow.f64 (/.f64 p (*.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))
(*.f64 x (*.f64 (/.f64 #s(literal 1 binary64) p) #s(literal 1/4 binary64)))
(*.f64 x (/.f64 #s(literal 1/4 binary64) p))
(*.f64 #s(literal 1/4 binary64) (/.f64 x p))
(*.f64 (/.f64 x p) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (/.f64 p x)))
(*.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (*.f64 x #s(literal -1/4 binary64)) (/.f64 #s(literal -1 binary64) p))
(*.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))

simplify326.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
4560×*-lowering-*.f32
4560×*-lowering-*.f64
2440×+-lowering-+.f64
2440×+-lowering-+.f32
2030×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
06043219
118673054
264332997
081832997
Stop Event
1×iter limit
1×node limit
Counts
276 → 276
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) (/ 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 (/ 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 (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* x (- (* -1/8 (/ x (* (pow p 2) (pow (sqrt 2) 3)))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(+ (sqrt 2) (* x (- (* x (- (* -1/16 (/ x (* (pow p 3) (pow (sqrt 2) 5)))) (* 1/8 (/ 1 (* (pow p 2) (pow (sqrt 2) 3)))))) (* 1/2 (/ 1 (* p (sqrt 2)))))))
(* (sqrt (/ x p)) (sqrt -1))
(* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1))))))
(* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (/ 1 (sqrt -1)))))))
(* -1 (* (sqrt (/ x p)) (sqrt -1)))
(* -1 (* x (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ (pow p 3) (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ (pow p 5) (pow x 7))) (sqrt -1))) (+ (* (sqrt (/ 1 (* p x))) (sqrt -1)) (* (sqrt (/ p (pow x 3))) (sqrt -1)))))))
(* (sqrt (/ x p)) (sqrt -1))
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (sqrt (/ (pow p 3) x)) (/ 1 (sqrt -1)))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ p (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1)))))) p)
(/ (+ (* (sqrt (* p x)) (sqrt -1)) (* (pow p 2) (+ (* (sqrt (/ 1 (* p x))) (/ 1 (sqrt -1))) (* (pow p 2) (+ (* -1/2 (* (sqrt (/ 1 (* (pow p 3) (pow x 3)))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (pow (sqrt -1) 5))))))))) p)
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3))))))
(+ (sqrt 2) (+ (* -1/2 (/ x (* p (sqrt 2)))) (+ (* -1/8 (/ (pow x 2) (* (pow p 2) (pow (sqrt 2) 3)))) (* -1/16 (/ (pow x 3) (* (pow p 3) (pow (sqrt 2) 5)))))))
(sqrt 2)
(+ (sqrt 2) (* -1/2 (/ x (* p (sqrt 2)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(* -1 (/ x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* -1 (/ x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (/ x p))
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(* 1/4 (/ (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))
(* 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))
Outputs
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (*.f64 #s(literal 1/8 binary64) x) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) p)))
(+ (sqrt 1/2) (* x (+ (* -1/128 (/ x (* (pow p 2) (pow (sqrt 1/2) 3)))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (+.f64 (/.f64 (*.f64 #s(literal -1/128 binary64) (/.f64 x (*.f64 p p))) (*.f64 #s(literal 1/2 binary64) (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 #s(literal 1/2 binary64) x) (/.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 (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) (/ p (* x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (+ (* -1/2 (/ (pow p 2) (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ p (* x (sqrt 1/2)))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 p (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))))
(+ (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))))))
(+.f64 (+.f64 (/.f64 (neg.f64 (/.f64 (*.f64 p p) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x x)) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -16 binary64))) (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (*.f64 x x))))) (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ p (sqrt 1/2))) (* 1/2 (/ (pow p 2) (* x (pow (sqrt 1/2) 3))))) x)))
(-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (-.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 p p)) (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) (/.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) 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)))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 p (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (+.f64 (neg.f64 (/.f64 (*.f64 p p) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 p (*.f64 (*.f64 p p) #s(literal -16 binary64))) (/.f64 (*.f64 p (*.f64 p p)) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x))) x)) x))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
(+ (sqrt 1/2) (/ p (* x (sqrt 1/2))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 p (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))
(+ (sqrt 1/2) (* p (+ (* -1/2 (/ p (* (pow x 2) (pow (sqrt 1/2) 3)))) (/ 1 (* x (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (+.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 p (*.f64 x x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)))))
(+ (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))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 p (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (*.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 (*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal -16 binary64) (*.f64 x (*.f64 x x)))) (/.f64 p (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 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 #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))))))
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(sqrt 2)
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(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (*.f64 p (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* -1 (/ (+ (* 1/8 (/ (pow x 2) (* p (pow (sqrt 2) 3)))) (* 1/2 (/ x (sqrt 2)))) p)))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (*.f64 x x)) (*.f64 p (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) p))
(+ (sqrt 2) (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (pow x 2) (pow (sqrt 2) 3))) (* -1/16 (/ (pow x 3) (* p (pow (sqrt 2) 5))))) p)) (* 1/2 (/ x (sqrt 2)))) p)))
(-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (+.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (*.f64 #s(literal -1/16 binary64) (/.f64 (*.f64 x (*.f64 x x)) p)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64)))) p)) p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal -2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal -2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal -2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ (pow x 2) p))
(/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)
(* 1/4 (/ x p))
(/.f64 (*.f64 x #s(literal 1/4 binary64)) p)

eval96.0ms (1%)

Compiler

Compiled 15853 to 2219 computations (86% saved)

prune71.0ms (0.7%)

Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New7672769
Fresh011
Picked235
Done033
Total7699778
Accuracy
100.0%
Counts
778 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶51.6%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓52.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓29.8%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
✓54.1%
(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 #s(literal 1/4 binary64) (/.f64 x p)))))))
✓49.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
▶48.9%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓53.0%
(sqrt.f64 #s(literal 1/2 binary64))
▶26.8%
(neg.f64 (/.f64 p x))
✓38.8%
#s(literal 1 binary64)
Compiler

Compiled 83 to 64 computations (22.9% saved)

simplify14.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(/.f64 x p)
✓cost-diff0
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓cost-diff0
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓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
162×sum3-define
120×fma-define
80×+-lowering-+.f64
80×+-lowering-+.f32
70×fma-lowering-fma.f32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01664
13464
25864
38458
412058
515658
619558
724658
838658
939658
1039858
039858
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
(pow (- 2 (/ x p)) -1/2)
(- 2 (/ x p))
2
(/ x p)
x
p
-1/2
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 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64)))
(* x (+ (/ 1/4 p) (/ 1/2 x)))
(+.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) p) #s(literal 1/2 binary64))
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)
(pow (- 2 (/ x p)) -1/2)
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(- 2 (/ x p))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(/ x p)
(/.f64 x p)
x
p
-1/2
#s(literal -1/2 binary64)

localize89.0ms (0.9%)

Localize:

Found 9 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 x p)
✓accuracy100.0%
(-.f64 #s(literal 2 binary64) (/.f64 x p))
✓accuracy100.0%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1/4 binary64) p)
✓accuracy100.0%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓accuracy100.0%
(+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))
✓accuracy99.9%
(*.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
48.0ms121×0valid
22.0ms135×0invalid
Compiler

Compiled 67 to 17 computations (74.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 51.0ms
ival-div: 35.0ms (68.3% of total)
ival-pow: 5.0ms (9.8% of total)
ival-sub: 4.0ms (7.8% of total)
ival-mult: 2.0ms (3.9% of total)
ival-sqrt: 2.0ms (3.9% of total)
ival-add: 1.0ms (2% of total)
const: 1.0ms (2% of total)
ival-neg: 1.0ms (2% of total)
backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts
9 → 204
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 (pow (- 2 (/ x p)) -1/2)>
#<alt (- 2 (/ x p))>
#<alt (/ x 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 (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))>
#<alt (* (sqrt (/ p x)) (sqrt -1))>
#<alt (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))>
#<alt (+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (* -1 (/ x p))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* x (- (* 2 (/ 1 x)) (/ 1 p)))>
#<alt (* -1 (/ x p))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))>
#<alt (* -1 (/ x p))>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt (/ (- (* 2 p) x) p)>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt 2>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (+ 2 (* -1 (/ x p)))>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
#<alt (/ x p)>
Calls

51 calls:

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

rewrite272.0ms (2.8%)

Algorithm
1×batch-egg-rewrite
Rules
4220×*-lowering-*.f32
4220×*-lowering-*.f64
3772×/-lowering-/.f32
3772×/-lowering-/.f64
2134×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01651
19651
287045
0846945
Stop Event
1×iter limit
1×node limit
Counts
9 → 387
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)
(pow (- 2 (/ x p)) -1/2)
(- 2 (/ x p))
(/ x p)
Outputs
(+.f64 #s(literal 0 binary64) (/.f64 p x))
(exp.f64 (*.f64 (log.f64 (/.f64 x p)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(/.f64 p x)
(/.f64 (/.f64 p x) #s(literal 1 binary64))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) p) x) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) p) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 x p))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) p))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(/.f64 (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(pow.f64 (/.f64 p x) #s(literal 1 binary64))
(pow.f64 (/.f64 x p) #s(literal -1 binary64))
(*.f64 p (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 p x) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal -1 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 -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) p))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) p) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) p) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x p) #s(literal -1/2 binary64)))
(+.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 p x))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))) (/.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 p x)) (/.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (/.f64 p x)))
(neg.f64 (/.f64 p x))
(/.f64 p (-.f64 #s(literal 0 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) p) x)
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x p) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 p x) (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))))
(/.f64 #s(literal -1 binary64) (/.f64 x p))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 p x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (neg.f64 (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p)))) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (-.f64 #s(literal 0 binary64) p) x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (/.f64 (/.f64 p x) (/.f64 x p)) (*.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x)))))
(pow.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal -1 binary64))
(*.f64 p (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 p (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 p x) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) p) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(*.f64 #s(literal -1 binary64) (/.f64 p x))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (/.f64 p x) (/.f64 x p)) #s(literal 0 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (/.f64 p x) (/.f64 x p))) (/.f64 x p))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))) #s(literal 1/8 binary64))) (sqrt.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 x x)) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/4 binary64))) (sqrt.f64 (+.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))))) (pow.f64 (*.f64 p x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) p)) (/.f64 x #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 x (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal -1/2 binary64) x))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))) x)) (pow.f64 (*.f64 p x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 p (*.f64 p p))) (/.f64 #s(literal 1/8 binary64) (*.f64 x (*.f64 x x)))) x)) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/4 binary64) p)) (/.f64 x #s(literal 1/2 binary64))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) x)) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal -1/2 binary64) x))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
(*.f64 (sqrt.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
(*.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64)))) #s(literal 1/4 binary64)))
(+.f64 #s(literal 1/2 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(+.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 x x)) (+.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal -1/2 binary64))))
(fma.f64 x (/.f64 #s(literal 1/4 binary64) p) #s(literal 1/2 binary64))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) x) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 x p) #s(literal 1/2 binary64))
(fma.f64 (/.f64 #s(literal 1/4 binary64) p) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) #s(literal 1 binary64) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) x (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) p) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x) (/.f64 x (/.f64 p #s(literal 1/4 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 x x)) (-.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal 1/2 binary64)))) (+.f64 (/.f64 (*.f64 x (*.f64 x x)) (/.f64 (*.f64 p (*.f64 p p)) #s(literal 1/64 binary64))) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x (/.f64 p #s(literal 1/4 binary64))) #s(literal -1/2 binary64)) (+.f64 (*.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 p p)) (*.f64 x x)) #s(literal -1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 p x) (*.f64 x (+.f64 (*.f64 x #s(literal 1/4 binary64)) (*.f64 p #s(literal 1/2 binary64))))))
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(/.f64 (-.f64 (/.f64 x (/.f64 p (/.f64 x p))) #s(literal 4 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal 2 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))) (*.f64 (/.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x)) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x)) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))) (+.f64 (/.f64 #s(literal 8 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (/.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x)) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))) (*.f64 (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p))))) (+.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p))) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p))))))
(*.f64 (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (-.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 #s(literal 2 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))))))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (/.f64 x p)))
(*.f64 (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 8 binary64) (/.f64 (/.f64 x (/.f64 p (/.f64 x p))) (/.f64 p x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 x p) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (/.f64 x (/.f64 p (/.f64 x p))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 2 binary64) (/.f64 x p)))))
(exp.f64 (*.f64 (log.f64 (/.f64 p x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) p)) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(/.f64 x p)
(/.f64 (/.f64 x p) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) p))
(/.f64 #s(literal 1 binary64) (/.f64 p x))
(/.f64 (/.f64 #s(literal 1 binary64) p) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 x p)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) p) x))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) p)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (/.f64 p x) #s(literal -1 binary64))
(pow.f64 (/.f64 x p) #s(literal 1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) p))
(*.f64 (/.f64 x p) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) p))
(*.f64 #s(literal 1 binary64) (/.f64 x p))
(*.f64 (/.f64 #s(literal 1 binary64) p) x)
(*.f64 (/.f64 #s(literal 1 binary64) p) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x p)))
(*.f64 (/.f64 #s(literal -1 binary64) p) (-.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) p) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) p))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) p))
(*.f64 (pow.f64 (/.f64 p x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 p x) #s(literal -1/2 binary64)))

simplify307.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
5202×*-lowering-*.f32
5202×*-lowering-*.f64
2794×/-lowering-/.f32
2794×/-lowering-/.f64
2580×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03331968
19881796
235811747
379001747
082681747
Stop Event
1×iter limit
1×node limit
Counts
204 → 204
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 (+ (* 1/2 (/ (* x (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(+ (sqrt 1/2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (* 1/16 (/ 1 (pow p 3))) (* 1/8 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (* p (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (- (* 1/8 (/ 1 (pow p 2))) (* 1/64 (/ 1 (* (pow p 2) (pow (sqrt 1/2) 2))))) (sqrt 1/2))))) (* 1/8 (/ 1 (* p (sqrt 1/2)))))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 (* p (pow x 7)))) (/ (+ (* 8 (pow p 4)) (/ (* (pow p 3) x) (pow (sqrt -1) 2))) (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))
(* (sqrt (/ p x)) (sqrt -1))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/8 (/ x (* p (sqrt 1/2)))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(* -1 (/ x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(* -1 (/ x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(* -1 (/ x p))
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
(/ (- (* 2 p) x) p)
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
2
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(+ 2 (* -1 (/ x p)))
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
(/ x p)
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))
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(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (sqrt.f64 (/.f64 p x)) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))))
(+ (* -2 (* (sqrt (/ (pow p 5) (pow x 5))) (sqrt -1))) (+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (* (sqrt (/ p x)) (sqrt -1))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (-.f64 (sqrt.f64 (/.f64 p x)) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x))))) (*.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 (pow.f64 p #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (* p x))) (* (sqrt -1) (+ (* -1 (* (pow p 3) x)) (* 8 (pow p 4)))))) (* 2 (* (sqrt (* (pow p 5) x)) (sqrt -1)))) (pow x 3))) (* (sqrt (/ p x)) (sqrt -1))))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (sqrt.f64 (/.f64 p x)) (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p x)))) (-.f64 (*.f64 #s(literal 8 binary64) (*.f64 (*.f64 p p) (*.f64 p p))) (*.f64 x (*.f64 p (*.f64 p p))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (*.f64 x (pow.f64 p #s(literal 5 binary64))))))) (*.f64 x (*.f64 x x))))
(* (sqrt (/ p x)) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 p x)))
(+ (* -1 (* (sqrt (/ (pow p 3) (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ p x)) (sqrt -1)))
(-.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 p x))) (/.f64 (sqrt.f64 (/.f64 (*.f64 p (*.f64 p p)) (*.f64 x (*.f64 x x)))) (sqrt.f64 #s(literal -1 binary64))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -2 (* (sqrt (/ p (pow x 5))) (/ 1 (sqrt -1)))) (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 p x))) (*.f64 (/.f64 (*.f64 #s(literal 1 binary64) (*.f64 p p)) (sqrt.f64 #s(literal -1 binary64))) (-.f64 (*.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 p (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) p)))))
(+ (* (sqrt (/ p x)) (sqrt -1)) (* (pow p 2) (+ (* -1 (* (sqrt (/ 1 (* p (pow x 3)))) (/ 1 (sqrt -1)))) (* p (+ (* -2 (* (sqrt (/ 1 (* p (pow x 5)))) (/ 1 (sqrt -1)))) (* -1/2 (* (sqrt (* p x)) (/ (+ (/ 1 (* p (* (pow x 3) (pow (sqrt -1) 2)))) (* 8 (/ 1 (pow x 4)))) (sqrt -1)))))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 p x))) (*.f64 (*.f64 p p) (+.f64 (*.f64 p (*.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 x (*.f64 x x))) p) (/.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (*.f64 p x))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))) p))) (*.f64 p (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 p (pow.f64 x #s(literal 5 binary64))))) #s(literal -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 x (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2))))))
(+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (*.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))) (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) (/.f64 #s(literal -1/2 binary64) (*.f64 p (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))))
(+ (sqrt 1/2) (+ (* -1/2 (/ (+ (* -1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2))) (* -1/16 (pow x 3))) (* (pow p 3) (sqrt 1/2)))) (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* (pow p 2) (sqrt 1/2)))) (* 1/8 (/ x (* p (sqrt 1/2)))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) (*.f64 p p)) (/.f64 (*.f64 x (+.f64 (/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 (*.f64 x x) #s(literal -1/16 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 x (/.f64 #s(literal 1/8 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64))))))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1/8 (/ x (sqrt 1/2))) (* 1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (* p (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 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) p))
(+ (sqrt 1/2) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (/ (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 1/2 (/ (+ (* 1/16 (pow x 3)) (* 1/8 (/ (* x (+ (* -1/8 (pow x 2)) (* 1/64 (/ (pow x 2) (pow (sqrt 1/2) 2))))) (pow (sqrt 1/2) 2)))) (* p (sqrt 1/2))))) p)) (* -1/8 (/ x (sqrt 1/2)))) p)))
(-.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 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 (*.f64 x (+.f64 (*.f64 (*.f64 x x) #s(literal 1/16 binary64)) (/.f64 (*.f64 (+.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 (*.f64 x x) #s(literal 1/32 binary64))) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 p (sqrt.f64 #s(literal 1/2 binary64)))))) p)) p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* x (- (* 2 (/ 1 x)) (/ 1 p)))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (* x (- (/ 1 p) (* 2 (/ 1 x)))))
(*.f64 x (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal -1 binary64) p)))
(* -1 (/ x p))
(-.f64 #s(literal 0 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ (- (* 2 p) x) p)
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
2
#s(literal 2 binary64)
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(+ 2 (* -1 (/ x p)))
(-.f64 #s(literal 2 binary64) (/.f64 x p))
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)
(/ x p)
(/.f64 x p)

eval67.0ms (0.7%)

Compiler

Compiled 9882 to 1715 computations (82.6% saved)

prune72.0ms (0.7%)

Pruning

9 alts after pruning (0 fresh and 9 done)

PrunedKeptTotal
New5910591
Fresh000
Picked033
Done066
Total5919600
Accuracy
100.0%
Counts
600 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓51.6%
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
✓52.3%
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓29.8%
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
✓54.1%
(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 #s(literal 1/4 binary64) (/.f64 x p)))))))
✓49.0%
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
✓48.9%
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
✓53.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓26.8%
(neg.f64 (/.f64 p x))
✓38.8%
#s(literal 1 binary64)
Compiler

Compiled 229 to 127 computations (44.5% saved)

regimes62.0ms (0.6%)

Counts
15 → 2
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x 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 #s(literal 1/4 binary64) (/.f64 x p)))))))
(+.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.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 p p)) (*.f64 x x))))))))
Outputs
(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:

22.0ms
(+.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x)))))
5.0ms
x
5.0ms
p
5.0ms
(*.f64 (*.f64 #s(literal 4 binary64) p) p)
4.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 #s(literal 4 binary64) p) p) (*.f64 x x))))
Results
AccuracySegmentsBranch
79.3%1p
85.6%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))))
79.3%1(*.f64 (*.f64 #s(literal 4 binary64) p) p)
Compiler

Compiled 80 to 56 computations (30% saved)

regimes10.0ms (0.1%)

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

2 calls:

4.0ms
p
4.0ms
x
Results
AccuracySegmentsBranch
73.8%4p
71.9%3x
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts
10 → 4
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p))))
(sqrt.f64 (*.f64 x (+.f64 (/.f64 #s(literal 1/4 binary64) p) (/.f64 #s(literal 1/2 binary64) x))))
Outputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p))))
Calls

2 calls:

6.0ms
x
4.0ms
p
Results
AccuracySegmentsBranch
71.5%3x
73.4%4p
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts
7 → 4
Calls
Call 1
Inputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
(-.f64 #s(literal 0 binary64) (/.f64 p x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (/.f64 (/.f64 (*.f64 p p) x) x)))
(sqrt.f64 #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
Outputs
#s(literal 1 binary64)
(neg.f64 (/.f64 p x))
#s(literal 1 binary64)
(pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64))
Calls

1 calls:

3.0ms
p
Results
AccuracySegmentsBranch
73.2%4p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0%)

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

1 calls:

3.0ms
p
Results
AccuracySegmentsBranch
73.1%4p
Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes5.0ms (0%)

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

2 calls:

2.0ms
p
2.0ms
x
Results
AccuracySegmentsBranch
59.3%2x
42.8%3p
Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

2 calls:

1.0ms
x
1.0ms
p
Results
AccuracySegmentsBranch
38.8%1p
38.8%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.0
-2.686707122280172e-5
Compiler

Compiled 24 to 18 computations (25% saved)

bsearch88.0ms (0.9%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
19.0ms
1.2763517171873255e+20
4.588502315515582e+23
24.0ms
1.0935138108643122e-153
1.3035028191106508e-151
34.0ms
3.618812269111273e-280
3.8769665967010335e-276
Results
28.0ms243×0valid
23.0ms73×2valid
9.0ms39×1valid
5.0ms13×3valid
Compiler

Compiled 389 to 305 computations (21.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-mult: 17.0ms (35.2% of total)
ival-add: 11.0ms (22.7% of total)
ival-sqrt: 9.0ms (18.6% of total)
ival-div: 6.0ms (12.4% of total)
backward-pass: 5.0ms (10.3% of total)
const: 1.0ms (2.1% of total)

bsearch87.0ms (0.9%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
20.0ms
1.2763517171873255e+20
4.588502315515582e+23
24.0ms
1.0935138108643122e-153
1.3035028191106508e-151
34.0ms
3.618812269111273e-280
3.8769665967010335e-276
Results
24.0ms84×2valid
21.0ms224×0valid
10.0ms18×3valid
9.0ms42×1valid
Compiler

Compiled 309 to 257 computations (16.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 47.0ms
ival-mult: 21.0ms (44.8% of total)
ival-sqrt: 10.0ms (21.3% of total)
ival-add: 6.0ms (12.8% of total)
ival-div: 5.0ms (10.7% of total)
backward-pass: 4.0ms (8.5% of total)
const: 1.0ms (2.1% of total)

bsearch119.0ms (1.2%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
37.0ms
1.2763517171873255e+20
4.588502315515582e+23
25.0ms
1.0935138108643122e-153
1.3035028191106508e-151
47.0ms
3.618812269111273e-280
3.8769665967010335e-276
Results
45.0ms89×2valid
37.0ms219×0valid
9.0ms44×1valid
6.0ms16×3valid
Compiler

Compiled 301 to 249 computations (17.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 80.0ms
ival-mult: 36.0ms (45.2% of total)
ival-div: 22.0ms (27.6% of total)
ival-sqrt: 10.0ms (12.6% of total)
ival-add: 7.0ms (8.8% of total)
backward-pass: 4.0ms (5% of total)
const: 1.0ms (1.3% of total)

bsearch109.0ms (1.1%)

Algorithm
3×binary-search
Stop Event
1×narrow-enough
1×narrow-enough
1×narrow-enough
Steps
TimeLeftRight
24.0ms
1.2763517171873255e+20
4.588502315515582e+23
38.0ms
1.0935138108643122e-153
1.3035028191106508e-151
31.0ms
3.618812269111273e-280
3.8769665967010335e-276
Results
36.0ms223×0valid
26.0ms90×2valid
11.0ms37×1valid
7.0ms18×3valid
Compiler

Compiled 261 to 225 computations (13.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 48.0ms
ival-mult: 18.0ms (37.6% of total)
ival-add: 11.0ms (23% of total)
ival-sqrt: 10.0ms (20.9% of total)
ival-div: 5.0ms (10.5% of total)
backward-pass: 4.0ms (8.4% of total)
const: 1.0ms (2.1% of total)

bsearch30.0ms (0.3%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
27.0ms
-4.202394224787915e-140
-7.854935603733687e-146
Results
10.0ms107×0valid
5.0ms18×2valid
4.0ms19×1valid
Compiler

Compiled 123 to 99 computations (19.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 6.0ms (43.9% of total)
ival-sqrt: 3.0ms (22% of total)
ival-div: 2.0ms (14.6% of total)
ival-add: 2.0ms (14.6% of total)
backward-pass: 1.0ms (7.3% of total)
const: 0.0ms (0% of total)

simplify16.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
075153
198153
2109153
3116153
4119153
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 4311015068594995/159667224762777584932509817042947085285396100834836603320203779394976951349517125262796637239410856087147395747535399619517795039071487492859133743862786513625600453836086854121403017715549038974612268539563513919466464836409669631111108421475843532600569672550060483331388679618427520794230784 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7170528607160929/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 135000000000000000000 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 #s(literal 1/4 binary64) (/.f64 x p))))))))))
(if (<=.f64 p #s(literal 8781697361952767/9979201547673599058281863565184192830337256302177287707512736212186059459344820328924789827463178505446712234220962476219862189941967968303695858991424157101600028364755428382587688607221814935913266783722719619966654052275604351944444276342240220787535604534378780208211792476151720049639424 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 5307134659905293/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 36000000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
(if (<=.f64 p #s(literal 5488560851220479/2494800386918399764570465891296048207584314075544321926878184053046514864836205082231197456865794626361678058555240619054965547485491992075923964747856039275400007091188857095646922151805453733978316695930679904991663513068901087986111069085560055196883901133594695052052948119037930012409856 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7371020360979573/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 220000000000000000000 binary64)) #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64)))))
(if (<=.f64 p #s(literal 5588352866697215/39916806190694396233127454260736771321349025208709150830050944848744237837379281315699159309852714021786848936883849904879448759767871873214783435965696628406400113459021713530350754428887259743653067134890878479866616209102417407777777105368960883150142418137515120832847169904606880198557696 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6227038000955543/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 132000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal -5736115088042575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184 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 #s(literal 0 binary64) (/.f64 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 4311015068594995/159667224762777584932509817042947085285396100834836603320203779394976951349517125262796637239410856087147395747535399619517795039071487492859133743862786513625600453836086854121403017715549038974612268539563513919466464836409669631111108421475843532600569672550060483331388679618427520794230784 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7170528607160929/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 135000000000000000000 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 #s(literal 1/4 binary64) (/.f64 x p))))))))))
(if (<=.f64 p #s(literal 4311015068594995/159667224762777584932509817042947085285396100834836603320203779394976951349517125262796637239410856087147395747535399619517795039071487492859133743862786513625600453836086854121403017715549038974612268539563513919466464836409669631111108421475843532600569672550060483331388679618427520794230784 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7170528607160929/1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 135000000000000000000 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 #s(literal 1/4 binary64) (/.f64 x p))))))))))
(if (<=.f64 p #s(literal 8781697361952767/9979201547673599058281863565184192830337256302177287707512736212186059459344820328924789827463178505446712234220962476219862189941967968303695858991424157101600028364755428382587688607221814935913266783722719619966654052275604351944444276342240220787535604534378780208211792476151720049639424 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 5307134659905293/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 36000000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
(if (<=.f64 p #s(literal 8781697361952767/9979201547673599058281863565184192830337256302177287707512736212186059459344820328924789827463178505446712234220962476219862189941967968303695858991424157101600028364755428382587688607221814935913266783722719619966654052275604351944444276342240220787535604534378780208211792476151720049639424 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 5307134659905293/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 36000000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 x p)))))))
(if (<=.f64 p #s(literal 5488560851220479/2494800386918399764570465891296048207584314075544321926878184053046514864836205082231197456865794626361678058555240619054965547485491992075923964747856039275400007091188857095646922151805453733978316695930679904991663513068901087986111069085560055196883901133594695052052948119037930012409856 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7371020360979573/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 220000000000000000000 binary64)) #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64)))))
(if (<=.f64 p #s(literal 5488560851220479/2494800386918399764570465891296048207584314075544321926878184053046514864836205082231197456865794626361678058555240619054965547485491992075923964747856039275400007091188857095646922151805453733978316695930679904991663513068901087986111069085560055196883901133594695052052948119037930012409856 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 7371020360979573/58968162887836583628774290327941701420576894069006881693378223441337877537377325813845730080900918242835443359855685076558915384842574884883772410178635875682021801984 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 220000000000000000000 binary64)) #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) (/.f64 x p)) #s(literal -1/2 binary64)))))
(if (<=.f64 p #s(literal 5588352866697215/39916806190694396233127454260736771321349025208709150830050944848744237837379281315699159309852714021786848936883849904879448759767871873214783435965696628406400113459021713530350754428887259743653067134890878479866616209102417407777777105368960883150142418137515120832847169904606880198557696 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6227038000955543/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (neg.f64 (/.f64 p x)) (if (<=.f64 p #s(literal 132000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 p #s(literal 5588352866697215/39916806190694396233127454260736771321349025208709150830050944848744237837379281315699159309852714021786848936883849904879448759767871873214783435965696628406400113459021713530350754428887259743653067134890878479866616209102417407777777105368960883150142418137515120832847169904606880198557696 binary64)) #s(literal 1 binary64) (if (<=.f64 p #s(literal 6227038000955543/3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395326976 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) (if (<=.f64 p #s(literal 132000000000000000000 binary64)) #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 x #s(literal -5736115088042575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184 binary64)) (neg.f64 (/.f64 p x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal -5736115088042575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 p x)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.5s (16%)

Rules
6406×*-lowering-*.f32
6406×*-lowering-*.f64
6258×*-lowering-*.f32
6258×*-lowering-*.f64
4058×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01416
13016
24015
34515
44715
54815
04815
02495
113393
2110693
0847093
01364
16262
252362
3764362
0850262
07215562
123525312
083935312
03872233
112342164
244242125
087992125
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×saturated
Compiler

Compiled 616 to 399 computations (35.2% saved)

preprocess93.0ms (1%)

Compiler

Compiled 470 to 244 computations (48.1% saved)

end0.0ms (0%)

Profiling

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