Falkner and Boettcher, Equation (22+)

Time bar (total: 10.3s)

analyze4.0ms (0%)

Memory
7.9MiB live, 7.9MiB allocated
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 18 computations (18.2% saved)

sample1.0s (10.1%)

Memory
0.8MiB live, 1 912.6MiB allocated
Samples
720.0ms8 256×0valid
1.0ms8×0invalid
Precisions
Click to see histograms. Total time spent on operations: 528.0ms
ival-mult: 273.0ms (51.7% of total)
ival-sub: 74.0ms (14% of total)
ival-sqrt: 65.0ms (12.3% of total)
ival-div: 56.0ms (10.6% of total)
ival-pi: 35.0ms (6.6% of total)
exact: 16.0ms (3% of total)
ival-true: 5.0ms (0.9% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

preprocess290.0ms (2.8%)

Memory
24.7MiB live, 500.6MiB allocated
Algorithm
2×egg-herbie
Rules
4 898×accelerator-lowering-fma.f32
4 898×accelerator-lowering-fma.f64
2 702×*-lowering-*.f32
2 702×*-lowering-*.f64
1 796×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02660
18355
220254
367454
4203254
5417554
6638254
7726554
01620
14118
210818
330918
488518
5148418
6282118
7564118
8772118
0823416
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 #s(literal -4/3 binary64) (fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
Call 2
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ (/ 4/3 (- (PI) (* v (* (PI) v)))) (sqrt (+ 2 (* (* v v) -6))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(/ (/ 4/3 (- (PI) (* v (* (PI) v)))) (sqrt (+ 2 (* (* v v) -6))))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
(/ (/ 4/3 (- (* v (* (PI) v)) (PI))) (sqrt (+ 2 (* (* v v) -6))))
Symmetry

(abs v)

explain173.0ms (1.7%)

Memory
2.8MiB live, 466.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-#s(literal 3 binary64)
00-0-(*.f64 v v)
00-0-#s(literal 1 binary64)
00-0-#s(literal 4 binary64)
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-(*.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-(*.f64 #s(literal 3 binary64) (PI.f64))
00-0-#s(literal 6 binary64)
00-0-v
00-0-#s(literal 2 binary64)
00-0-(-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))
01(6.589913936806429e-163)0-(*.f64 #s(literal 6 binary64) (*.f64 v v))
00-0-(-.f64 #s(literal 1 binary64) (*.f64 v v))
00-0-(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
00-0-(PI.f64)
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
51.0ms512×0valid
Compiler

Compiled 216 to 68 computations (68.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 33.0ms
ival-mult: 17.0ms (51.8% of total)
ival-sub: 4.0ms (12.2% of total)
ival-sqrt: 4.0ms (12.2% of total)
ival-div: 3.0ms (9.1% of total)
ival-pi: 2.0ms (6.1% of total)
exact: 1.0ms (3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Compiler

Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory
2.2MiB live, 2.2MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.4%
(/.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 21 to 16 computations (23.8% saved)

simplify252.0ms (2.4%)

Memory
15.8MiB live, 437.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff128
(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff192
(-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))
✓cost-diff384
(/.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
4 898×accelerator-lowering-fma.f32
4 898×accelerator-lowering-fma.f64
2 702×*-lowering-*.f32
2 702×*-lowering-*.f64
1 796×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01685
14183
210883
330983
488583
5148483
6282183
7564183
8772183
0823476
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
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 #s(literal -4/3 binary64) (fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
4
#s(literal 4 binary64)
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))
(fma.f64 (fma.f64 (PI.f64) (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 3 binary64)) #s(literal 0 binary64)) (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 0 binary64))
(* (* 3 (PI)) (- 1 (* v v)))
(fma.f64 (PI.f64) (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -3 binary64) #s(literal 3 binary64)) #s(literal 0 binary64))
(* 3 (PI))
(fma.f64 #s(literal 3 binary64) (PI.f64) #s(literal 0 binary64))
3
#s(literal 3 binary64)
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(sqrt (- 2 (* 6 (* v v))))
(sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64)))
(- 2 (* 6 (* v v)))
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* 6 (* v v))
(fma.f64 v (fma.f64 v #s(literal 6 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
6
#s(literal 6 binary64)

localize42.0ms (0.4%)

Memory
13.3MiB live, 91.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(*.f64 #s(literal 6 binary64) (*.f64 v v))
✓accuracy98.4%
(/.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))))))
Samples
25.0ms256×0valid
Compiler

Compiled 87 to 18 computations (79.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 7.0ms (46.6% of total)
ival-sub: 2.0ms (13.3% of total)
ival-div: 2.0ms (13.3% of total)
ival-sqrt: 2.0ms (13.3% of total)
ival-pi: 1.0ms (6.7% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory
-21.1MiB live, 17.7MiB allocated
Counts
6 → 60
Calls
Call 1
Inputs
#<alt (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (- 2 (* 6 (* v v)))>
#<alt (* (* 3 (PI)) (- 1 (* v v)))>
#<alt (PI)>
#<alt (* 6 (* v v))>
#<alt (sqrt (- 2 (* 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 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 (* 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 (* 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

15 calls:

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

rewrite340.0ms (3.3%)

Memory
27.0MiB live, 508.0MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
4 770×*-lowering-*.f32
4 770×*-lowering-*.f64
4 634×accelerator-lowering-fma.f32
4 634×accelerator-lowering-fma.f64
2 134×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01650
19148
261648
3577048
0843643
Stop Event
1×iter limit
1×node limit
Counts
6 → 346
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(- 2 (* 6 (* v v)))
(* (* 3 (PI)) (- 1 (* v v)))
(PI)
(* 6 (* v v))
(sqrt (- 2 (* 6 (* v v))))
Outputs
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))) #s(literal 3/4 binary64)))))
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(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 216 binary64) #s(literal 8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64)))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 216 binary64) #s(literal 8 binary64))) (pow.f64 (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 216 binary64) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 216 binary64) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) #s(literal 36 binary64) #s(literal 12 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (pow.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal 6 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))

simplify582.0ms (5.7%)

Memory
-54.8MiB live, 773.9MiB allocated
Algorithm
1×egg-herbie
Rules
16 800×accelerator-lowering-fma.f32
16 800×accelerator-lowering-fma.f64
5 540×*-lowering-*.f32
5 540×*-lowering-*.f64
2 680×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01761142
1510985
21851943
36391932
08093883
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
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)))
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))
(* 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)))))
(* 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)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+.f64 (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (fma.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) (fma.f64 (*.f64 v v) (fma.f64 v (/.f64 (*.f64 #s(literal 27/16 binary64) v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(fma.f64 (fma.f64 #s(literal 4/3 binary64) (fma.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 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 #s(literal 9/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (fma.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) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (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 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.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 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v))))) (/.f64 (*.f64 #s(literal -4/3 binary64) (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))) (+ (* 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 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (-.f64 (fma.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 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (pow.f64 v #s(literal 6 binary64)))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.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)))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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))) (* 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 (fma.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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))) (+ (* 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 (fma.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (fma.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 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v v)))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* 3 (PI))
(*.f64 (PI.f64) #s(literal 3 binary64))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(+ (* -3 (* (pow v 2) (PI))) (* 3 (PI)))
(*.f64 (PI.f64) (fma.f64 v (*.f64 v #s(literal -3 binary64)) #s(literal 3 binary64)))
(* -3 (* (pow v 2) (PI)))
(*.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(* -3 (* (pow v 2) (PI)))
(*.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (*.f64 v v)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64)))
(* (pow v 2) (+ (* -3 (PI)) (* 3 (/ (PI) (pow v 2)))))
(fma.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64)) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 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)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 v (*.f64 (/.f64 v (sqrt.f64 #s(literal 2 binary64))) #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))))))
(fma.f64 (*.f64 v v) (fma.f64 v (*.f64 v (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #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)))) (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)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(fma.f64 v (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))) (fma.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 v (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 #s(literal 0 binary64) (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (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 v (/.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64))))) (fma.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))

eval54.0ms (0.5%)

Memory
22.5MiB live, 139.4MiB allocated
Compiler

Compiled 12 197 to 1 690 computations (86.1% saved)

prune48.0ms (0.5%)

Memory
-21.1MiB live, 109.8MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New4024406
Fresh000
Picked101
Done000
Total4034407
Accuracy
100.0%
Counts
407 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.4%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶98.0%
(/.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))))))
▶99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
▶98.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 59 to 48 computations (18.6% saved)

simplify255.0ms (2.5%)

Memory
13.3MiB live, 401.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(PI.f64)
✓cost-diff128
(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff384
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓cost-diff0
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
✓cost-diff0
(PI.f64)
✓cost-diff192
(-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))
✓cost-diff384
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
✓cost-diff0
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Rules
5 056×accelerator-lowering-fma.f32
5 056×accelerator-lowering-fma.f64
2 720×*-lowering-*.f32
2 720×*-lowering-*.f64
1 848×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036223
194219
2207219
3496219
41094219
51692219
63132219
75936219
87760219
08268200
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
4/3
(/ (sqrt 1/2) (PI))
(sqrt 1/2)
1/2
(PI)
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))
4/3
(* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1)))
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
v
(* v -6)
-6
2
(* (PI) (+ (* v v) 1))
(PI)
(+ (* v v) 1)
1
(/ 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
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))))
4
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))
(* (* 3 (PI)) (- 1 (* v v)))
(* 3 (PI))
3
(PI)
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ (* (* v v) -6) 2))
(+ (* (* v v) -6) 2)
-6
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
#s(literal 4/3 binary64)
(/ (sqrt 1/2) (PI))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(PI)
(PI.f64)
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))
(/.f64 #s(literal 4/3 binary64) (fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
4/3
#s(literal 4/3 binary64)
(* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1)))
(fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(sqrt (+ (* v (* v -6)) 2))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(+ (* v (* v -6)) 2)
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
v
(* v -6)
(fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)
(* (PI) (+ (* v v) 1))
(fma.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)) #s(literal 0 binary64))
(PI)
(PI.f64)
(+ (* v v) 1)
(fma.f64 v v #s(literal 1 binary64))
1
#s(literal 1 binary64)
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 #s(literal 4/3 binary64) (fma.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64)))
4
#s(literal 4 binary64)
(* (* (PI) 3) (sqrt (- 2 (* 6 (* v v)))))
(fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (PI.f64) #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (PI) 3)
(fma.f64 (PI.f64) #s(literal 3 binary64) #s(literal 0 binary64))
(PI)
(PI.f64)
3
#s(literal 3 binary64)
(sqrt (- 2 (* 6 (* v v))))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(- 2 (* 6 (* v v)))
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* 6 (* v v))
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal 6 binary64) #s(literal 0 binary64))
6
#s(literal 6 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))))
(/.f64 #s(literal -4/3 binary64) (fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
4
#s(literal 4 binary64)
(* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2)))
(fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (fma.f64 (PI.f64) #s(literal -3 binary64) #s(literal 0 binary64)) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (* 3 (PI)) (- 1 (* v v)))
(fma.f64 (fma.f64 (PI.f64) #s(literal -3 binary64) #s(literal 0 binary64)) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64))
(* 3 (PI))
(fma.f64 (PI.f64) #s(literal 3 binary64) #s(literal 0 binary64))
3
#s(literal 3 binary64)
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(sqrt (+ (* (* v v) -6) 2))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(+ (* (* v v) -6) 2)
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)

localize134.0ms (1.3%)

Memory
-13.2MiB live, 186.2MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 #s(literal 3 binary64) (PI.f64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓accuracy100.0%
(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
✓accuracy100.0%
(PI.f64)
✓accuracy99.7%
(*.f64 #s(literal 6 binary64) (*.f64 v v))
✓accuracy98.4%
(/.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 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
✓accuracy100.0%
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
✓accuracy100.0%
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
✓accuracy100.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
Samples
68.0ms256×0valid
Compiler

Compiled 213 to 38 computations (82.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 44.0ms
ival-mult: 20.0ms (45% of total)
ival-sqrt: 7.0ms (15.7% of total)
ival-div: 6.0ms (13.5% of total)
const: 4.0ms (9% of total)
ival-add: 3.0ms (6.7% of total)
ival-sub: 2.0ms (4.5% of total)
ival-pi: 1.0ms (2.2% of total)
exact: 1.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory
15.8MiB live, 15.8MiB allocated
Counts
18 → 156
Calls
Call 1
Inputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (/ (sqrt 1/2) (PI))>
#<alt (sqrt 1/2)>
#<alt (PI)>
#<alt (/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))>
#<alt (sqrt (+ (* v (* v -6)) 2))>
#<alt (+ (* v (* v -6)) 2)>
#<alt (/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))>
#<alt (- 2 (* 6 (* v v)))>
#<alt (sqrt (- 2 (* 6 (* v v))))>
#<alt (/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))))>
#<alt (* (* 3 (PI)) (- 1 (* v v)))>
#<alt (- 1 (* v v))>
#<alt (* (PI) (+ (* v v) 1))>
#<alt (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1)))>
#<alt (* 6 (* v v))>
#<alt (sqrt (+ (* (* v v) -6) 2))>
#<alt (* 3 (PI))>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* 4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (- (* -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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 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)))))) (* 1/36 (/ 1 (* (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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 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)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt 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 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt 2>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (+ 2 (* -6 (pow v 2)))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* -6 (pow v 2))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<alt (* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))>
#<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 (* (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))>
#<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 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 (PI)>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (+ (PI) (* (pow v 2) (PI)))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))>
#<alt (* (PI) (sqrt 2))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))>
#<alt (* (pow v 3) (* (PI) (sqrt -6)))>
#<alt (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))>
#<alt (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))>
#<alt (* -1 (* (pow v 3) (* (PI) (sqrt -6))))>
#<alt (* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))>
#<alt (* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -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

39 calls:

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

rewrite406.0ms (3.9%)

Memory
21.3MiB live, 759.9MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
6 364×accelerator-lowering-fma.f32
6 364×accelerator-lowering-fma.f64
4 884×*-lowering-*.f32
4 884×*-lowering-*.f64
3 850×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036148
1197144
21251144
08807132
Stop Event
1×iter limit
1×node limit
Counts
18 → 987
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/ (sqrt 1/2) (PI))
(sqrt 1/2)
(PI)
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1))))
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
(/ 4 (* (* (PI) 3) (sqrt (- 2 (* 6 (* v v))))))
(- 2 (* 6 (* v v)))
(sqrt (- 2 (* 6 (* v v))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (+ (* (* v v) -6) 2))))
(* (* 3 (PI)) (- 1 (* v v)))
(- 1 (* v v))
(* (PI) (+ (* v v) 1))
(* (sqrt (+ (* v (* v -6)) 2)) (* (PI) (+ (* v v) 1)))
(* 6 (* v v))
(sqrt (+ (* (* v v) -6) 2))
(* 3 (PI))
Outputs
(neg.f64 (*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) #s(literal 4/3 binary64)))
(neg.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))))
(neg.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4/3 binary64)) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 4/3 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (*.f64 #s(literal 4/3 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))))))
(/.f64 #s(literal -4/3 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4/3 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4/3 binary64))) (PI.f64))
(/.f64 (neg.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (neg.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (PI.f64) (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal 4/3 binary64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(*.f64 #s(literal -4/3 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(*.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -4/3 binary64)) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 4/3 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (cbrt.f64 (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64)))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (log.f64 (PI.f64)))))
(exp.f64 (fma.f64 #s(literal -1 binary64) (log.f64 (PI.f64)) (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (log.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(sqrt.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (PI.f64) (PI.f64))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(/.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(pow.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal -1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) (PI.f64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (sqrt.f64 (/.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (PI.f64)))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (cbrt.f64 (PI.f64))) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (PI.f64)) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(log.f64 (/.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))))
(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)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (PI.f64) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1 binary64))
(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)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.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 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
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(*.f64 (PI.f64) #s(literal 3 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) #s(literal 3 binary64)))
(*.f64 #s(literal 3 binary64) (PI.f64))
(*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 3 binary64)))
(*.f64 (*.f64 #s(literal 3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))

simplify722.0ms (7%)

Memory
19.6MiB live, 1 027.6MiB allocated
Algorithm
1×egg-herbie
Rules
12 362×accelerator-lowering-fma.f32
12 362×accelerator-lowering-fma.f64
5 332×*-lowering-*.f32
5 332×*-lowering-*.f64
4 904×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03353352
110782912
242892806
084322702
Stop Event
1×iter limit
1×node limit
Counts
156 → 156
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (+ (* -1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))))) (* 4/3 (- (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))))))))))
(* 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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 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)))))) (* 1/36 (/ 1 (* (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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (* 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 (/ (+ (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (/ (sqrt -1/6) (PI)))) (pow v 4))) (+ (* 4/3 (/ (- (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (- (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* -1/2 (/ (+ 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)))))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 6)))))) (pow v 3)))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
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 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
2
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(+ 2 (* -6 (pow v 2)))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* -6 (pow v 2))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(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 (* (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))
(+ (* -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)))))
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))
(PI)
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(+ (PI) (* (pow v 2) (PI)))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (PI))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(* (PI) (sqrt 2))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(* (pow v 3) (* (PI) (sqrt -6)))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -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 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (* (pow v 2) (+ (* -1 (/ (sqrt 1/2) (PI))) (* 3/4 (/ 1 (* (PI) (sqrt 1/2))))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(*.f64 #s(literal 4/3 binary64) (fma.f64 (*.f64 v v) (-.f64 (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
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1
#s(literal 1 binary64)
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(+ 1 (* -1 (pow v 2)))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* -1 (pow v 2))
(-.f64 #s(literal 0 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(PI)
(PI.f64)
(+ (PI) (* (pow v 2) (PI)))
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(+ (PI) (* (pow v 2) (PI)))
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(+ (PI) (* (pow v 2) (PI)))
(*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (pow v 2) (+ (PI) (/ (PI) (pow v 2))))
(*.f64 v (*.f64 v (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v)))))
(* (PI) (sqrt 2))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (PI) (sqrt 2)))))
(fma.f64 v (/.f64 (*.f64 v (*.f64 (PI.f64) #s(literal -3 binary64))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2)))))))))
(fma.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (fma.f64 (PI.f64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 v (*.f64 v (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -21/4 binary64)))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (PI) (pow (sqrt 2) 3))) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (PI) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))))))
(fma.f64 (*.f64 v v) (fma.f64 (PI.f64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (fma.f64 #s(literal -27/2 binary64) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -9/4 binary64))) (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -21/4 binary64))))) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(* (pow v 3) (* (PI) (sqrt -6)))
(*.f64 (*.f64 v (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))
(* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))
(*.f64 (*.f64 v (*.f64 v v)) (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))
(*.f64 (*.f64 v (*.f64 v v)) (+.f64 (fma.f64 (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/12 binary64) (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))))
(* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2)))))))))
(*.f64 (*.f64 v (*.f64 v v)) (fma.f64 (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/12 binary64) (+.f64 (fma.f64 (/.f64 (PI.f64) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* (pow v 3) (* (PI) (sqrt -6))))
(*.f64 (*.f64 v (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(* -1 (* (pow v 3) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))
(*.f64 (+.f64 (fma.f64 (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/12 binary64) (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(* -1 (* (pow v 3) (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* -1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (+ (/ (PI) (* (pow v 2) (sqrt -6))) (+ (/ (PI) (* (pow v 4) (sqrt -6))) (/ (* (PI) (sqrt -6)) (pow v 2))))))))))
(*.f64 (fma.f64 (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal 1/12 binary64) (+.f64 (fma.f64 (/.f64 (PI.f64) (pow.f64 v #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (PI.f64) (/.f64 (PI.f64) (*.f64 v v))) (/.f64 (PI.f64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))))) (/.f64 (PI.f64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.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))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 #s(literal -3 binary64) (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (fma.f64 #s(literal -27/2 binary64) (*.f64 v (/.f64 v (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)))) (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)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (*.f64 (*.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 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 (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 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 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 (sqrt.f64 #s(literal -6 binary64)) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 (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))))))) (-.f64 #s(literal 0 binary64) v))
(* -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 #s(literal 0 binary64) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))))

eval224.0ms (2.2%)

Memory
28.4MiB live, 393.2MiB allocated
Compiler

Compiled 35 637 to 4 226 computations (88.1% saved)

prune144.0ms (1.4%)

Memory
-19.5MiB live, 429.4MiB allocated
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1 30141 305
Fresh000
Picked224
Done000
Total1 30361 309
Accuracy
100.0%
Counts
1 309 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.4%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶98.0%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
▶99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
▶99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
✓98.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 78 to 65 computations (16.7% saved)

simplify310.0ms (3%)

Memory
17.4MiB live, 526.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff384
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓cost-diff0
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(PI.f64)
✓cost-diff192
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
✓cost-diff0
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
✓cost-diff-64
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
Rules
6 774×accelerator-lowering-fma.f32
6 774×accelerator-lowering-fma.f64
2 928×*-lowering-*.f32
2 928×*-lowering-*.f64
2 242×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028184
161184
298184
3178184
4447184
5859184
61735184
74684184
87502184
08150171
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt 2)))
4/3
(* (PI) (sqrt 2))
(PI)
(sqrt 2)
2
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (PI)))
4/3
(* (sqrt (+ (* v (* v -6)) 2)) (PI))
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
v
(* v -6)
-6
2
(PI)
(/ 4/3 (* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))
4/3
(* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))
(* (PI) (- 1 (* v v)))
(PI)
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
(* v -6)
-6
2
(/ 4 (* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2))))
4
(* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2)))
(* (PI) 3)
(PI)
3
(sqrt (+ (* (* v v) -6) 2))
(+ (* (* v v) -6) 2)
(* v v)
v
-6
2
Outputs
(/ 4/3 (* (PI) (sqrt 2)))
(/.f64 #s(literal 4/3 binary64) (fma.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
4/3
#s(literal 4/3 binary64)
(* (PI) (sqrt 2))
(fma.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(PI)
(PI.f64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (PI)))
(/.f64 #s(literal 4/3 binary64) (fma.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64)))
4/3
#s(literal 4/3 binary64)
(* (sqrt (+ (* v (* v -6)) 2)) (PI))
(fma.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
(sqrt (+ (* v (* v -6)) 2))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(+ (* v (* v -6)) 2)
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
v
(* v -6)
(fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)
(PI)
(PI.f64)
(/ 4/3 (* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))
(/.f64 #s(literal -4/3 binary64) (fma.f64 (PI.f64) (fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
4/3
#s(literal 4/3 binary64)
(* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2)))
(fma.f64 (fma.f64 v v #s(literal -1 binary64)) (fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (PI) (- 1 (* v v)))
(fma.f64 (fma.f64 v v #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal 0 binary64))
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64)))
1
#s(literal 1 binary64)
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(sqrt (+ (* v (* v -6)) 2))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(+ (* v (* v -6)) 2)
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
(* v -6)
(fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)
(/ 4 (* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2))))
(/.f64 #s(literal 4/3 binary64) (fma.f64 (PI.f64) (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64)))
4
#s(literal 4 binary64)
(* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2)))
(fma.f64 (sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))) (fma.f64 (PI.f64) #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* (PI) 3)
(fma.f64 (PI.f64) #s(literal 3 binary64) #s(literal 0 binary64))
(PI)
(PI.f64)
3
#s(literal 3 binary64)
(sqrt (+ (* (* v v) -6) 2))
(sqrt.f64 (fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64)))
(+ (* (* v v) -6) 2)
(fma.f64 #s(literal -6 binary64) (fma.f64 v v #s(literal 0 binary64)) #s(literal 2 binary64))
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)

localize118.0ms (1.1%)

Memory
-4.8MiB live, 195.8MiB allocated
Localize:

Found 16 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(*.f64 v v)
✓accuracy100.0%
(sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
✓accuracy100.0%
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓accuracy100.0%
(*.f64 v #s(literal -6 binary64))
✓accuracy100.0%
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
✓accuracy100.0%
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(PI.f64)
Samples
52.0ms256×0valid
Compiler

Compiled 176 to 30 computations (83% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-mult: 15.0ms (41.7% of total)
ival-div: 6.0ms (16.7% of total)
ival-sqrt: 5.0ms (13.9% of total)
const: 4.0ms (11.1% of total)
ival-add: 3.0ms (8.3% of total)
ival-pi: 1.0ms (2.8% of total)
ival-sub: 1.0ms (2.8% of total)
exact: 1.0ms (2.8% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series5.0ms (0%)

Memory
4.9MiB live, 4.9MiB allocated
Counts
15 → 132
Calls
Call 1
Inputs
#<alt (/ 4/3 (* (PI) (sqrt 2)))>
#<alt (PI)>
#<alt (sqrt 2)>
#<alt (* (PI) (sqrt 2))>
#<alt (/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (PI)))>
#<alt (sqrt (+ (* v (* v -6)) 2))>
#<alt (+ (* v (* v -6)) 2)>
#<alt (/ 4/3 (* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))>
#<alt (- 1 (* v v))>
#<alt (/ 4 (* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2))))>
#<alt (sqrt (+ (* (* v v) -6) 2))>
#<alt (+ (* (* v v) -6) 2)>
#<alt (* v -6)>
#<alt (* (PI) (- 1 (* v v)))>
#<alt (* v v)>
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 (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 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 (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 (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<alt (* -6 v)>
#<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 (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)>
Calls

33 calls:

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

rewrite664.0ms (6.5%)

Memory
-281.8MiB live, 660.2MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
5 382×*-lowering-*.f32
5 382×*-lowering-*.f64
4 688×accelerator-lowering-fma.f32
4 688×accelerator-lowering-fma.f64
3 234×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028103
1146103
2820103
37092103
0812796
Stop Event
1×iter limit
1×node limit
Counts
15 → 841
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt 2)))
(PI)
(sqrt 2)
(* (PI) (sqrt 2))
(/ 4/3 (* (sqrt (+ (* v (* v -6)) 2)) (PI)))
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
(/ 4/3 (* (* (PI) (- 1 (* v v))) (sqrt (+ (* v (* v -6)) 2))))
(- 1 (* v v))
(/ 4 (* (* (PI) 3) (sqrt (+ (* (* v v) -6) 2))))
(sqrt (+ (* (* v v) -6) 2))
(+ (* (* v v) -6) 2)
(* v -6)
(* (PI) (- 1 (* v v)))
(* v v)
Outputs
(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (PI.f64) #s(literal 3 binary64))))
(/.f64 #s(literal -4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (PI.f64) #s(literal -3 binary64))))
(/.f64 #s(literal -4/3 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3/4 binary64))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -3/4 binary64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (PI.f64) #s(literal 3/4 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (PI.f64))
(/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) #s(literal 1 binary64)) (*.f64 #s(literal 3 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (cbrt.f64 (PI.f64))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64))))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64)))) (PI.f64))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 4/3 binary64)) (PI.f64))
(/.f64 (*.f64 #s(literal 4 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (PI.f64) #s(literal 3 binary64)))
(/.f64 (*.f64 #s(literal -4 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (PI.f64) #s(literal -3 binary64)))
(/.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 4 binary64) (*.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 #s(literal 4 binary64) (/.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 4/3 binary64))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -4/3 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 4 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1/3 binary64) (PI.f64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (PI.f64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 3/4 binary64))) #s(literal -1/2 binary64)))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(+.f64 (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64)))) (log.f64 (pow.f64 (E.f64) (/.f64 (PI.f64) #s(literal 2 binary64)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(exp.f64 (log.f64 (PI.f64)))
(exp.f64 (*.f64 (fma.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64)) #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 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64)) #s(literal 2 binary64)))
(fabs.f64 (PI.f64))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.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 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) #s(literal 3 binary64)))
(*.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 (*.f64 (PI.f64) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64))) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.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 (*.f64 (PI.f64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) #s(literal 1/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (exp.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (exp.f64 (fma.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))))
(*.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))) (exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (*.f64 (PI.f64) (*.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 (*.f64 (PI.f64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (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 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.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 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (PI.f64)) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)) (log.f64 (PI.f64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 (PI.f64) (PI.f64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (PI.f64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (PI.f64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 1 binary64)))
(*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
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(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (exp.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (exp.f64 (fma.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))) (exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (PI.f64)) #s(literal 0 binary64))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (sqrt.f64 (PI.f64))))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 4/3 binary64))) (cbrt.f64 (PI.f64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.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 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.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 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.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 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)) (PI.f64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (PI.f64))
(fma.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(fma.f64 (*.f64 (PI.f64) v) (-.f64 #s(literal 0 binary64) v) (PI.f64))
(fma.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) v)) v (PI.f64))
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (PI.f64))
(/.f64 (PI.f64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 v v #s(literal 1 binary64)) (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))) (fma.f64 v v #s(literal 1 binary64)))
(/.f64 (neg.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal 1 binary64))))
(/.f64 (fma.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)) (pow.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) #s(literal 3 binary64))) (fma.f64 (PI.f64) (PI.f64) (-.f64 (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))) (*.f64 (PI.f64) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))))
(/.f64 (-.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))) (-.f64 (PI.f64) (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))))
(/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (PI.f64) (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal 1 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (PI.f64)) (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (PI.f64)) (-.f64 #s(literal 0 binary64) (fma.f64 v v #s(literal 1 binary64))))
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 #s(literal 1 binary64) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64))
(*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (cbrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (cbrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))) (PI.f64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))) (/.f64 (PI.f64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 1 binary64))) (PI.f64)))
(*.f64 (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)) (/.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64)))))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) (fma.f64 v v #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 1 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (PI.f64))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (fma.f64 (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64)))) (*.f64 (*.f64 v v) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64)))))) #s(literal 1 binary64))) (fma.f64 (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64)))) (-.f64 (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64)))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64)))))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (fma.f64 v v #s(literal 1 binary64))))))
(*.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (/.f64 (*.f64 (PI.f64) (fma.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))) (fma.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)) #s(literal 1 binary64))) (fma.f64 (*.f64 v v) (-.f64 (*.f64 v v) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 v) #s(literal 0 binary64)))
(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 #s(literal 1 binary64) (*.f64 v v))
(*.f64 (*.f64 v v) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 v)) (exp.f64 (log.f64 v)))

simplify632.0ms (6.1%)

Memory
3.2MiB live, 1 114.7MiB allocated
Algorithm
1×egg-herbie
Rules
19 824×accelerator-lowering-fma.f32
19 824×accelerator-lowering-fma.f64
6 198×*-lowering-*.f32
6 198×*-lowering-*.f64
3 456×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02242270
16841885
224991807
083691725
Stop Event
1×iter limit
1×node limit
Counts
132 → 132
Calls
Call 1
Inputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(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)))
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))
(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))
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(* -6 v)
(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))))
(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)
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(fma.f64 (*.f64 v v) (fma.f64 v (/.f64 (*.f64 v #s(literal 9/4 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (fma.f64 v (/.f64 (*.f64 v #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64)))) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (PI.f64) v))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (PI.f64) v)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)))))
(/ (- (+ (* -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 (fma.f64 #s(literal 4/3 binary64) (/.f64 (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 v (*.f64 v (*.f64 v v))))))) (/.f64 #s(literal -1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (fma.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 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))) (/.f64 #s(literal -1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (*.f64 (PI.f64) v))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (fma.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) (fma.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (PI.f64) (*.f64 v (*.f64 v (*.f64 v v)))))))) 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 (fma.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (fma.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 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))) (/.f64 #s(literal -1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))))) (-.f64 #s(literal 0 binary64) v))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 v (*.f64 (/.f64 v (sqrt.f64 #s(literal 2 binary64))) #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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #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)))) (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)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (*.f64 (*.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 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v))))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v))))))))
(* -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 #s(literal 0 binary64) (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v)))))))))
(* -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 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) v))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 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 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
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(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 v (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v)))))))))
(* -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 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1/12 binary64) (*.f64 (sqrt.f64 #s(literal -6 binary64)) (*.f64 v (*.f64 v (*.f64 v v))))))) (-.f64 #s(literal 0 binary64) v))
2
#s(literal 2 binary64)
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(+ 2 (* -6 (pow v 2)))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(* -6 v)
(*.f64 v #s(literal -6 binary64))
(PI)
(PI.f64)
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (PI.f64))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.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))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.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))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.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)
(pow v 2)
(*.f64 v v)

eval198.0ms (1.9%)

Memory
17.3MiB live, 322.6MiB allocated
Compiler

Compiled 30 509 to 3 262 computations (89.3% saved)

prune121.0ms (1.2%)

Memory
33.7MiB live, 303.3MiB allocated
Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New1 28511 286
Fresh000
Picked044
Done112
Total1 28661 292
Accuracy
100.0%
Counts
1 292 → 6
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.0%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
▶100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
✓99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
✓98.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 77 to 64 computations (16.9% saved)

simplify273.0ms (2.7%)

Memory
-19.8MiB live, 469.6MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))
✓cost-diff0
(PI.f64)
✓cost-diff192
(fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64))
✓cost-diff192
(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
Rules
8 156×accelerator-lowering-fma.f32
8 156×accelerator-lowering-fma.f64
2 512×*-lowering-*.f32
2 512×*-lowering-*.f64
1 512×--lowering--.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01676
13173
27173
314773
432073
552973
686173
7134573
8307073
9551373
10767273
0807268
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 4/3 (* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2))))
4/3
(* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2)))
(+ (* -1 (* (* v v) (PI))) (PI))
-1
(* (* v v) (PI))
(* v v)
v
(PI)
(sqrt (+ (* v (* v -6)) 2))
(+ (* v (* v -6)) 2)
(* v -6)
-6
2
Outputs
(/ 4/3 (* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2))))
(/.f64 #s(literal -4/3 binary64) (fma.f64 (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) (fma.f64 (PI.f64) (fma.f64 v v #s(literal -1 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
4/3
#s(literal 4/3 binary64)
(* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2)))
(fma.f64 (fma.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64))) #s(literal 0 binary64)) (sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))) #s(literal 0 binary64))
(+ (* -1 (* (* v v) (PI))) (PI))
(fma.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (fma.f64 v v #s(literal 0 binary64))) #s(literal 0 binary64))
-1
#s(literal -1 binary64)
(* (* v v) (PI))
(fma.f64 v (fma.f64 v (PI.f64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* v v)
(fma.f64 v v #s(literal 0 binary64))
v
(PI)
(PI.f64)
(sqrt (+ (* v (* v -6)) 2))
(sqrt.f64 (fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64)))
(+ (* v (* v -6)) 2)
(fma.f64 (fma.f64 v v #s(literal 0 binary64)) #s(literal -6 binary64) #s(literal 2 binary64))
(* v -6)
(fma.f64 v #s(literal -6 binary64) #s(literal 0 binary64))
-6
#s(literal -6 binary64)
2
#s(literal 2 binary64)

localize75.0ms (0.7%)

Memory
16.0MiB live, 94.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓accuracy99.7%
(*.f64 (*.f64 v v) (PI.f64))
Samples
55.0ms256×0valid
Compiler

Compiled 74 to 18 computations (75.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 9.0ms (46.2% of total)
const: 4.0ms (20.6% of total)
ival-add: 2.0ms (10.3% of total)
ival-sqrt: 2.0ms (10.3% of total)
ival-pi: 1.0ms (5.1% of total)
ival-div: 1.0ms (5.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory
4.2MiB live, 4.2MiB allocated
Counts
5 → 48
Calls
Call 1
Inputs
#<alt (/ 4/3 (* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2))))>
#<alt (+ (* -1 (* (* v v) (PI))) (PI))>
#<alt (PI)>
#<alt (sqrt (+ (* v (* v -6)) 2))>
#<alt (* (* v v) (PI))>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))>
#<alt (* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))>
#<alt (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))>
#<alt (* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))>
#<alt (* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))>
#<alt (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 (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 (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
#<alt (* (pow v 2) (PI))>
Calls

12 calls:

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

rewrite801.0ms (7.8%)

Memory
9.5MiB live, 713.3MiB allocated
Algorithm
1×batch-egg-rewrite
Rules
9 856×accelerator-lowering-fma.f32
9 856×accelerator-lowering-fma.f64
5 384×*-lowering-*.f32
5 384×*-lowering-*.f64
2 060×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01641
18339
260839
3637939
0802337
Stop Event
1×iter limit
1×node limit
Counts
5 → 381
Calls
Call 1
Inputs
(/ 4/3 (* (+ (* -1 (* (* v v) (PI))) (PI)) (sqrt (+ (* v (* v -6)) 2))))
(+ (* -1 (* (* v v) (PI))) (PI))
(PI)
(sqrt (+ (* v (* v -6)) 2))
(* (* v v) (PI))
Outputs
(exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3/4 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))))
(neg.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))))))))
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(*.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 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (sqrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (pow.f64 (E.f64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) #s(literal 1 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (log.f64 (pow.f64 (E.f64) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (log.f64 (exp.f64 (cbrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64))))
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(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (log.f64 (pow.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))
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(*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64))))
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(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/3 binary64)) (PI.f64))
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(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
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(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))
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(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
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(/.f64 (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) #s(literal 36 binary64)) #s(literal -12 binary64)) #s(literal 4 binary64))) (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64))) (sqrt.f64 (fma.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64)))) #s(literal -1 binary64))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) #s(literal 36 binary64)) #s(literal -12 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) #s(literal 36 binary64)) #s(literal -12 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 (*.f64 v (*.f64 v v)) (*.f64 (*.f64 v (*.f64 v v)) #s(literal -216 binary64)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (*.f64 v v) (-.f64 (*.f64 (*.f64 v v) #s(literal 36 binary64)) #s(literal -12 binary64)) #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 v v) #s(literal 6 binary64) #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v (*.f64 (*.f64 v v) #s(literal 36 binary64))) #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal -2 binary64)))))
(*.f64 (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (*.f64 (*.f64 v v) (PI.f64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) (PI.f64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) (PI.f64))))
(pow.f64 (*.f64 v (sqrt.f64 (PI.f64))) #s(literal 2 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) (PI.f64))))
(*.f64 v (*.f64 v (PI.f64)))
(*.f64 v (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v (PI.f64)))))
(*.f64 v (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v (PI.f64))) #s(literal -1 binary64)))
(*.f64 (*.f64 v v) (PI.f64))
(*.f64 (*.f64 v v) (neg.f64 (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (*.f64 v v) (*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1 binary64)))
(*.f64 (PI.f64) (*.f64 v v))
(*.f64 (PI.f64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(*.f64 (PI.f64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 v v) (PI.f64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) (PI.f64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (PI.f64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (*.f64 (*.f64 v v) (cbrt.f64 (PI.f64)))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (*.f64 v (*.f64 v (sqrt.f64 (PI.f64))))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (*.f64 v v) (cbrt.f64 (PI.f64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 v (*.f64 v (sqrt.f64 (PI.f64)))))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 (*.f64 v (PI.f64)) v)
(*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 (sqrt.f64 (sqrt.f64 (PI.f64))) (*.f64 v (*.f64 v (sqrt.f64 (PI.f64))))))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 (*.f64 v (sqrt.f64 (PI.f64))) (*.f64 v (sqrt.f64 (PI.f64))))
(*.f64 (-.f64 #s(literal 0 binary64) v) (-.f64 #s(literal 0 binary64) (*.f64 v (PI.f64))))
(*.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (neg.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (*.f64 (cbrt.f64 (PI.f64)) #s(literal -1 binary64)))
(*.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))
(*.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (*.f64 (sqrt.f64 (PI.f64)) #s(literal -1 binary64)))
(*.f64 (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (cbrt.f64 (PI.f64)) v))
(*.f64 (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 v (*.f64 v (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 v v) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
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(*.f64 (neg.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) (PI.f64))
(*.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (*.f64 v v))
(*.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) v)) (*.f64 v (PI.f64)))
(*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64))))) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 1 binary64)) (cbrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (PI.f64)) #s(literal 1/3 binary64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (sqrt.f64 (PI.f64)))) #s(literal 1 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (sqrt.f64 (PI.f64)))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (*.f64 (*.f64 v (*.f64 v (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64)))) (sqrt.f64 (sqrt.f64 (PI.f64))))

simplify948.0ms (9.2%)

Memory
-24.0MiB live, 917.4MiB allocated
Algorithm
1×egg-herbie
Rules
17 066×accelerator-lowering-fma.f32
17 066×accelerator-lowering-fma.f64
5 298×*-lowering-*.f32
5 298×*-lowering-*.f64
2 802×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671037
1493877
21790847
36241823
08218793
Stop Event
1×iter limit
1×node limit
Counts
48 → 48
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)))
(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))))
(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)))))))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
(* (pow v 2) (PI))
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 (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (fma.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) (fma.f64 (*.f64 v v) (fma.f64 v (/.f64 (*.f64 #s(literal 27/16 binary64) v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(fma.f64 v (*.f64 (fma.f64 #s(literal 4/3 binary64) (fma.f64 v (*.f64 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 (fma.f64 v v #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (/.f64 #s(literal 9/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (*.f64 v (*.f64 v v))) (+.f64 (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (fma.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) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (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 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.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 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (fma.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)) (/.f64 (+.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (/.f64 #s(literal 1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 v (*.f64 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 (fma.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (fma.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 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64)))) (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.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)))
(/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 (fma.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 v v))) (*.f64 v (-.f64 #s(literal 0 binary64) (*.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 (fma.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (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))) (+ (* 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 (fma.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (-.f64 (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (fma.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 (/.f64 #s(literal 1/36 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))) (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v v)))
(PI)
(PI.f64)
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(+ (PI) (* -1 (* (pow v 2) (PI))))
(*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.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))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.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))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(* (pow v 2) (+ (* -1 (PI)) (/ (PI) (pow v 2))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v v))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(fma.f64 (*.f64 v v) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 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))))))
(fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (fma.f64 (*.f64 v v) (/.f64 #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)))) (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)))))
(fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(+.f64 (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(fma.f64 v (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))) (fma.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (fma.f64 v (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(+.f64 (/.f64 #s(literal -1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) v) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (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)))))))
(fma.f64 v (/.f64 #s(literal -1/12 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (/.f64 #s(literal 1 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))
(* (pow v 2) (PI))
(*.f64 (PI.f64) (*.f64 v v))

eval133.0ms (1.3%)

Memory
-13.3MiB live, 101.7MiB allocated
Compiler

Compiled 14 674 to 1 959 computations (86.6% saved)

prune118.0ms (1.1%)

Memory
-4.4MiB live, 118.4MiB allocated
Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New4891490
Fresh000
Picked101
Done145
Total4915496
Accuracy
100.0%
Counts
496 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓98.0%
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (*.f64 v v) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
✓99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
✓99.5%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
✓98.0%
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Compiler

Compiled 216 to 103 computations (52.3% saved)

regimes14.0ms (0.1%)

Memory
19.7MiB live, 19.7MiB allocated
Counts
11 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 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 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (*.f64 v v) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (fma.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (PI.f64)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Outputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (*.f64 v v) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
Calls

4 calls:

4.0ms
v
3.0ms
(*.f64 v v)
3.0ms
(/.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))))))
3.0ms
(*.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)

regimes23.0ms (0.2%)

Memory
-18.3MiB live, 21.0MiB allocated
Counts
7 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 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 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
Outputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
Calls

4 calls:

15.0ms
(/.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))))))
3.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(*.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%)

Memory
19.1MiB live, 19.1MiB allocated
Counts
6 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (PI.f64) #s(literal 3 binary64)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 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 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (fma.f64 v v #s(literal 1 binary64)))))
Outputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
Calls

4 calls:

2.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(/.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))))))
2.0ms
(*.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
99.5%1v
99.5%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))))))
99.5%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)))))
99.5%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes6.0ms (0.1%)

Memory
12.5MiB live, 12.5MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
Outputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
Calls

4 calls:

2.0ms
v
1.0ms
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
1.0ms
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
1.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.5%1v
99.5%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))))))
99.5%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)))))
99.5%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes22.0ms (0.2%)

Memory
-28.0MiB live, 11.6MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

4 calls:

1.0ms
v
1.0ms
(*.f64 v v)
1.0ms
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
1.0ms
(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
Results
AccuracySegmentsBranch
98.0%1v
98.0%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))))))
98.0%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)))))
98.0%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify9.0ms (0.1%)

Memory
14.5MiB live, 14.5MiB allocated
Algorithm
1×egg-herbie
Rules
24×*-commutative_binary64
12×+-commutative_binary64
12×sub-neg_binary64
8×neg-sub0_binary64
8×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02757
14757
26257
37057
47557
57657
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (*.f64 v v) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
Outputs
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (*.f64 v v) (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64))) (PI.f64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v #s(literal -6 binary64)) #s(literal 2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))

soundness1.0s (9.9%)

Memory
-10.0MiB live, 802.2MiB allocated
Rules
16 800×accelerator-lowering-fma.f32
16 800×accelerator-lowering-fma.f64
12 362×accelerator-lowering-fma.f32
12 362×accelerator-lowering-fma.f64
9 856×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028103
1146103
2820103
37092103
0812796
01761142
1510985
21851943
36391932
08093883
01641
18339
260839
3637939
0802337
036148
1197144
21251144
08807132
01650
19148
261648
3577048
0843643
03353352
110782912
242892806
084322702
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 163 to 110 computations (32.5% saved)

preprocess65.0ms (0.6%)

Memory
-12.6MiB live, 105.4MiB allocated
Remove

(abs v)

Compiler

Compiled 302 to 190 computations (37.1% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...