Falkner and Boettcher, Equation (22+)

Time bar (total: 10.0s)

analyze5.0ms (0%)

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 (39.6% 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)

sample2.5s (25.3%)

Results
1.7s8256×0valid
1.0ms8×0invalid
Precisions
Click to see histograms. Total time spent on operations: 1.3s
ival-mult: 496.0ms (38.6% of total)
ival-sqrt: 294.0ms (22.9% of total)
ival-sub: 259.0ms (20.1% of total)
ival-pi: 144.0ms (11.2% of total)
ival-div: 67.0ms (5.2% of total)
const: 23.0ms (1.8% of total)
backward-pass: 3.0ms (0.2% of total)
Bogosity

preprocess348.0ms (3.5%)

Algorithm
2×egg-herbie
Rules
2664×fma-define
2636×*-lowering-*.f32
2636×*-lowering-*.f64
1670×+-lowering-+.f64
1670×+-lowering-+.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02660
18355
220248
370548
4224248
5592248
01620
14118
210816
333116
499416
5186716
6469216
0810416
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 (fnmsub v v -1)) (PI)) (sqrt (fnmsub v (* v 6) -2)))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(/ (/ (/ 4/3 (fnmsub v v -1)) (PI)) (sqrt (fnmsub v (* v 6) -2)))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
(/ (/ 4/3 (* (PI) (fmsub v v 1))) (sqrt (fnmsub v (* v 6) -2)))
Symmetry

(abs v)

explain188.0ms (1.9%)

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))
00-0-(*.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
123.0ms512×0valid
Compiler

Compiled 195 to 50 computations (74.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 19.0ms (53% of total)
ival-sub: 5.0ms (14% of total)
ival-sqrt: 4.0ms (11.2% of total)
ival-div: 3.0ms (8.4% of total)
ival-pi: 2.0ms (5.6% of total)
const: 2.0ms (5.6% 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)

simplify180.0ms (1.8%)

Algorithm
1×egg-herbie
Localize:

Found 8 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))))))
Rules
2798×*-lowering-*.f32
2798×*-lowering-*.f64
1826×fnmadd-define
1696×+-lowering-+.f64
1696×+-lowering-+.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025154
157143
2147136
3419136
41225136
52142136
65133136
08205136
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
(PI)
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* 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 #s(literal 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))))))))
(* (* 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)
(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 (* 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))))
2
#s(literal 2 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)

localize131.0ms (1.3%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓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%
(*.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 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy99.8%
(*.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))))))
Results
98.0ms256×0valid
Compiler

Compiled 154 to 26 computations (83.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 65.0ms
ival-mult: 45.0ms (68.8% of total)
ival-div: 6.0ms (9.2% of total)
ival-sqrt: 4.0ms (6.1% of total)
...c/correct-round.rkt:119:19: 4.0ms (6.1% of total)
ival-sub: 3.0ms (4.6% of total)
ival-pi: 1.0ms (1.5% of total)
ival-add: 1.0ms (1.5% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series12.0ms (0.1%)

Counts
10 → 84
Calls
Call 1
Inputs
#<alt (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))>
#<alt (* (* 3 (PI)) (- 1 (* v v)))>
#<alt (* 3 (PI))>
#<alt (/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ (/ 4/3 (PI)) (- 1 (* v v)))>
#<alt (/ 4/3 (PI))>
#<alt (PI)>
#<alt (* 6 (* v v))>
#<alt (* v (* v -6))>
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 (* 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)))))>
#<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 (/ 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 (* 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 (* -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))>
Calls

21 calls:

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

rewrite413.0ms (4.1%)

Algorithm
1×batch-egg-rewrite
Rules
3842×*-lowering-*.f32
3842×*-lowering-*.f64
2924×/-lowering-/.f32
2924×/-lowering-/.f64
1418×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02593
114486
2114381
0855281
Stop Event
1×iter limit
1×node limit
Counts
10 → 626
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
(* (* 3 (PI)) (- 1 (* v v)))
(* 3 (PI))
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/ 4/3 (PI))
(PI)
(* 6 (* v v))
(* v (* v -6))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 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 (*.f64 v v) #s(literal -6 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 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 (*.f64 v v) #s(literal -6 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (/.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 (*.f64 v 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 (*.f64 v 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 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))))
(neg.f64 (*.f64 #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 (*.f64 v v) #s(literal -6 binary64)))))))
(neg.f64 (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 4/3 binary64) (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 (*.f64 v v) #s(literal -6 binary64)))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(neg.f64 (/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (PI.f64))) #s(literal -4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 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 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64))))) (PI.f64)))
(/.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 #s(literal 1 binary64) (*.f64 v v)))))
(/.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 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (neg.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (PI.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 (*.f64 v 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 (*.f64 v 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 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (PI.f64))))
(/.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 (*.f64 v 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 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64))))))
(/.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)))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal -4/3 binary64) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
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(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (exp.f64 (PI.f64)))))
(+.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64))) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(expm1.f64 (log1p.f64 (PI.f64)))
(neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))
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(log1p.f64 (expm1.f64 (PI.f64)))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 1/3 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(*.f64 (PI.f64) #s(literal 1 binary64))
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 #s(literal 1 binary64) (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
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(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
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(*.f64 (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1/3 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64))))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))))
(*.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (cbrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
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(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
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(*.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(*.f64 #s(literal 6 binary64) (*.f64 v v))
(*.f64 #s(literal -6 binary64) (*.f64 v (-.f64 #s(literal 0 binary64) v)))
(*.f64 (*.f64 v #s(literal -6 binary64)) (-.f64 #s(literal 0 binary64) v))
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(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal -6 binary64)))
(*.f64 (*.f64 v #s(literal 6 binary64)) v)
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(-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))
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(*.f64 #s(literal -6 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal -6 binary64)) v)
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(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal 6 binary64)))
(*.f64 (*.f64 v #s(literal 6 binary64)) (-.f64 #s(literal 0 binary64) v))
(*.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))

simplify288.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
5870×+-lowering-+.f64
5870×+-lowering-+.f32
4276×*-lowering-*.f32
4276×*-lowering-*.f64
1316×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02192144
17441807
232711685
084211685
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
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)))
(* 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)))))
(* 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)))
(/ 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))
(* 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))
(* -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))
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 (* (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) #s(literal 3/4 binary64)) (*.f64 (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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.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) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (*.f64 v v))))
(+ (* 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 v v) (*.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 (+.f64 (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 27/8 binary64) (PI.f64)) (/.f64 #s(literal 135/16 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) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (*.f64 v v)))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 3/4 binary64)) (*.f64 (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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.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))))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 (*.f64 v v) (*.f64 v v))))))) (*.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)))
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(* -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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.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))))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 (*.f64 v v) (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v v))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (/.f64 (*.f64 v v) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 v v)))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -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))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -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))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* 6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 6 binary64))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))

eval91.0ms (0.9%)

Compiler

Compiled 19793 to 2060 computations (89.6% saved)

prune74.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New7647771
Fresh000
Picked202
Done000
Total7667773
Accuracy
100.0%
Counts
773 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (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) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶99.4%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶97.8%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
▶97.8%
(/.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))))))
▶99.3%
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))))
▶100.0%
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
Compiler

Compiled 204 to 168 computations (17.6% saved)

simplify160.0ms (1.6%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓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
(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
(*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓cost-diff128
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓cost-diff0
(*.f64 (*.f64 v v) #s(literal -6 binary64))
✓cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
✓cost-diff0
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))
✓cost-diff0
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
Rules
2558×*-lowering-*.f32
2558×*-lowering-*.f64
1564×/-lowering-/.f32
1564×/-lowering-/.f64
1402×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038209
180197
2152193
3266193
4525193
5818193
61756193
75296193
08238193
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* (pow (+ 2 (* (* v v) -6)) -1/2) (/ 4/3 (* (PI) (- 1 (* v v)))))
(pow (+ 2 (* (* v v) -6)) -1/2)
(+ 2 (* (* v v) -6))
2
(* (* v v) -6)
(* v v)
v
-6
-1/2
(/ 4/3 (* (PI) (- 1 (* v v))))
4/3
(* (PI) (- 1 (* v v)))
(PI)
(- 1 (* v v))
1
(/ (* 4/3 (sqrt 1/2)) (PI))
(* 4/3 (sqrt 1/2))
4/3
(sqrt 1/2)
1/2
(PI)
(/ 4 (* (PI) (* 3 (sqrt 2))))
4
(* (PI) (* 3 (sqrt 2)))
(PI)
(* 3 (sqrt 2))
3
(sqrt 2)
2
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ 4/3 (PI))
4/3
(PI)
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
4
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(* (PI) 3)
(PI)
3
(sqrt (- 2 (* 6 (* v v))))
(- 2 (* 6 (* v v)))
2
(* 6 (* v v))
6
(* v v)
v
Outputs
(* (pow (+ 2 (* (* v v) -6)) -1/2) (/ 4/3 (* (PI) (- 1 (* v v)))))
(/.f64 (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(pow (+ 2 (* (* v v) -6)) -1/2)
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))
(+ 2 (* (* v v) -6))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* (* v v) -6)
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* v v)
(*.f64 v v)
v
-6
#s(literal -6 binary64)
-1/2
#s(literal -1/2 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
#s(literal 4/3 binary64)
(* (PI) (- 1 (* v v)))
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(/ (* 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))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
4/3
#s(literal 4/3 binary64)
(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))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
4
#s(literal 4 binary64)
(* (PI) (* 3 (sqrt 2)))
(*.f64 #s(literal 3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(PI)
(PI.f64)
(* 3 (sqrt 2))
(*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))
3
#s(literal 3 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (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))
4/3
#s(literal 4/3 binary64)
(PI)
(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)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (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 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(* (PI) 3)
(*.f64 (PI.f64) #s(literal 3 binary64))
(PI)
(PI.f64)
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 v (*.f64 v #s(literal 6 binary64)))
6
#s(literal 6 binary64)
(* v v)
(*.f64 v v)
v

localize224.0ms (2.2%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓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)))))
✓accuracy99.8%
(*.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%
(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)
✓accuracy98.4%
(/.f64 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))))
✓accuracy98.4%
(*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy98.4%
(*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓accuracy100.0%
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal -6 binary64))
✓accuracy98.5%
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
Results
170.0ms256×0valid
Compiler

Compiled 213 to 39 computations (81.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 91.0ms
ival-mult: 36.0ms (39.6% of total)
ival-pi: 14.0ms (15.4% of total)
ival-pow: 14.0ms (15.4% of total)
ival-div: 9.0ms (9.9% of total)
ival-sqrt: 7.0ms (7.7% of total)
...c/correct-round.rkt:119:19: 4.0ms (4.4% of total)
ival-add: 3.0ms (3.3% of total)
ival-sub: 3.0ms (3.3% of total)
const: 1.0ms (1.1% of total)
backward-pass: 0.0ms (0% of total)

series9.0ms (0.1%)

Counts
21 → 144
Calls
Call 1
Inputs
#<alt (* (pow (+ 2 (* (* v v) -6)) -1/2) (/ 4/3 (* (PI) (- 1 (* v v)))))>
#<alt (pow (+ 2 (* (* v v) -6)) -1/2)>
#<alt (+ 2 (* (* v v) -6))>
#<alt (* (* v v) -6)>
#<alt (/ (* 4/3 (sqrt 1/2)) (PI))>
#<alt (* 4/3 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (PI)>
#<alt (/ 4 (* (PI) (* 3 (sqrt 2))))>
#<alt (* (PI) (* 3 (sqrt 2)))>
#<alt (* 3 (sqrt 2))>
#<alt (/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ 4/3 (PI))>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))>
#<alt (* (PI) 3)>
#<alt (/ 4/3 (* (PI) (- 1 (* v v))))>
#<alt (* (PI) (- 1 (* v v)))>
#<alt (* v (* v -6))>
#<alt (* 6 (* v v))>
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 (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 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))>
#<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)))))))>
#<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 (* 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 (/ 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 (PI)>
#<alt (+ (PI) (* -1 (* (pow v 2) (PI))))>
#<alt (+ (PI) (* -1 (* (pow v 2) (PI))))>
#<alt (+ (PI) (* -1 (* (pow v 2) (PI))))>
#<alt (* -1 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))>
#<alt (* -1 (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (* -1 (PI)) (/ (PI) (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 (* -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 (* 6 (pow v 2))>
Calls

36 calls:

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

rewrite280.0ms (2.8%)

Algorithm
1×batch-egg-rewrite
Rules
4014×*-lowering-*.f32
4014×*-lowering-*.f64
2990×/-lowering-/.f32
2990×/-lowering-/.f64
1088×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038147
1202136
21269133
08512133
Stop Event
1×iter limit
1×node limit
Counts
21 → 873
Calls
Call 1
Inputs
(* (pow (+ 2 (* (* v v) -6)) -1/2) (/ 4/3 (* (PI) (- 1 (* v v)))))
(pow (+ 2 (* (* v v) -6)) -1/2)
(+ 2 (* (* v v) -6))
(* (* v v) -6)
(/ (* 4/3 (sqrt 1/2)) (PI))
(* 4/3 (sqrt 1/2))
(sqrt 1/2)
(PI)
(/ 4 (* (PI) (* 3 (sqrt 2))))
(* (PI) (* 3 (sqrt 2)))
(* 3 (sqrt 2))
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ 4/3 (PI))
(sqrt (+ 2 (* v (* v -6))))
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(* (PI) 3)
(/ 4/3 (* (PI) (- 1 (* v v))))
(* (PI) (- 1 (* v v)))
(* v (* v -6))
(* 6 (* v v))
Outputs
(neg.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64))))
(neg.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(neg.f64 (*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 #s(literal -4/3 binary64) (PI.f64))))
(neg.f64 (/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(neg.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.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 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))) (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.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 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.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 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))))))
(/.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64)) (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal -1 binary64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) #s(literal 4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (PI.f64) #s(literal 3 binary64))))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) #s(literal -4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (PI.f64) #s(literal -3 binary64))))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 3 binary64)))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (cbrt.f64 (PI.f64))))
(/.f64 (*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(/.f64 (neg.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(pow.f64 (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal -1 binary64))
(*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)))
(*.f64 #s(literal 4/3 binary64) (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(*.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))))
(*.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) #s(literal 3/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/4 binary64)) (*.f64 (PI.f64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (PI.f64)) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (PI.f64)))
(*.f64 (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (*.f64 (cbrt.f64 (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
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(*.f64 #s(literal -6 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))
(*.f64 (*.f64 v #s(literal -6 binary64)) (-.f64 #s(literal 0 binary64) v))
(*.f64 #s(literal 6 binary64) (*.f64 v v))
(*.f64 #s(literal 6 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -6 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal -6 binary64)))
(*.f64 (*.f64 v #s(literal 6 binary64)) v)
(*.f64 (*.f64 v #s(literal 6 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) v)))
(*.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v))) #s(literal 6 binary64))

simplify292.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
5038×*-lowering-*.f32
5038×*-lowering-*.f64
3574×+-lowering-+.f64
3574×+-lowering-+.f32
1756×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03342788
111382270
244102222
084372222
Stop Event
1×iter limit
1×node limit
Counts
144 → 144
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)))
(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))
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))
(* -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)))))))
(* 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))
(* 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)))))))))
(/ 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))
(PI)
(+ (PI) (* -1 (* (pow v 2) (PI))))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(* -1 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* -1 (* (pow v 2) (PI)))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (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))
(* -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))
(* 6 (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 (* (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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (*.f64 v v) (+.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))))))
(+ (* 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 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 v v)) (+.f64 (+.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 (*.f64 v v) (+.f64 (+.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 (/.f64 #s(literal 27/16 binary64) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64))))))))
(+ (* 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))))))))))
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(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (/.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 v v)) (PI.f64)))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (/.f64 (*.f64 #s(literal 4/3 binary64) (*.f64 v v)) (PI.f64)))))))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ (- (* -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))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ (- (* -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))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 v v)))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(PI)
(PI.f64)
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v)))
(* -1 (* (pow v 2) (PI)))
(-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* -1 (* (pow v 2) (PI)))
(-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (-.f64 (/.f64 (PI.f64) (*.f64 v v)) (PI.f64))))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* 6 (pow v 2))
(*.f64 v (*.f64 v #s(literal 6 binary64)))

eval175.0ms (1.7%)

Compiler

Compiled 25819 to 3080 computations (88.1% saved)

prune128.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New125381261
Fresh112
Picked415
Done000
Total1258101268
Accuracy
100.0%
Counts
1268 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶97.8%
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
99.4%
(/.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 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
▶100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
▶100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
▶99.4%
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
99.4%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
▶99.3%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.8%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
97.8%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
Compiler

Compiled 279 to 229 computations (17.9% saved)

simplify184.0ms (1.8%)

Algorithm
1×egg-herbie
Localize:

Found 20 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)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4 binary64) (PI.f64))
✓cost-diff128
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
✓cost-diff0
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓cost-diff0
(-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))
✓cost-diff0
(pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 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)))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
Rules
2176×fnmadd-define
2030×*-lowering-*.f32
2030×*-lowering-*.f64
1840×sum4-define
1456×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032263
167247
2140238
3224238
4507238
5998238
62264238
75968238
08132238
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v))) (PI))
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v)))
(/ 4/3 (sqrt (- 2 (* (* v v) 6))))
4/3
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
(* v v)
v
6
(- 1 (* v v))
1
(PI)
(/ (/ 4/3 (PI)) (sqrt 2))
(/ 4/3 (PI))
4/3
(PI)
(sqrt 2)
2
(/ (pow (- 2 (* (* v v) 6)) -1/2) (/ (PI) 4/3))
(pow (- 2 (* (* v v) 6)) -1/2)
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
(* v v)
v
6
-1/2
(/ (PI) 4/3)
(PI)
4/3
(/ (/ 4 (PI)) (* 3 (sqrt (- 2 (* (* v v) 6)))))
(/ 4 (PI))
4
(PI)
(* 3 (sqrt (- 2 (* (* v v) 6))))
3
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
(* v v)
v
6
(/ (/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6)))) (- 1 (* v v)))
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6))))
(/ 4/3 (PI))
4/3
(PI)
(sqrt (+ 2 (* (* v v) -6)))
(+ 2 (* (* v v) -6))
2
(* (* v v) -6)
(* v v)
v
-6
(- 1 (* v v))
1
Outputs
(/ (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v))) (PI))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (-.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 (sqrt (- 2 (* (* v v) 6))))
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
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))))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* v v)
(*.f64 v v)
v
6
#s(literal 6 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(PI)
(PI.f64)
(/ (/ 4/3 (PI)) (sqrt 2))
(/.f64 (/.f64 #s(literal 4/3 binary64) (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)
(/ (pow (- 2 (* (* v v) 6)) -1/2) (/ (PI) 4/3))
(/.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)))
(pow (- 2 (* (* v v) 6)) -1/2)
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
(- 2 (* (* v v) 6))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* v v)
(*.f64 v v)
v
6
#s(literal 6 binary64)
-1/2
#s(literal -1/2 binary64)
(/ (PI) 4/3)
(/.f64 (PI.f64) #s(literal 4/3 binary64))
(PI)
(PI.f64)
4/3
#s(literal 4/3 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 v (*.f64 v #s(literal -6 binary64))))))
(/ 4 (PI))
(/.f64 #s(literal 4 binary64) (PI.f64))
4
#s(literal 4 binary64)
(PI)
(PI.f64)
(* 3 (sqrt (- 2 (* (* v v) 6))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64))
3
#s(literal 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))))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* v v)
(*.f64 v v)
v
6
#s(literal 6 binary64)
(/ (/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6)))) (- 1 (* v v)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(PI)
(PI.f64)
(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))))
2
#s(literal 2 binary64)
(* (* v v) -6)
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* v v)
(*.f64 v v)
v
-6
#s(literal -6 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)

localize183.0ms (1.8%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal -6 binary64))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓accuracy98.5%
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 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))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓accuracy98.5%
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
Results
123.0ms256×0valid
Compiler

Compiled 263 to 33 computations (87.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 66.0ms
ival-div: 32.0ms (48.8% of total)
ival-mult: 9.0ms (13.7% of total)
ival-sqrt: 6.0ms (9.1% of total)
...c/correct-round.rkt:119:19: 6.0ms (9.1% of total)
ival-pow: 6.0ms (9.1% of total)
ival-sub: 3.0ms (4.6% of total)
ival-pi: 1.0ms (1.5% of total)
ival-add: 1.0ms (1.5% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series10.0ms (0.1%)

Counts
19 → 168
Calls
Call 1
Inputs
#<alt (/ (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v))) (PI))>
#<alt (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v)))>
#<alt (/ 4/3 (sqrt (- 2 (* (* v v) 6))))>
#<alt (sqrt (- 2 (* (* v v) 6)))>
#<alt (/ (/ 4/3 (PI)) (sqrt 2))>
#<alt (/ 4/3 (PI))>
#<alt (PI)>
#<alt (sqrt 2)>
#<alt (/ (pow (- 2 (* (* v v) 6)) -1/2) (/ (PI) 4/3))>
#<alt (pow (- 2 (* (* v v) 6)) -1/2)>
#<alt (- 2 (* (* v v) 6))>
#<alt (* (* v v) 6)>
#<alt (/ (/ 4 (PI)) (* 3 (sqrt (- 2 (* (* v v) 6)))))>
#<alt (/ 4 (PI))>
#<alt (* 3 (sqrt (- 2 (* (* v v) 6))))>
#<alt (/ (/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6)))) (- 1 (* v v)))>
#<alt (/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6))))>
#<alt (* v v)>
#<alt (* (* v v) -6)>
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 (* 4/3 (sqrt 1/2))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* 4/3 (* (pow v 2) (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2)))))))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 4/3 (* (pow v 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))))))) (* 4/3 (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2))))))))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 4/3 (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (sqrt 1/2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2)))))))) (* 4/3 (+ (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 (* -4/3 (/ (sqrt -1/6) (pow v 3)))>
#<alt (/ (+ (* -4/3 (sqrt -1/6)) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 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)))) (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6)))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (sqrt -1/6)) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 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)))) (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6)))))) (pow v 6)))))) (pow v 3)))>
#<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 (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 (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 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))>
#<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 (* 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 (* 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 (* 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 (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (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 (* -6 (pow v 2))>
Calls

42 calls:

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

rewrite298.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
3386×*-lowering-*.f32
3386×*-lowering-*.f64
3022×/-lowering-/.f32
3022×/-lowering-/.f64
1332×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032163
1199148
21638145
08440145
Stop Event
1×iter limit
1×node limit
Counts
19 → 874
Calls
Call 1
Inputs
(/ (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v))) (PI))
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (- 1 (* v v)))
(/ 4/3 (sqrt (- 2 (* (* v v) 6))))
(sqrt (- 2 (* (* v v) 6)))
(/ (/ 4/3 (PI)) (sqrt 2))
(/ 4/3 (PI))
(PI)
(sqrt 2)
(/ (pow (- 2 (* (* v v) 6)) -1/2) (/ (PI) 4/3))
(pow (- 2 (* (* v v) 6)) -1/2)
(- 2 (* (* v v) 6))
(* (* v v) 6)
(/ (/ 4 (PI)) (* 3 (sqrt (- 2 (* (* v v) 6)))))
(/ 4 (PI))
(* 3 (sqrt (- 2 (* (* v v) 6))))
(/ (/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6)))) (- 1 (* v v)))
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* (* v v) -6))))
(* v v)
(* (* v v) -6)
Outputs
(+.f64 (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) #s(literal 1 binary64)) (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal 1 binary64)))))
(+.f64 (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal 1 binary64)))) (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 v v)))
(+.f64 (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 v v)) (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) #s(literal 1 binary64)) (*.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 v v)))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (*.f64 (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))))
(+.f64 (*.f64 (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal 1 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))))
(+.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (*.f64 (*.f64 v v) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))))
(+.f64 (*.f64 (*.f64 v v) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))))
(+.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (*.f64 (*.f64 v v) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 4/3 binary64) (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)))))
(-.f64 (/.f64 #s(literal 0 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(neg.f64 (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (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)))))
(neg.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64)))))
(neg.f64 (*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (/.f64 #s(literal -4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
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(*.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (PI.f64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4 binary64) (PI.f64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal -3 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (PI.f64))))
(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/4 binary64)) (PI.f64)) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/4 binary64)) #s(literal 3/4 binary64)))
(*.f64 (/.f64 #s(literal -4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 1/3 binary64))
(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -4/3 binary64))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 3 binary64)) #s(literal 4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (pow.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 3 binary64)) #s(literal -4 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (PI.f64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (/.f64 #s(literal 4/3 binary64) (PI.f64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (*.f64 v v) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 v)) #s(literal 2 binary64))
(*.f64 v v)
(*.f64 v (neg.f64 (-.f64 #s(literal 0 binary64) v)))
(*.f64 (*.f64 v v) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 v v))
(*.f64 (-.f64 #s(literal 0 binary64) v) (-.f64 #s(literal 0 binary64) v))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) v)) v)
(+.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))
(neg.f64 (*.f64 v (*.f64 v #s(literal 6 binary64))))
(/.f64 (*.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 216 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) #s(literal 36 binary64))) (*.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))))
(/.f64 (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64)))))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(*.f64 #s(literal 6 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 6 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal 6 binary64)))
(*.f64 (*.f64 v #s(literal 6 binary64)) (-.f64 #s(literal 0 binary64) v))
(*.f64 (*.f64 v #s(literal -6 binary64)) v)
(*.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))

simplify309.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
3992×*-lowering-*.f32
3992×*-lowering-*.f64
2254×+-lowering-+.f64
2254×+-lowering-+.f32
1826×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03874221
113423197
251143110
081883110
Stop Event
1×iter limit
1×node limit
Counts
168 → 168
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)))
(* 4/3 (sqrt 1/2))
(+ (* 4/3 (sqrt 1/2)) (* 4/3 (* (pow v 2) (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2)))))))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 4/3 (* (pow v 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))))))) (* 4/3 (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2))))))))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 4/3 (+ (sqrt 1/2) (* 3/4 (/ 1 (sqrt 1/2))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (sqrt 1/2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2)))))))) (* 4/3 (+ (sqrt 1/2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2)))))))))))
(* -4/3 (/ (sqrt -1/6) (pow v 3)))
(/ (+ (* -4/3 (sqrt -1/6)) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 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)))) (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6)))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (pow v 3)))
(* -1 (/ (+ (* -4/3 (sqrt -1/6)) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (sqrt -1/6)) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (* 1/36 (/ 1 (sqrt -1/6)))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 1 (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (sqrt -1/6)) (+ (* 1/36 (/ 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)))) (sqrt -1/6))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (sqrt -1/6)))))) (pow v 6)))))) (pow v 3)))
(* 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))
(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))
(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))
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))
(* 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))
(* 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)))))))
(* 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)))
(* 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))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(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))
(* -6 (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 (* (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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (*.f64 v v) (+.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))))))
(+ (* 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 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (+.f64 (+.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 (*.f64 v v) (+.f64 (+.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 (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))))) (*.f64 v v))))
(+ (* 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 #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 #s(literal 4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (+.f64 (+.f64 (+.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 (/.f64 #s(literal 27/16 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))) (*.f64 (*.f64 v v) (+.f64 (+.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 (/.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 v v)))))))
(* -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 #s(literal 4/3 binary64) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal 1/144 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (*.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) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal 1/144 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 v v)))) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.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)))
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(/ (- (+ (* -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 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (PI.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)))))) 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 #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 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (PI.f64)))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) v)
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (PI.f64))) (-.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 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (PI.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 #s(literal 0 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 -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 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (PI.f64)))) (-.f64 #s(literal 0 binary64) v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))

eval274.0ms (2.7%)

Compiler

Compiled 37824 to 3501 computations (90.7% saved)

prune181.0ms (1.8%)

Pruning

10 alts after pruning (4 fresh and 6 done)

PrunedKeptTotal
New167801678
Fresh044
Picked055
Done011
Total1678101688
Accuracy
100.0%
Counts
1688 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓97.8%
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
▶99.4%
(/.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 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓99.4%
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
▶99.4%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
✓99.3%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.8%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
▶97.8%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
Compiler

Compiled 143 to 118 computations (17.5% saved)

simplify159.0ms (1.6%)

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
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓cost-diff0
(-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓cost-diff0
(*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64))
✓cost-diff128
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
Rules
2416×*-lowering-*.f32
2416×*-lowering-*.f64
1488×sum4-define
1364×fma-define
1346×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029236
162213
2122209
3215209
4509209
51029209
62268209
75930209
08204209
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 4 (* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3))
4
(* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3)
(* (PI) (sqrt (- 2 (* (* v v) 6))))
(PI)
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
(* v v)
v
6
3
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (PI))
(/ 4/3 (sqrt (- 2 (* (* v v) 6))))
4/3
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
(* v v)
v
6
(PI)
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (- 2 (* (* v v) 6))))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/ 4/3 (- 1 (* v v)))
4/3
(- 1 (* v v))
1
(* v v)
v
(PI)
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
2
(* (* v v) 6)
6
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4 (PI)) 3)
(/ 4 (PI))
4
(PI)
3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
Outputs
(/ 4 (* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
4
#s(literal 4 binary64)
(* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3)
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(* (PI) (sqrt (- 2 (* (* v v) 6))))
(*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(PI)
(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)))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* v v)
(*.f64 v v)
v
6
#s(literal 6 binary64)
3
#s(literal 3 binary64)
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (PI))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/ 4/3 (sqrt (- 2 (* (* v v) 6))))
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
4/3
#s(literal 4/3 binary64)
(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)))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
(* v v)
(*.f64 v v)
v
6
#s(literal 6 binary64)
(PI)
(PI.f64)
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (- 2 (* (* v v) 6))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/ 4/3 (- 1 (* v v)))
(/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
4/3
#s(literal 4/3 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(PI)
(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)))
2
#s(literal 2 binary64)
(* (* v v) 6)
(*.f64 v (*.f64 v #s(literal 6 binary64)))
6
#s(literal 6 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 (*.f64 v v) #s(literal -6 binary64)))))
(/ (/ 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)
(PI)
(PI.f64)
3
#s(literal 3 binary64)
(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)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)

localize188.0ms (1.9%)

Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓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 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓accuracy100.0%
(PI.f64)
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
✓accuracy98.5%
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓accuracy100.0%
(*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓accuracy100.0%
(*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64))
✓accuracy99.8%
(*.f64 (*.f64 v v) #s(literal 6 binary64))
✓accuracy98.5%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
Results
121.0ms256×0valid
Compiler

Compiled 236 to 30 computations (87.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 68.0ms
ival-div: 32.0ms (46.8% of total)
ival-mult: 21.0ms (30.7% of total)
ival-sqrt: 4.0ms (5.9% of total)
...c/correct-round.rkt:119:19: 4.0ms (5.9% of total)
ival-sub: 3.0ms (4.4% of total)
ival-pi: 1.0ms (1.5% of total)
ival-add: 1.0ms (1.5% of total)
const: 1.0ms (1.5% of total)
backward-pass: 0.0ms (0% of total)

series7.0ms (0.1%)

Counts
18 → 180
Calls
Call 1
Inputs
#<alt (/ 4 (* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3))>
#<alt (* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3)>
#<alt (* (PI) (sqrt (- 2 (* (* v v) 6))))>
#<alt (PI)>
#<alt (/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (PI))>
#<alt (/ 4/3 (sqrt (- 2 (* (* v v) 6))))>
#<alt (sqrt (- 2 (* (* v v) 6)))>
#<alt (- 2 (* (* v v) 6))>
#<alt (/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (- 2 (* (* v v) 6))))>
#<alt (/ (/ 4/3 (- 1 (* v v))) (PI))>
#<alt (/ 4/3 (- 1 (* v v)))>
#<alt (- 1 (* v v))>
#<alt (/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ (/ 4 (PI)) 3)>
#<alt (/ 4 (PI))>
#<alt (* (* v v) 6)>
#<alt (* v (* v -6))>
#<alt (sqrt (+ 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 (* 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 (* (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 (* 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 (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 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))>
#<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 (/ 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>
#<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 (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<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 (* -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)))))))>
Calls

45 calls:

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

rewrite359.0ms (3.6%)

Algorithm
1×batch-egg-rewrite
Rules
4074×/-lowering-/.f32
4074×/-lowering-/.f64
4028×*-lowering-*.f32
4028×*-lowering-*.f64
1418×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
029155
1178137
21396133
08411133
Stop Event
1×iter limit
1×node limit
Counts
18 → 1336
Calls
Call 1
Inputs
(/ 4 (* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3))
(* (* (PI) (sqrt (- 2 (* (* v v) 6)))) 3)
(* (PI) (sqrt (- 2 (* (* v v) 6))))
(PI)
(/ (/ 4/3 (sqrt (- 2 (* (* v v) 6)))) (PI))
(/ 4/3 (sqrt (- 2 (* (* v v) 6))))
(sqrt (- 2 (* (* v v) 6)))
(- 2 (* (* v v) 6))
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (- 2 (* (* v v) 6))))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/ 4/3 (- 1 (* v v)))
(- 1 (* v v))
(/ (/ (/ 4 (PI)) 3) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4 (PI)) 3)
(/ 4 (PI))
(* (* v v) 6)
(* v (* v -6))
(sqrt (+ 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 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 4 binary64) (*.f64 (/.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 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64)))
(-.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) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64)))) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64))) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64))))
(neg.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64)))
(neg.f64 (/.f64 #s(literal 4 binary64) (*.f64 (/.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 #s(literal 4 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (*.f64 (PI.f64) #s(literal 3 binary64))))
(/.f64 #s(literal 4 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) #s(literal 3 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 binary64) (*.f64 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 0 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 4 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal 4 binary64) (neg.f64 (*.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 4/3 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 4/3 binary64) (*.f64 (-.f64 #s(literal 0 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 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 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (-.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 #s(literal 4/3 binary64) (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))))
(/.f64 #s(literal 4/3 binary64) (neg.f64 (*.f64 (PI.f64) (-.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) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
(/.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 #s(literal 0 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64))) (-.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 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (/.f64 (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) (neg.f64 (-.f64 #s(literal 0 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 (-.f64 #s(literal 0 binary64) (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 (*.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))) #s(literal -4 binary64)))
(/.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 (*.f64 (PI.f64) #s(literal 3 binary64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -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))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.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) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 3/4 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal -3 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 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal -3 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64)))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (neg.f64 (*.f64 #s(literal -3 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)) (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) (PI.f64)) (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)))))) (PI.f64)))
(/.f64 #s(literal -4/3 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 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (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 -4 binary64) (*.f64 (/.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 #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) (*.f64 (PI.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 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 #s(literal -4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 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 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) #s(literal 3 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 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal -4 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) #s(literal 3 binary64))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 #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 (/.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 (/.f64 #s(literal -4 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64))))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -3 binary64)))
(/.f64 (/.f64 #s(literal -4 binary64) (PI.f64)) (*.f64 #s(literal 3 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 binary64) (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 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 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1/3 binary64) (/.f64 (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 1/3 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 4 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.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 #s(literal -1 binary64) (-.f64 #s(literal 0 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 #s(literal 0 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64))) (PI.f64)))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 3 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (-.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 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64)))))
(/.f64 #s(literal -1 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) #s(literal 4/3 binary64))))
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(*.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 4 binary64) (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(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 0 binary64) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(neg.f64 (-.f64 #s(literal 0 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 #s(literal 0 binary64) (*.f64 (PI.f64) #s(literal 3 binary64)))))
(/.f64 #s(literal 4 binary64) (neg.f64 (*.f64 #s(literal 3 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
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(/.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 4 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4 binary64))))
(pow.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal -1 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))))
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(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 4 binary64) (PI.f64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(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)))
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(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4 binary64) (sqrt.f64 (PI.f64)))))
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(*.f64 (*.f64 v #s(literal 6 binary64)) v)
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(*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v #s(literal 6 binary64))))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(*.f64 #s(literal 6 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal -6 binary64)) v)
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 6 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal 6 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal 6 binary64))))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/2 binary64)))
(-.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)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1 binary64))
(/.f64 #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) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.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))))))) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal -1 binary64))
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(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (sqrt.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64)) (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 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)))))))))
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(/.f64 (sqrt.f64 (+.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64)) #s(literal -4 binary64))) (sqrt.f64 (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))
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(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 1 binary64))
(*.f64 #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 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (pow.f64 (/.f64 #s(literal 1 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))))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) (+.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal -2 binary64)))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 (*.f64 v v) (*.f64 v v))) #s(literal 216 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 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)))))))))
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(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) #s(literal 36 binary64)))) (/.f64 #s(literal 1 binary64) (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 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal 1/4 binary64)))

simplify321.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
5030×*-lowering-*.f32
5030×*-lowering-*.f64
3012×+-lowering-+.f64
3012×+-lowering-+.f32
1906×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03763691
112943050
250442977
087742977
Stop Event
1×iter limit
1×node limit
Counts
180 → 180
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))
(* 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)))))))))
(* (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))
(* 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))
(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)))))))
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))
(* 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)))
(/ 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
(+ 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
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* 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))
(* -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)))))))
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
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(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(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 v (*.f64 v (+.f64 (*.f64 (/.f64 (*.f64 v v) (sqrt.f64 #s(literal 2 binary64))) #s(literal -9/4 binary64)) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (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 v (*.f64 v (+.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v 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 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 (+.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 1/2 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (*.f64 #s(literal 6 binary64) (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 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.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 1/2 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* v (sqrt -6)))
(*.f64 v (-.f64 #s(literal 0 binary64) (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 #s(literal 0 binary64) (*.f64 v (+.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 1/2 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (*.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 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.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 1/2 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))) (-.f64 #s(literal 0 binary64) v))

eval280.0ms (2.8%)

Compiler

Compiled 45734 to 3940 computations (91.4% saved)

prune220.0ms (2.2%)

Pruning

10 alts after pruning (0 fresh and 10 done)

PrunedKeptTotal
New195101951
Fresh000
Picked044
Done066
Total1951101961
Accuracy
100.0%
Counts
1961 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓97.8%
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓99.4%
(/.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 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓99.4%
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
✓99.4%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
✓99.3%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.8%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓97.8%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
Compiler

Compiled 386 to 188 computations (51.3% saved)

regimes20.0ms (0.2%)

Counts
17 → 1
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 4/3 binary64) (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 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (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 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 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) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 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))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (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) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.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) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
Calls

4 calls:

6.0ms
(/.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))))))
5.0ms
v
4.0ms
(*.f64 v v)
4.0ms
(*.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)))))
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)

regimes9.0ms (0.1%)

Counts
12 → 1
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 4/3 binary64) (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 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (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 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 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) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 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))))))
Outputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
Calls

2 calls:

5.0ms
v
3.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes7.0ms (0.1%)

Counts
10 → 1
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 4/3 binary64) (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 #s(literal 4 binary64) (*.f64 (PI.f64) (*.f64 #s(literal 3 binary64) (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 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
(/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v 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 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 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) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
Calls

2 calls:

3.0ms
v
3.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.4%1v
99.4%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes6.0ms (0.1%)

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

2 calls:

3.0ms
v
2.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.4%1v
99.4%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes3.0ms (0%)

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

1 calls:

3.0ms
v
Results
AccuracySegmentsBranch
99.4%1v
Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

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

2.0ms
v
Results
AccuracySegmentsBranch
99.3%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 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Outputs
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Calls

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
97.8%1v
Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03886
15886
27386
38186
48686
58786
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
(/.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 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Outputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64)))) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal 6 binary64))))) (PI.f64))
(/.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 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))

soundness1.4s (14.2%)

Rules
5870×+-lowering-+.f64
5870×+-lowering-+.f32
4276×*-lowering-*.f32
4276×*-lowering-*.f64
4014×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01620
14118
210816
333116
499416
5186716
6469216
0810416
038147
1202136
21269133
08512133
02593
114486
2114381
0855281
02192144
17441807
232711685
084211685
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 211 to 144 computations (31.8% saved)

preprocess43.0ms (0.4%)

Remove

(abs v)

Compiler

Compiled 292 to 164 computations (43.8% saved)

end0.0ms (0%)

Profiling

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