Falkner and Boettcher, Equation (22+)

Time bar (total: 13.4s)

analyze7.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%50%0%0%50%0%3
50%25%25%0%0%50%0%4
75%37.5%12.5%0%0%50%0%5
87.5%43.7%6.2%0%0%50%0%6
93.8%46.9%3.1%0%0%50%0%7
96.9%48.4%1.6%0%0%50%0%8
98.4%49.2%0.8%0%0%50%0%9
99.2%49.6%0.4%0%0%50%0%10
99.6%49.8%0.2%0%0%50%0%11
99.8%49.9%0.1%0%0%50%0%12
Compiler

Compiled 22 to 17 computations (22.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (37.2% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-div: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.4s (10.7%)

Results
1.0s8256×0valid
1.0ms8×0invalid
Precisions
Click to see histograms. Total time spent on operations: 810.0ms
ival-mult: 380.0ms (46.9% of total)
ival-sub: 152.0ms (18.8% of total)
ival-pi: 92.0ms (11.4% of total)
ival-sqrt: 85.0ms (10.5% of total)
ival-div: 72.0ms (8.9% of total)
const: 25.0ms (3.1% of total)
backward-pass: 3.0ms (0.4% of total)
Bogosity

preprocess427.0ms (3.2%)

Algorithm
2×egg-herbie
Rules
4898×accelerator-lowering-fma.f32
4898×accelerator-lowering-fma.f64
2702×*-lowering-*.f32
2702×*-lowering-*.f64
1796×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02660
18355
220254
367454
4203254
5417554
6638254
7726554
01620
14118
210818
330918
488518
5148418
6282118
7564118
8772118
0823416
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Call 2
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ (/ 4/3 (- (PI) (* v (* (PI) v)))) (sqrt (+ 2 (* (* v v) -6))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(/ (/ 4/3 (- (PI) (* v (* (PI) v)))) (sqrt (+ 2 (* (* v v) -6))))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
(/ (/ 4/3 (- (* v (* (PI) v)) (PI))) (sqrt (+ 2 (* (* v v) -6))))
Symmetry

(abs v)

explain272.0ms (2%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(PI.f64)
00-0-(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
00-0-(-.f64 #s(literal 1 binary64) (*.f64 v v))
01(1.0794661700142657e-162)0-(*.f64 #s(literal 6 binary64) (*.f64 v v))
00-0-(-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))
00-0-#s(literal 2 binary64)
00-0-v
00-0-#s(literal 6 binary64)
00-0-(*.f64 #s(literal 3 binary64) (PI.f64))
00-0-(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
00-0-(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
00-0-(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
00-0-#s(literal 4 binary64)
00-0-#s(literal 1 binary64)
00-0-#s(literal 3 binary64)
00-0-(*.f64 v v)
Results
157.0ms512×0valid
Compiler

Compiled 195 to 122 computations (37.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 112.0ms
ival-mult: 63.0ms (56.4% of total)
ival-sub: 24.0ms (21.5% of total)
ival-sqrt: 12.0ms (10.7% of total)
const: 6.0ms (5.4% of total)
ival-div: 4.0ms (3.6% of total)
ival-pi: 3.0ms (2.7% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 19 to 15 computations (21.1% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶98.5%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Compiler

Compiled 40 to 31 computations (22.5% saved)

localize821.0ms (6.1%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(*.f64 #s(literal 3 binary64) (PI.f64))
✓cost-diff0
(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
✓cost-diff128
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓accuracy100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(*.f64 #s(literal 6 binary64) (*.f64 v v))
✓accuracy98.5%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Rules
4714×accelerator-lowering-fma.f32
4714×accelerator-lowering-fma.f64
2856×*-lowering-*.f32
2856×*-lowering-*.f64
2108×unsub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025142
157138
2144138
3393138
41088138
51710138
63449138
76356138
08130126
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
4
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
(* (* 3 (PI)) (- 1 (* v v)))
(* 3 (PI))
3
(PI)
(- 1 (* v v))
1
(* v v)
v
(sqrt (- 2 (* 6 (* v v))))
(- 2 (* 6 (* v v)))
2
(* 6 (* v v))
6
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/ 4/3 (PI))
4/3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
(* v (* v -6))
(* v -6)
-6
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
4
#s(literal 4 binary64)
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
(*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(* (* 3 (PI)) (- 1 (* v v)))
(*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(* 3 (PI))
(*.f64 #s(literal 3 binary64) (PI.f64))
3
#s(literal 3 binary64)
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(sqrt (- 2 (* 6 (* v v))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
(- 2 (* 6 (* v v)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
2
#s(literal 2 binary64)
(* 6 (* v v))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
6
#s(literal 6 binary64)
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(* v (* v -6))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
Results
382.0ms256×0valid
Compiler

Compiled 154 to 94 computations (39% saved)

Precisions
Click to see histograms. Total time spent on operations: 345.0ms
ival-mult: 292.0ms (84.7% of total)
ival-div: 16.0ms (4.6% of total)
ival-sub: 14.0ms (4.1% of total)
ival-sqrt: 10.0ms (2.9% of total)
const: 5.0ms (1.5% of total)
ival-add: 4.0ms (1.2% of total)
ival-pi: 3.0ms (0.9% of total)
backward-pass: 0.0ms (0% of total)

series27.0ms (0.2%)

Counts
11 → 96
Calls
Call 1
Inputs
#<alt (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (* 6 (* v v))>
#<alt (PI)>
#<alt (sqrt (- 2 (* 6 (* v v))))>
#<alt (/ 4/3 (PI))>
#<alt (* v (* v -6))>
#<alt (/ (/ 4/3 (PI)) (- 1 (* v v)))>
#<alt (/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))>
#<alt (* (* 3 (PI)) (- 1 (* v v)))>
#<alt (* 3 (PI))>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (/ 4/3 (PI))>
#<alt (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))>
#<alt (* -3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))>
#<alt (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* 3 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))>
#<alt (* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))>
#<alt (* 3 (PI))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* -3 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
#<alt (* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))>
Calls

24 calls:

TimeVariablePointExpression
5.0ms
v
@inf
(/ (/ 4/3 (PI)) (- 1 (* v v)))
2.0ms
v
@inf
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
2.0ms
v
@0
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
1.0ms
v
@inf
(* (* 3 (PI)) (- 1 (* v v)))
1.0ms
v
@inf
(* 6 (* v v))

rewrite762.0ms (5.7%)

Algorithm
1×batch-egg-rewrite
Rules
6750×accelerator-lowering-fma.f32
6750×accelerator-lowering-fma.f64
6596×*-lowering-*.f32
6596×*-lowering-*.f64
2822×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025101
114097
2110897
0917689
Stop Event
1×iter limit
1×node limit
Counts
11 → 983
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(* 6 (* v v))
(PI)
(sqrt (- 2 (* 6 (* v v))))
(/ 4/3 (PI))
(* v (* v -6))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
(* (* 3 (PI)) (- 1 (* v v)))
(* 3 (PI))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))) (/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(neg.f64 (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) #s(literal 4/3 binary64)) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (PI.f64)) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) #s(literal -4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (*.f64 #s(literal 4/3 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 #s(literal 4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/.f64 #s(literal -4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (*.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
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(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 #s(literal 3 binary64) (neg.f64 (*.f64 (*.f64 v v) (PI.f64)))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (*.f64 (PI.f64) (neg.f64 (*.f64 v v))) #s(literal 3 binary64)))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 #s(literal 3 binary64) (neg.f64 (*.f64 (*.f64 v v) (PI.f64)))))
(fma.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (*.f64 (PI.f64) (neg.f64 (*.f64 v v))) #s(literal 3 binary64)))
(/.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))))
(/.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))))) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 3 binary64) (PI.f64))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (neg.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (neg.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v)))))) (+.f64 (neg.f64 (*.f64 v v)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (PI.f64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 3 binary64) (PI.f64)))) (+.f64 (neg.f64 (*.f64 v v)) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (PI.f64))) (-.f64 (*.f64 (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64)))) (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64)))))))
(/.f64 (+.f64 (pow.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))) #s(literal 3 binary64))) (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (PI.f64))) (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v))))) (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v))))))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (PI.f64))) (*.f64 (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64))))) (-.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 (neg.f64 (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64)))))
(/.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (PI.f64))) (*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v)))))) (-.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (neg.f64 (*.f64 v v))))))
(*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)))
(*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (PI.f64) (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 #s(literal 3 binary64) (PI.f64)))
(*.f64 (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v)))))) (*.f64 #s(literal 3 binary64) (PI.f64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (*.f64 #s(literal 3 binary64) (PI.f64))))
(*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3 binary64))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)) (PI.f64))
(*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
(*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (*.f64 #s(literal 3 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 3 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)) #s(literal 1 binary64)) (PI.f64))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
(*.f64 (PI.f64) #s(literal 3 binary64))
(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64))))
(*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 3 binary64) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64)))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))

simplify1.0s (7.8%)

Algorithm
1×egg-herbie
Rules
16218×accelerator-lowering-fma.f32
16218×accelerator-lowering-fma.f64
6506×+-lowering-+.f64
6506×+-lowering-+.f32
5410×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02602434
18142103
232211987
083771919
Stop Event
1×iter limit
1×node limit
Counts
96 → 96
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(/ 4/3 (PI))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(* 3 (* (PI) (sqrt 2)))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(* 3 (PI))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* -3 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (*.f64 (*.f64 v v) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(*.f64 #s(literal 4/3 binary64) (+.f64 (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 27/16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))))) (*.f64 v v)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(+.f64 (*.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 135/16 binary64) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64))))) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))))) (/.f64 #s(literal 9/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (*.f64 (*.f64 v v) (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (PI.f64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v (*.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 4/3 binary64) (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v v))) (*.f64 v (*.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v v) (*.f64 v v)))))) (*.f64 v (*.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))))) (*.f64 v (*.f64 v v)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (PI.f64) (*.f64 v (*.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 4/3 binary64) (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
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(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 4/3 binary64) (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v v) (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* 3 (* (PI) (sqrt 2)))
(*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 3 (* (PI) (sqrt 2))) (* 3 (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2)))))))
(*.f64 #s(literal 3 binary64) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (*.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2)))))) (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))))))
(*.f64 #s(literal 3 binary64) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (+.f64 (*.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 v (*.f64 v (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64))))) (*.f64 v v))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 3 (+ (* -3 (/ (PI) (sqrt 2))) (* -1 (* (PI) (sqrt 2))))) (* (pow v 2) (+ (* 3 (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* 9/2 (/ (PI) (pow (sqrt 2) 3)))))) (* 3 (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* 3 (/ (PI) (sqrt 2))))))))))
(+.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 v v) (*.f64 #s(literal 3 binary64) (+.f64 (*.f64 (PI.f64) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (+.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/4 binary64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (PI.f64) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))))) (*.f64 v v))))))
(* -3 (* (pow v 3) (* (PI) (sqrt -6))))
(*.f64 (*.f64 (PI.f64) (*.f64 v (*.f64 v v))) (*.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal -3 binary64)))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2)))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (*.f64 #s(literal 3 binary64) (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v v)))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (*.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))))))))
(* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(*.f64 v (*.f64 (*.f64 v v) (+.f64 (*.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (*.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))))) (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (*.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (*.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64)))))))
(* 3 (* (pow v 3) (* (PI) (sqrt -6))))
(*.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v v)))) (sqrt.f64 #s(literal -6 binary64)))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))))))
(*.f64 (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (*.f64 #s(literal 3 binary64) (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4)))))))
(*.f64 (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (*.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -3 (* (PI) (sqrt -6))) (+ (* 3 (/ (+ (* -1 (/ (PI) (sqrt -6))) (* (PI) (sqrt -6))) (pow v 2))) (+ (* 3 (/ (+ (* -1/2 (/ (PI) (pow (sqrt -6) 3))) (* -1/2 (/ (PI) (pow (sqrt -6) 5)))) (pow v 6))) (* 3 (/ (+ (* 1/2 (/ (PI) (pow (sqrt -6) 3))) (/ (PI) (sqrt -6))) (pow v 4))))))))
(*.f64 (+.f64 (*.f64 #s(literal 3 binary64) (+.f64 (/.f64 (-.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v v)) (/.f64 (*.f64 #s(literal 11/12 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v))))) (+.f64 (*.f64 (PI.f64) (*.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (*.f64 #s(literal -3/2 binary64) (+.f64 (/.f64 (PI.f64) (*.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (pow.f64 v #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(* 3 (PI))
(*.f64 (PI.f64) #s(literal 3 binary64))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (+.f64 #s(literal 3 binary64) (*.f64 (*.f64 v v) #s(literal -3 binary64))))
(* -3 (* (pow v 2) (PI)))
(*.f64 v (*.f64 v (*.f64 (PI.f64) #s(literal -3 binary64))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(* -3 (* (pow v 2) (PI)))
(*.f64 v (*.f64 v (*.f64 (PI.f64) #s(literal -3 binary64))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(*.f64 (*.f64 v v) (*.f64 (PI.f64) (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) (*.f64 v v)))))

eval486.0ms (3.6%)

Compiler

Compiled 30809 to 19759 computations (35.9% saved)

prune176.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New113941143
Fresh000
Picked202
Done000
Total114141145
Accuracy
100.0%
Counts
1145 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶97.7%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
▶97.7%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 54 to 46 computations (14.8% saved)

localize1.1s (8.1%)

Algorithm
1×egg-herbie
Localize:

Found 32 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 (*.f64 v v) #s(literal -1 binary64))
✓cost-diff0
(/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
✓cost-diff0
(/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) #s(literal 3 binary64))
✓cost-diff0
(*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
✓cost-diff128
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
✓cost-diff0
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
✓accuracy99.7%
(*.f64 #s(literal 6 binary64) (*.f64 v v))
✓accuracy98.5%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓accuracy100.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
Rules
16858×accelerator-lowering-fma.f32
16858×accelerator-lowering-fma.f64
2664×*-lowering-*.f32
2664×*-lowering-*.f64
2380×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031154
162150
2129150
3257150
4677150
51491150
62597150
73919150
86030150
08137138
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
4/3
(/ (sqrt 1/2) (PI))
(sqrt 1/2)
1/2
(PI)
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
4
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(* (PI) 3)
3
(sqrt (- 2 (* 6 (* v v))))
(- 2 (* 6 (* v v)))
2
(* 6 (* v v))
6
(* v v)
v
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ 4/3 (PI))
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
(* v (* v -6))
(* v -6)
-6
(/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ -4/3 (+ (* v v) -1)) (PI))
(/ -4/3 (+ (* v v) -1))
-4/3
(+ (* v v) -1)
-1
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
4/3
#s(literal 4/3 binary64)
(/ (sqrt 1/2) (PI))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(PI)
(PI.f64)
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
4
#s(literal 4 binary64)
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(* (PI) 3)
(*.f64 (PI.f64) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(sqrt (- 2 (* 6 (* v v))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(- 2 (* 6 (* v v)))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* 6 (* v v))
(*.f64 #s(literal 6 binary64) (*.f64 v v))
6
#s(literal 6 binary64)
(* v v)
(*.f64 v v)
v
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
(* v (* v -6))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/ (/ -4/3 (+ (* v v) -1)) (PI))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/ -4/3 (+ (* v v) -1))
(/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
-4/3
#s(literal -4/3 binary64)
(+ (* v v) -1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))
-1
#s(literal -1 binary64)
Results
189.0ms256×0valid
Compiler

Compiled 189 to 124 computations (34.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 138.0ms
ival-mult: 69.0ms (50.1% of total)
ival-sqrt: 21.0ms (15.2% of total)
ival-div: 19.0ms (13.8% of total)
ival-add: 15.0ms (10.9% of total)
const: 7.0ms (5.1% of total)
ival-sub: 5.0ms (3.6% of total)
ival-pi: 1.0ms (0.7% of total)
backward-pass: 0.0ms (0% of total)

series24.0ms (0.2%)

Counts
16 → 120
Calls
Call 1
Inputs
#<alt (/ (sqrt 1/2) (PI))>
#<alt (PI)>
#<alt (sqrt 1/2)>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (* 6 (* v v))>
#<alt (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))>
#<alt (/ 4/3 (PI))>
#<alt (* v (* v -6))>
#<alt (/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ (/ -4/3 (+ (* v v) -1)) (PI))>
#<alt (/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (* (PI) 3)>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ -4/3 (+ (* v v) -1))>
#<alt (+ (* v v) -1)>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 6 (pow v 2))>
#<alt (* 3 (* (PI) (sqrt 2)))>
#<alt (+ (* -9 (/ (* (pow v 2) (PI)) (sqrt 2))) (* 3 (* (PI) (sqrt 2))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -9 (/ (PI) (sqrt 2))))))>
#<alt (+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -27/2 (/ (PI) (pow (sqrt 2) 3))))))))>
#<alt (* 3 (* v (* (PI) (sqrt -6))))>
#<alt (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (* -3 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (/ 4/3 (PI))>
#<alt (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* -4/3 (* (pow v 2) (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* -4/3 (* (pow v 2) (- (+ (* -1 (/ (sqrt 1/2) (PI))) (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* -4/3 (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* -4/3 (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* -4/3 (* (pow v 2) (- (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* -1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* -4/3 (- (+ (* -1 (/ (sqrt 1/2) (PI))) (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))))) (pow v 3)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 4/3>
#<alt (+ 4/3 (* 4/3 (pow v 2)))>
#<alt (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))>
#<alt (+ 4/3 (* (pow v 2) (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))))>
#<alt (/ -4/3 (pow v 2))>
#<alt (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (/ -4/3 (pow v 2))>
#<alt (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))>
#<alt -1>
#<alt (- (pow v 2) 1)>
#<alt (- (pow v 2) 1)>
#<alt (- (pow v 2) 1)>
#<alt (pow v 2)>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (pow v 2)>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
Calls

30 calls:

TimeVariablePointExpression
1.0ms
v
@0
(/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))
1.0ms
v
@0
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
1.0ms
v
@inf
(/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))
1.0ms
v
@inf
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
0.0ms
v
@inf
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))

rewrite683.0ms (5.1%)

Algorithm
1×batch-egg-rewrite
Rules
5700×*-lowering-*.f32
5700×*-lowering-*.f64
4826×accelerator-lowering-fma.f32
4826×accelerator-lowering-fma.f64
3526×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031116
1159112
21217112
09197103
Stop Event
1×iter limit
1×node limit
Counts
16 → 918
Calls
Call 1
Inputs
(/ (sqrt 1/2) (PI))
(PI)
(sqrt 1/2)
(* 4/3 (/ (sqrt 1/2) (PI)))
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(* 6 (* v v))
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(/ 4/3 (PI))
(* v (* v -6))
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ -4/3 (+ (* v v) -1)) (PI))
(/ (/ (/ -4/3 (+ (* v v) -1)) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(* (PI) 3)
(sqrt (+ 2 (* v (* v -6))))
(/ -4/3 (+ (* v v) -1))
(+ (* v v) -1)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) (PI.f64)))))
(exp.f64 (+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (PI.f64))) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (log.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (neg.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (PI.f64))))
(neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
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(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v)))) (neg.f64 (-.f64 #s(literal -1 binary64) (*.f64 v v))))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64)))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64)))) (*.f64 (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64)))))))
(/.f64 (*.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 (*.f64 v v) (*.f64 v v)))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64)))))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal 1 binary64))))))
(*.f64 (+.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal 1 binary64))))
(*.f64 (+.f64 v #s(literal 1 binary64)) (+.f64 v #s(literal -1 binary64)))
(*.f64 (+.f64 v #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) v)))
(*.f64 (+.f64 v #s(literal -1 binary64)) (+.f64 v #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 (*.f64 v v) (*.f64 v v)))))))
(*.f64 (+.f64 (neg.f64 (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 v v))))
(*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) v)) (-.f64 #s(literal 1 binary64) v))
(*.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) v))) (+.f64 v #s(literal -1 binary64)))

simplify764.0ms (5.7%)

Algorithm
1×egg-herbie
Rules
11378×accelerator-lowering-fma.f32
11378×accelerator-lowering-fma.f64
5456×*-lowering-*.f32
5456×*-lowering-*.f64
4552×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03012527
19332162
234162084
082172000
Stop Event
1×iter limit
1×node limit
Counts
120 → 120
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 6 (pow v 2))
(* 3 (* (PI) (sqrt 2)))
(+ (* -9 (/ (* (pow v 2) (PI)) (sqrt 2))) (* 3 (* (PI) (sqrt 2))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -9 (/ (PI) (sqrt 2))))))
(+ (* 3 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* -9 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -81/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -27/2 (/ (PI) (pow (sqrt 2) 3))))))))
(* 3 (* v (* (PI) (sqrt -6))))
(* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))
(* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))
(* -3 (* v (* (PI) (sqrt -6))))
(* -1 (* v (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6))))))))
(* -1 (* v (+ (* -3/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 3/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* 3 (* (PI) (sqrt -6))) (* 3 (/ (PI) (* (pow v 2) (sqrt -6)))))))))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/ 4/3 (PI))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* -4/3 (* (pow v 2) (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* -4/3 (* (pow v 2) (- (+ (* -1 (/ (sqrt 1/2) (PI))) (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* -4/3 (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* -4/3 (- (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* -4/3 (* (pow v 2) (- (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* -1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* -4/3 (- (+ (* -1 (/ (sqrt 1/2) (PI))) (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2))))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6))) (+ (* -4/3 (/ (- (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 4))) (* -4/3 (/ (- (/ (sqrt -1/6) (PI)) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))))) (pow v 3)))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
4/3
(+ 4/3 (* 4/3 (pow v 2)))
(+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))
(+ 4/3 (* (pow v 2) (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))))
(/ -4/3 (pow v 2))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
(/ -4/3 (pow v 2))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
-1
(- (pow v 2) 1)
(- (pow v 2) 1)
(- (pow v 2) 1)
(pow v 2)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(pow v 2)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
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(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))
(pow v 2)
(*.f64 v v)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v))))

eval405.0ms (3%)

Compiler

Compiled 27109 to 17811 computations (34.3% saved)

prune299.0ms (2.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New128321285
Fresh000
Picked044
Done000
Total128361289
Accuracy
100.0%
Counts
1289 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.2%
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.7%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓97.7%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 76 to 66 computations (13.2% saved)

localize137.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4 binary64) (PI.f64))
✓cost-diff128
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64))
✓cost-diff128
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
Rules
64×/-lowering-/.f32
64×/-lowering-/.f64
58×*-lowering-*.f32
58×*-lowering-*.f64
40×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01761
12859
24259
35759
47459
58459
68459
08456
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (/ 4/3 (PI)) (sqrt 2))
(/ 4/3 (PI))
4/3
(PI)
(sqrt 2)
2
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4 (PI)) 3)
(/ 4 (PI))
4
3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
(* v (* v -6))
v
(* v -6)
-6
Outputs
(/ (/ 4/3 (PI)) (sqrt 2))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(PI)
(PI.f64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
(/ (/ 4 (PI)) 3)
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
3
#s(literal 3 binary64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
Results
72.0ms256×0valid
Compiler

Compiled 67 to 51 computations (23.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-mult: 17.0ms (34.9% of total)
ival-div: 16.0ms (32.9% of total)
ival-sqrt: 8.0ms (16.4% of total)
ival-add: 4.0ms (8.2% of total)
const: 3.0ms (6.2% of total)
ival-pi: 1.0ms (2.1% of total)
backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts
9 → 36
Calls
Call 1
Inputs
#<alt (/ 4/3 (PI))>
#<alt (PI)>
#<alt (sqrt 2)>
#<alt (/ (/ 4/3 (PI)) (sqrt 2))>
#<alt (* v (* v -6))>
#<alt (/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ (/ 4 (PI)) 3)>
#<alt (/ 4 (PI))>
Outputs
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
Calls

9 calls:

TimeVariablePointExpression
0.0ms
v
@0
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@inf
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@-inf
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@0
(* v (* v -6))
0.0ms
v
@0
(sqrt (+ 2 (* v (* v -6))))

rewrite625.0ms (4.7%)

Algorithm
1×batch-egg-rewrite
Rules
4592×*-lowering-*.f32
4592×*-lowering-*.f64
2722×/-lowering-/.f32
2722×/-lowering-/.f64
2588×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01745
19643
266843
3570143
0817441
Stop Event
1×iter limit
1×node limit
Counts
9 → 715
Calls
Call 1
Inputs
(/ 4/3 (PI))
(PI)
(sqrt 2)
(/ (/ 4/3 (PI)) (sqrt 2))
(* v (* v -6))
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
(sqrt (+ 2 (* v (* v -6))))
(/ (/ 4 (PI)) 3)
(/ 4 (PI))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (PI.f64)))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)))
(neg.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal 1 binary64)))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) #s(literal 3 binary64)))
(/.f64 #s(literal 4 binary64) (neg.f64 (*.f64 (PI.f64) #s(literal -3 binary64))))
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal -3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))))
(/.f64 #s(literal -4/3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) #s(literal -3 binary64))
(/.f64 #s(literal -4 binary64) (*.f64 (PI.f64) #s(literal -3 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 3/4 binary64))
(/.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) #s(literal -3/4 binary64)))
(/.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal -1/3 binary64) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 #s(literal 3 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) #s(literal 4/3 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 4/3 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)))
(/.f64 (/.f64 #s(literal 1/3 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 #s(literal 4 binary64) (/.f64 #s(literal 1/3 binary64) (PI.f64)))
(*.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1/3 binary64)))
(*.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1/3 binary64))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 #s(literal -4/3 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) #s(literal -1/3 binary64))
(*.f64 #s(literal -4 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -3 binary64)))
(*.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal -3 binary64))))
(*.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1/3 binary64)))
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(/.f64 (/.f64 #s(literal 1/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)))
(/.f64 (/.f64 #s(literal 1/3 binary64) (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 #s(literal 4 binary64) (/.f64 #s(literal 1/3 binary64) (PI.f64)))
(*.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1/3 binary64)))
(*.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1/3 binary64))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 #s(literal -4/3 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) #s(literal -1/3 binary64))
(*.f64 #s(literal -4 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -3 binary64)))
(*.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal -3 binary64))))
(*.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1/3 binary64)))
(*.f64 #s(literal -4 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 3 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 4/3 binary64))
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4/3 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) #s(literal 4 binary64))
(*.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -4/3 binary64))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal -1/3 binary64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -4 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) #s(literal 4 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(neg.f64 (/.f64 #s(literal -4 binary64) (PI.f64)))
(/.f64 #s(literal 4 binary64) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))))
(/.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1/4 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal -4 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)))
(/.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/4 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4 binary64) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) #s(literal 4 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) #s(literal 4 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal -4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal -4 binary64) (sqrt.f64 (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 2/9 binary64))) (pow.f64 (PI.f64) #s(literal 1/9 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(pow.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64))
(pow.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))) #s(literal -1 binary64))
(*.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 #s(literal -4 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 #s(literal -4 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 4 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -4 binary64))
(*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (PI.f64) #s(literal -1/3 binary64)))
(*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -2/3 binary64)) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal -1/2 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1/2 binary64)))

simplify939.0ms (7%)

Algorithm
1×egg-herbie
Rules
17246×accelerator-lowering-fma.f32
17246×accelerator-lowering-fma.f64
5918×*-lowering-*.f32
5918×*-lowering-*.f64
2680×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0145677
1412567
21399546
34175531
08113508
Stop Event
1×iter limit
1×node limit
Counts
36 → 36
Calls
Call 1
Inputs
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
Outputs
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* 4/3 (/ (sqrt 1/2) (PI)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 (*.f64 v v) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 (*.f64 v v) #s(literal 9/4 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (*.f64 v (*.f64 v (/.f64 #s(literal 135/16 binary64) (PI.f64)))) (/.f64 #s(literal 27/8 binary64) (PI.f64)))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) v)
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (+.f64 (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -4/3 binary64) (*.f64 v (PI.f64))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))) (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))))) v)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (-.f64 (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 v v)))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 v (*.f64 v (+.f64 (/.f64 (*.f64 v (*.f64 v #s(literal -27/2 binary64))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(+.f64 (*.f64 v (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))) v))
(* -1 (* v (sqrt -6)))
(*.f64 (sqrt.f64 #s(literal -6 binary64)) (neg.f64 v))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 (/.f64 #s(literal -1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(+.f64 (/.f64 #s(literal -1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (-.f64 (/.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(+.f64 (/.f64 #s(literal -1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (neg.f64 v) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))))))

eval205.0ms (1.5%)

Compiler

Compiled 12419 to 9627 computations (22.5% saved)

prune144.0ms (1.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New8173820
Fresh000
Picked112
Done134
Total8197826
Accuracy
100.0%
Counts
826 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶97.7%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶99.2%
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))) #s(literal 3 binary64))
▶99.2%
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
✓99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.7%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 90 to 78 computations (13.3% saved)

localize338.0ms (2.5%)

Algorithm
1×egg-herbie
Localize:

Found 24 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
✓cost-diff0
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))
✓cost-diff0
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64)))
✓cost-diff128
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))) #s(literal 3 binary64))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff128
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓cost-diff128
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))
✓accuracy100.0%
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64)))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy98.5%
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓accuracy98.4%
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
Rules
74×*-lowering-*.f32
74×*-lowering-*.f64
60×/-lowering-/.f32
60×/-lowering-/.f64
32×associate-/r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021122
138122
254122
368122
470122
578122
689122
797122
899122
099112
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ (/ 4 (* 3 (sqrt (+ 2 (* v (* v -6)))))) (PI))
(/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))
4
(* 3 (sqrt (+ 2 (* v (* v -6)))))
3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
(PI)
(/ (/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI))) 3)
(/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))
(* (sqrt (+ 2 (* v (* v -6)))) (PI))
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(pow (+ 2 (* v (* v -6))) -1/2)
-1/2
(/ (PI) 4/3)
4/3
Outputs
(/ (/ 4 (* 3 (sqrt (+ 2 (* v (* v -6)))))) (PI))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))) (PI.f64))
(/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
4
#s(literal 4 binary64)
(* 3 (sqrt (+ 2 (* v (* v -6)))))
(*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
3
#s(literal 3 binary64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(PI)
(PI.f64)
(/ (/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI))) 3)
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))) (PI.f64))
(/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))) (PI.f64)))
(* (sqrt (+ 2 (* v (* v -6)))) (PI))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))) (PI.f64))
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(pow (+ 2 (* v (* v -6))) -1/2)
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(/ (PI) 4/3)
(/.f64 (PI.f64) #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
Results
213.0ms256×0valid
Compiler

Compiled 178 to 132 computations (25.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 167.0ms
ival-mult: 74.0ms (44.2% of total)
ival-div: 28.0ms (16.7% of total)
ival-sqrt: 20.0ms (11.9% of total)
ival-add: 18.0ms (10.8% of total)
ival-pow: 14.0ms (8.4% of total)
const: 7.0ms (4.2% of total)
ival-pi: 5.0ms (3% of total)
backward-pass: 0.0ms (0% of total)

series24.0ms (0.2%)

Counts
12 → 132
Calls
Call 1
Inputs
#<alt (/ (/ 4 (* 3 (sqrt (+ 2 (* v (* v -6)))))) (PI))>
#<alt (/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))>
#<alt (* 3 (sqrt (+ 2 (* v (* v -6)))))>
#<alt (* v (* v -6))>
#<alt (/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))>
#<alt (* (sqrt (+ 2 (* v (* v -6)))) (PI))>
#<alt (PI)>
#<alt (/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))>
#<alt (pow (+ 2 (* v (* v -6))) -1/2)>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ (/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI))) 3)>
#<alt (+ 2 (* v (* v -6)))>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* 4/3 (sqrt 1/2))>
#<alt (+ (* 4/3 (sqrt 1/2)) (/ (pow v 2) (sqrt 1/2)))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (/ 1 (sqrt 1/2)))))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (/ 1 (sqrt 1/2)))))>
#<alt (* 4/3 (/ (sqrt -1/6) v))>
#<alt (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) v))>
#<alt (* -1 (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* 3 (sqrt 2))>
#<alt (+ (* -9 (/ (pow v 2) (sqrt 2))) (* 3 (sqrt 2)))>
#<alt (+ (* 3 (sqrt 2)) (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 9 (/ 1 (sqrt 2))))))>
#<alt (+ (* 3 (sqrt 2)) (* (pow v 2) (- (* (pow v 2) (- (* -81/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 27/2 (/ 1 (pow (sqrt 2) 3))))) (* 9 (/ 1 (sqrt 2))))))>
#<alt (* 3 (* v (sqrt -6)))>
#<alt (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -3 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 4 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 3 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (* 4 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 3 (/ 1 (* (PI) (sqrt 1/2)))))))>
#<alt (+ (* 4 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (* 3 (/ 1 (* (PI) (sqrt 1/2)))))))>
#<alt (* 4 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4 (/ (sqrt -1/6) (PI))) (* 1/9 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI)))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI))))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4 (/ (sqrt -1/6) (PI))) (* 1/9 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI)))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI))))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* (PI) (sqrt 2))>
#<alt (+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))>
#<alt (* v (* (PI) (sqrt -6)))>
#<alt (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (/ (sqrt -1/6) v)>
#<alt (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (* -1 (/ (sqrt -1/6) v))>
#<alt (* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
Calls

33 calls:

TimeVariablePointExpression
2.0ms
v
@inf
(/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))
1.0ms
v
@-inf
(* (sqrt (+ 2 (* v (* v -6)))) (PI))
1.0ms
v
@inf
(/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))
1.0ms
v
@0
(/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))
0.0ms
v
@0
(/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))

rewrite613.0ms (4.6%)

Algorithm
1×batch-egg-rewrite
Rules
4886×*-lowering-*.f32
4886×*-lowering-*.f64
3206×/-lowering-/.f32
3206×/-lowering-/.f64
2050×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021108
1120108
2787108
36797108
0835898
Stop Event
1×iter limit
1×node limit
Counts
12 → 1172
Calls
Call 1
Inputs
(/ (/ 4 (* 3 (sqrt (+ 2 (* v (* v -6)))))) (PI))
(/ 4 (* 3 (sqrt (+ 2 (* v (* v -6))))))
(* 3 (sqrt (+ 2 (* v (* v -6)))))
(* v (* v -6))
(/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI)))
(* (sqrt (+ 2 (* v (* v -6)))) (PI))
(PI)
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(pow (+ 2 (* v (* v -6))) -1/2)
(sqrt (+ 2 (* v (* v -6))))
(/ (/ 4 (* (sqrt (+ 2 (* v (* v -6)))) (PI))) 3)
(+ 2 (* v (* v -6)))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal 4/3 binary64) (PI.f64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4/3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(neg.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))) #s(literal 1/3 binary64)))
(neg.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal -4 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(neg.f64 (/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 4 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64))))
(/.f64 #s(literal 4 binary64) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (*.f64 #s(literal -3 binary64) (PI.f64)))))
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal -3 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 3/4 binary64)) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)))) #s(literal 3 binary64))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal 4/3 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 3/4 binary64)) (PI.f64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64)) (/.f64 #s(literal -4 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (/.f64 #s(literal 4 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) #s(literal 3/4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
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(*.f64 (/.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal -36 binary64))) (-.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal -216 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))

simplify703.0ms (5.3%)

Algorithm
1×egg-herbie
Rules
11120×accelerator-lowering-fma.f32
11120×accelerator-lowering-fma.f64
5798×*-lowering-*.f32
5798×*-lowering-*.f64
3816×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03393116
110862472
237252418
087272291
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* 4/3 (sqrt 1/2))
(+ (* 4/3 (sqrt 1/2)) (/ (pow v 2) (sqrt 1/2)))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (/ 1 (sqrt 1/2)))))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (/ 1 (sqrt 1/2)))))
(* 4/3 (/ (sqrt -1/6) v))
(/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)
(* -4/3 (/ (sqrt -1/6) v))
(* -1 (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))
(* 3 (sqrt 2))
(+ (* -9 (/ (pow v 2) (sqrt 2))) (* 3 (sqrt 2)))
(+ (* 3 (sqrt 2)) (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 9 (/ 1 (sqrt 2))))))
(+ (* 3 (sqrt 2)) (* (pow v 2) (- (* (pow v 2) (- (* -81/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 27/2 (/ 1 (pow (sqrt 2) 3))))) (* 9 (/ 1 (sqrt 2))))))
(* 3 (* v (sqrt -6)))
(* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6))))))
(* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -3 (* v (sqrt -6)))
(* -1 (* v (+ (* 3 (sqrt -6)) (* 3 (/ 1 (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (- (+ (* 3 (sqrt -6)) (/ 3 (* (pow v 2) (sqrt -6)))) (/ 3/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (* 3 (sqrt -6)) (+ (* 3/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))) (/ 3 (* (pow v 2) (sqrt -6))))) (* 3/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 4 (/ (sqrt 1/2) (PI)))
(+ (* 3 (/ (pow v 2) (* (PI) (sqrt 1/2)))) (* 4 (/ (sqrt 1/2) (PI))))
(+ (* 4 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 3 (/ 1 (* (PI) (sqrt 1/2)))))))
(+ (* 4 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (* 3 (/ 1 (* (PI) (sqrt 1/2)))))))
(* 4 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4 (/ (sqrt -1/6) (PI))) (* 1/9 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI)))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI))))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4 (/ (sqrt -1/6) (PI))) (* 1/9 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI)))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4 (/ (sqrt -1/6) (PI))))) (/ 1/9 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* (PI) (sqrt 2))
(+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))
(* v (* (PI) (sqrt -6)))
(* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (* (PI) (sqrt -6))))
(* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(sqrt 1/2)
(+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))
(/ (sqrt -1/6) v)
(/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(* -1 (/ (sqrt -1/6) v))
(* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (/.f64 (*.f64 v v) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
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(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (*.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))))) #s(literal -1 binary64)))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 #s(literal -6 binary64) (*.f64 (*.f64 v v) (*.f64 v v))))))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (/.f64 (*.f64 v v) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (/.f64 #s(literal 9/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 (*.f64 v v) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (*.f64 #s(literal 135/16 binary64) (/.f64 (*.f64 v v) (PI.f64))) (/.f64 #s(literal 27/8 binary64) (PI.f64))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) v)
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal -1/6 binary64)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (+.f64 (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (*.f64 v v) (*.f64 v v)))) (PI.f64)) (/.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (*.f64 (PI.f64) v))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (-.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (PI.f64) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal -1/6 binary64))))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)))) (-.f64 #s(literal 0 binary64) v))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 v (*.f64 v (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))

eval616.0ms (4.6%)

Compiler

Compiled 36372 to 25703 computations (29.3% saved)

prune247.0ms (1.8%)

Pruning

7 alts after pruning (0 fresh and 7 done)

PrunedKeptTotal
New166301663
Fresh000
Picked033
Done044
Total166371670
Accuracy
100.0%
Counts
1670 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓97.7%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓99.2%
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))) #s(literal 3 binary64))
✓99.2%
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
✓99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓99.2%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.7%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 240 to 190 computations (20.8% saved)

regimes8.0ms (0.1%)

Counts
11 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))) #s(literal 3 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Outputs
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Calls

4 calls:

4.0ms
v
2.0ms
(*.f64 v v)
1.0ms
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
1.0ms
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
100.0%1(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
100.0%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes5.0ms (0%)

Counts
8 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (PI.f64))) #s(literal 3 binary64))
(/.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Outputs
(/.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (PI.f64))
Calls

2 calls:

3.0ms
v
1.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.2%1v
99.2%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes4.0ms (0%)

Counts
5 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Outputs
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Calls

2 calls:

2.0ms
v
1.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.2%1v
99.2%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
Outputs
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
Calls

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
99.2%1v
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Outputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Calls

1 calls:

0.0ms
v
Results
AccuracySegmentsBranch
97.7%1v
Compiler

Compiled 2 to 1 computations (50% saved)

soundness1.0ms (0%)

Stop Event
1×done
Compiler

Compiled 57 to 45 computations (21.1% saved)

preprocess43.0ms (0.3%)

Remove

(abs v)

Compiler

Compiled 384 to 302 computations (21.4% saved)

end0.0ms (0%)

Profiling

Loading profile data...