Falkner and Boettcher, Equation (22+)

Time bar (total: 8.4s)

analyze5.0ms (0.1%)

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

Compiled 22 to 17 computations (22.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 1.0ms (38.4% of total)
ival-pi: 0.0ms (0% of total)
ival-sub: 0.0ms (0% of total)
ival-div: 0.0ms (0% of total)
const: 0.0ms (0% of total)
ival-sqrt: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample1.4s (16.6%)

Results
1.1s8256×0valid
1.0ms13×0invalid
Precisions
Click to see histograms. Total time spent on operations: 814.0ms
ival-mult: 421.0ms (51.7% of total)
ival-div: 132.0ms (16.2% of total)
ival-sub: 83.0ms (10.2% of total)
ival-pi: 75.0ms (9.2% of total)
ival-sqrt: 72.0ms (8.8% of total)
const: 27.0ms (3.3% of total)
backward-pass: 3.0ms (0.4% of total)
Bogosity

preprocess282.0ms (3.4%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
02660
18355
220248
370548
4224248
5592248
01620
14118
210816
333116
499416
5186716
6469216
0810416
Stop Event
1×iter limit
1×node limit
1×node limit
Calls
Call 1
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Call 2
Inputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
Outputs
(/ 4 (* (* (* 3 (PI)) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v))))))
(/ (/ (/ 4/3 (fnmsub v v -1)) (PI)) (sqrt (fnmsub v (* v 6) -2)))
(/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v)))))))
(/ (/ (/ 4/3 (fnmsub v v -1)) (PI)) (sqrt (fnmsub v (* v 6) -2)))
(neg (/ 4 (* (* (* 3 (PI)) (- 1 (* (neg v) (neg v)))) (sqrt (- 2 (* 6 (* (neg v) (neg v))))))))
(/ (/ 4/3 (* (PI) (fmsub v v 1))) (sqrt (fnmsub v (* v 6) -2)))
Symmetry

(abs v)

explain178.0ms (2.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(PI.f64)
00-0-(*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
00-0-(-.f64 #s(literal 1 binary64) (*.f64 v v))
00-0-(*.f64 #s(literal 6 binary64) (*.f64 v v))
00-0-(-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))
00-0-#s(literal 2 binary64)
00-0-v
00-0-#s(literal 6 binary64)
00-0-(*.f64 #s(literal 3 binary64) (PI.f64))
00-0-(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
00-0-(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
00-0-(sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))
00-0-#s(literal 4 binary64)
00-0-#s(literal 1 binary64)
00-0-#s(literal 3 binary64)
00-0-(*.f64 v v)
Results
94.0ms512×0valid
Compiler

Compiled 195 to 50 computations (74.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 61.0ms
ival-pi: 26.0ms (42.4% of total)
ival-mult: 20.0ms (32.6% of total)
ival-sub: 5.0ms (8.1% of total)
ival-div: 4.0ms (6.5% of total)
ival-sqrt: 4.0ms (6.5% of total)
const: 2.0ms (3.3% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 19 to 15 computations (21.1% saved)

prune1.0ms (0%)

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

Compiled 19 to 15 computations (21.1% saved)

simplify199.0ms (2.4%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Rules
2462×fnmadd-define
2100×sum4-define
1852×fma-lowering-fma.f32
1852×fma-lowering-fma.f64
1778×fmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01567
13064
25761
311161
431761
568061
6154161
7330861
8620961
0856861
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/ 4/3 (PI))
4/3
(PI)
(- 1 (* v v))
1
(* v v)
v
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
(* v -6)
-6
Outputs
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(PI)
(PI.f64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)

localize152.0ms (1.8%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
Results
100.0ms256×0valid
Compiler

Compiled 69 to 16 computations (76.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 6.0ms (28.5% of total)
ival-div: 5.0ms (23.7% of total)
...c/correct-round.rkt:119:19: 4.0ms (19% of total)
ival-sqrt: 2.0ms (9.5% of total)
ival-pi: 1.0ms (4.7% of total)
ival-add: 1.0ms (4.7% of total)
ival-sub: 1.0ms (4.7% of total)
const: 1.0ms (4.7% of total)
backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

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

12 calls:

TimeVariablePointExpression
2.0ms
v
@inf
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
2.0ms
v
@0
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
1.0ms
v
@inf
(/ (/ 4/3 (PI)) (- 1 (* v v)))
0.0ms
v
@inf
(sqrt (+ 2 (* v (* v -6))))
0.0ms
v
@0
(sqrt (+ 2 (* v (* v -6))))

rewrite361.0ms (4.3%)

Algorithm
1×batch-egg-rewrite
Rules
5116×*-lowering-*.f32
5116×*-lowering-*.f64
3678×/-lowering-/.f32
3678×/-lowering-/.f64
936×+-lowering-+.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01544
110042
275940
0813740
Stop Event
1×iter limit
1×node limit
Counts
6 → 499
Calls
Call 1
Inputs
(/ (/ (/ 4/3 (PI)) (- 1 (* v v))) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (PI)) (- 1 (* v v)))
(/ 4/3 (PI))
(PI)
(* v (* v -6))
(sqrt (+ 2 (* v (* v -6))))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) #s(literal -4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(neg.f64 (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(neg.f64 (/.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (*.f64 (PI.f64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
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(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (pow.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 (*.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 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(*.f64 (*.f64 v v) #s(literal -6 binary64))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal -6 binary64)) v)
(*.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 1 binary64))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))) #s(literal -8 binary64))) (sqrt.f64 (+.f64 (neg.f64 (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))) #s(literal -4 binary64))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -4 binary64) (neg.f64 (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) #s(literal 36 binary64))) #s(literal -4 binary64))) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))))
(/.f64 (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64))))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))))
(/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (*.f64 (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -216 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) (*.f64 #s(literal -6 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal -36 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)))

simplify271.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
4490×*-lowering-*.f32
4490×*-lowering-*.f64
3240×+-lowering-+.f64
3240×+-lowering-+.f32
1788×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01861116
1601949
22351890
08324890
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)))
(/ 4/3 (PI))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(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) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 27/16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (*.f64 v v))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(+.f64 (*.f64 (+.f64 (+.f64 (*.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 (+.f64 (*.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 27/16 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 #s(literal 4/3 binary64) (*.f64 v v))))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v (*.f64 v v)))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/.f64 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 (+.f64 (*.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 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 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 (+.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (+.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))))) (*.f64 v (*.f64 v v)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 (PI.f64) (*.f64 v (*.f64 v v))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal -4/3 binary64) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)))) (*.f64 v (*.f64 v v)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v))))))) (*.f64 v (*.f64 v v)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/.f64 (+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 #s(literal -4/3 binary64) (+.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (*.f64 v v)) (+.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (/.f64 (/.f64 #s(literal 1/144 binary64) (PI.f64)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/36 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64)))) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64)))) (pow.f64 v #s(literal 6 binary64))))))) (*.f64 v (*.f64 v v)))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (*.f64 v v) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 v v)) (PI.f64))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 v v)) (PI.f64))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(* -6 (pow v 2))
(*.f64 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))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 #s(literal -9/4 binary64) (*.f64 v v)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -6 binary64) (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 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 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 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -6 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) v))

eval147.0ms (1.8%)

Compiler

Compiled 14266 to 1734 computations (87.8% saved)

prune164.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New5443547
Fresh000
Picked011
Done000
Total5444548
Accuracy
100.0%
Counts
548 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶97.3%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify220.0ms (2.6%)

Algorithm
1×egg-herbie
Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 v v))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(sqrt.f64 #s(literal 1/2 binary64))
✓cost-diff0
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓cost-diff0
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Rules
2374×fnmadd-define
1904×fma-lowering-fma.f32
1904×fma-lowering-fma.f64
1830×fmsub-define
1708×sum4-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
021129
140123
270119
3132119
4364119
5753119
61451119
73043119
85750119
08199119
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ (* 4/3 (sqrt 1/2)) (PI))
(* 4/3 (sqrt 1/2))
4/3
(sqrt 1/2)
1/2
(PI)
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ 4/3 (PI))
4/3
(PI)
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/ 4/3 (- 1 (* v v)))
4/3
(- 1 (* v v))
1
(* v v)
v
(PI)
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
(* v -6)
-6
Outputs
(/ (* 4/3 (sqrt 1/2)) (PI))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(* 4/3 (sqrt 1/2))
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
4/3
#s(literal 4/3 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(PI)
(PI.f64)
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(PI)
(PI.f64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/ 4/3 (- 1 (* v v)))
(/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
4/3
#s(literal 4/3 binary64)
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
1
#s(literal 1 binary64)
(* v v)
(*.f64 v v)
v
(PI)
(PI.f64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)

localize100.0ms (1.2%)

Localize:

Found 12 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.4%
(/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓accuracy100.0%
(*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 1/2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Results
69.0ms256×0valid
Compiler

Compiled 131 to 22 computations (83.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 36.0ms
ival-div: 9.0ms (25.1% of total)
ival-sqrt: 8.0ms (22.3% of total)
ival-mult: 7.0ms (19.5% of total)
...c/correct-round.rkt:119:19: 5.0ms (13.9% of total)
ival-sub: 3.0ms (8.4% of total)
ival-add: 2.0ms (5.6% of total)
ival-pi: 1.0ms (2.8% of total)
const: 1.0ms (2.8% of total)
backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts
12 → 84
Calls
Call 1
Inputs
#<alt (/ (* 4/3 (sqrt 1/2)) (PI))>
#<alt (* 4/3 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (PI)>
#<alt (/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ 4/3 (PI))>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ (/ 4/3 (- 1 (* v v))) (PI))>
#<alt (/ 4/3 (- 1 (* v v)))>
#<alt (- 1 (* v v))>
#<alt (* v (* v -6))>
Outputs
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (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 (/ 4/3 (PI))>
#<alt (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt (/ -4/3 (* (pow v 2) (PI)))>
#<alt (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))>
#<alt 4/3>
#<alt (+ 4/3 (* 4/3 (pow v 2)))>
#<alt (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))>
#<alt (+ 4/3 (* (pow v 2) (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))))>
#<alt (/ -4/3 (pow v 2))>
#<alt (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))>
#<alt (/ -4/3 (pow v 2))>
#<alt (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))>
#<alt (/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))>
#<alt 1>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (+ 1 (* -1 (pow v 2)))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -1 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 1))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
Calls

21 calls:

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

rewrite371.0ms (4.4%)

Algorithm
1×batch-egg-rewrite
Rules
5724×*-lowering-*.f32
5724×*-lowering-*.f64
3490×/-lowering-/.f32
3490×/-lowering-/.f64
1196×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02180
112477
293973
0847973
Stop Event
1×iter limit
1×node limit
Counts
12 → 740
Calls
Call 1
Inputs
(/ (* 4/3 (sqrt 1/2)) (PI))
(* 4/3 (sqrt 1/2))
(sqrt 1/2)
(PI)
(/ (/ 4/3 (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ 4/3 (PI))
(sqrt (+ 2 (* v (* v -6))))
(/ (/ (/ 4/3 (- 1 (* v v))) (PI)) (sqrt (+ 2 (* v (* v -6)))))
(/ (/ 4/3 (- 1 (* v v))) (PI))
(/ 4/3 (- 1 (* v v)))
(- 1 (* v v))
(* v (* v -6))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 4/3 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64))))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64))))
(neg.f64 (*.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -4/3 binary64) (PI.f64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 4/3 binary64))))
(/.f64 #s(literal 4/3 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 4/3 binary64)))
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(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 #s(literal 4/3 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64))
(*.f64 #s(literal -4/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(*.f64 #s(literal -4/3 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 4/3 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) #s(literal 4/3 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 4/3 binary64)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(+.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (neg.f64 (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (neg.f64 (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(-.f64 #s(literal 1 binary64) (*.f64 v v))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 v v) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64)))
(fma.f64 v (-.f64 #s(literal 0 binary64) v) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) v) v #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 v v) #s(literal 1 binary64))
(neg.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 1 binary64))
(/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 v v)) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (*.f64 (*.f64 v v) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v (*.f64 v v)))))) #s(literal 1 binary64)) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))))) (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))) (+.f64 (*.f64 (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal 3 binary64))) (+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) (+.f64 (*.f64 (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (-.f64 (*.f64 v (*.f64 v (*.f64 v v))) #s(literal 1 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))) (*.f64 (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (/.f64 (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(/.f64 (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v)))) (*.f64 (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v))))) (+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 v (*.f64 v (*.f64 v v))) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 v v)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))))
(*.f64 #s(literal -1 binary64) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v (*.f64 v v)) (*.f64 v (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))))
(*.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v)))))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal -6 binary64)) v)
(*.f64 (*.f64 v (*.f64 v #s(literal -6 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(*.f64 (*.f64 v v) #s(literal -6 binary64))

simplify321.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
5110×*-lowering-*.f32
5110×*-lowering-*.f64
4000×+-lowering-+.f64
4000×+-lowering-+.f32
1398×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02541715
18451419
232791341
089201341
Stop Event
1×iter limit
1×node limit
Counts
84 → 84
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)))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (* (pow v 2) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))) (* 4/3 (/ (sqrt 1/2) (PI))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3))
(/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2)))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/ 4/3 (PI))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/ -4/3 (* (pow v 2) (PI)))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
4/3
(+ 4/3 (* 4/3 (pow v 2)))
(+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))
(+ 4/3 (* (pow v 2) (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))))
(/ -4/3 (pow v 2))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
(/ -4/3 (pow v 2))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
1
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(+ 1 (* -1 (pow v 2)))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* -1 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* (pow v 2) (- (/ 1 (pow v 2)) 1))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
Outputs
(* 4/3 (/ (sqrt 1/2) (PI)))
(*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (*.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))))))
(+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (*.f64 #s(literal 4/3 binary64) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) v)
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v))) (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 v (*.f64 v v)) v))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v (*.f64 v v)) v)) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) v) #s(literal -4/3 binary64)) (PI.f64))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (+.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (PI.f64))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v))) (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 v (*.f64 v v)) v))) (-.f64 #s(literal 0 binary64) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal -1/27 binary64) (*.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) v) v))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v (*.f64 v v)) v)) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -3 binary64) (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64)))) #s(literal -9/4 binary64)) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 v v)) v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 v v)) v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (sqrt -6)))
(*.f64 v (*.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal -1 binary64)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.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 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 v 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 (+.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v (*.f64 v v)) v)) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(* 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 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))) (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))))))
(*.f64 #s(literal 4/3 binary64) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (*.f64 (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 27/16 binary64)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))) (*.f64 v v))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 4/3 (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI)))) (* (pow v 2) (+ (* 4/3 (* (pow v 2) (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 1/2 (/ (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))) (* 4/3 (+ (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))) (+ (* 3/4 (/ 1 (* (PI) (sqrt 1/2)))) (/ (sqrt 1/2) (PI))))))))))
(+.f64 (*.f64 v (*.f64 (*.f64 v (*.f64 v v)) (+.f64 (*.f64 #s(literal 4/3 binary64) (+.f64 (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 #s(literal 27/8 binary64) (PI.f64)) (/.f64 #s(literal 135/16 binary64) (PI.f64))))) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (+.f64 (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)) (/.f64 #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 (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(* -4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 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 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (-.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 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 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))))) (pow v 3))
(/.f64 (+.f64 (*.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 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v (*.f64 v v)) v)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 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 (+.f64 (*.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 (/.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 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v (*.f64 v v)) v)) (/.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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))))) (pow.f64 v #s(literal 6 binary64)))))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (PI.f64))) (*.f64 v (*.f64 v v)))
(* 4/3 (/ (sqrt -1/6) (* (pow v 3) (PI))))
(/.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (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)))) (pow v 3)))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (*.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 v (*.f64 v v)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))))) (pow v 3)))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (*.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 (sqrt.f64 #s(literal -1/6 binary64)) (PI.f64))) (/.f64 #s(literal 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v (*.f64 v v)) v))))) (*.f64 v (*.f64 v v)))
(* -1 (/ (+ (* -4/3 (/ (sqrt -1/6) (PI))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (* 1/36 (/ 1 (* (PI) (sqrt -1/6))))) (pow v 2))) (+ (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))))) (pow v 4))) (* 4/3 (/ (+ (* -1 (/ (sqrt -1/6) (PI))) (+ (* 1/36 (/ 1 (* (PI) (sqrt -1/6)))) (+ (* 1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6)))) (* 1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (PI) (sqrt -1/6))))))) (pow v 6)))))) (pow v 3)))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (*.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 (/.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 1/144 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (*.f64 v (*.f64 v v)) v)) (/.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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (PI.f64)) (/.f64 #s(literal 5/1296 binary64) (PI.f64))))) (pow.f64 v #s(literal 6 binary64))))))) (*.f64 v (*.f64 v v)))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
(+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(+.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (*.f64 (/.f64 (*.f64 v v) (PI.f64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) #s(literal 4/3 binary64))))
(+ (* (pow v 2) (+ (* (pow v 2) (+ (* 4/3 (/ (pow v 2) (PI))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))) (* 4/3 (/ 1 (PI))))
(*.f64 (+.f64 (*.f64 (*.f64 v (*.f64 v v)) v) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 v v)) (PI.f64))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
(/ -4/3 (* (pow v 2) (PI)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (*.f64 v v)) (PI.f64))
(* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 2))) (* 4/3 (/ 1 (PI)))) (pow v 2))
(/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ (* 4/3 (/ 1 (PI))) (* 4/3 (/ 1 (* (pow v 2) (PI))))) (pow v 4))) (+ (* 4/3 (/ 1 (PI))) (/ 4/3 (* (pow v 2) (PI))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 v v)))) (*.f64 v v))) (*.f64 v v)) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (*.f64 v v))
4/3
#s(literal 4/3 binary64)
(+ 4/3 (* 4/3 (pow v 2)))
(*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) #s(literal 4/3 binary64))
(+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))
(+.f64 #s(literal 4/3 binary64) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) (*.f64 #s(literal 4/3 binary64) (*.f64 v v))))
(+ 4/3 (* (pow v 2) (+ 4/3 (* (pow v 2) (+ 4/3 (* 4/3 (pow v 2)))))))
(*.f64 (+.f64 (*.f64 (*.f64 v (*.f64 v v)) v) #s(literal 1 binary64)) (*.f64 (+.f64 (*.f64 v v) #s(literal 1 binary64)) #s(literal 4/3 binary64)))
(/ -4/3 (pow v 2))
(/.f64 #s(literal -4/3 binary64) (*.f64 v v))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v)) #s(literal -4/3 binary64)) (*.f64 v v))
(/ -4/3 (pow v 2))
(/.f64 #s(literal -4/3 binary64) (*.f64 v v))
(* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2)))
(/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 2))) 4/3) (pow v 2))
(/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v))
(/ (- (* -1 (/ (+ 4/3 (* 4/3 (/ 1 (pow v 2)))) (pow v 4))) (+ 4/3 (* 4/3 (/ 1 (pow v 2))))) (pow v 2))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -4/3 binary64) (*.f64 v v))) (*.f64 v v))) (*.f64 v v)) #s(literal -4/3 binary64)) (*.f64 v v))
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))
(* -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)))

eval122.0ms (1.5%)

Compiler

Compiled 22614 to 2600 computations (88.5% saved)

prune193.0ms (2.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New102451029
Fresh000
Picked123
Done011
Total102581033
Accuracy
100.0%
Counts
1033 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶97.3%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
▶98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
▶98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.3%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
▶98.8%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
▶97.3%
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
Compiler

Compiled 169 to 145 computations (14.2% saved)

simplify39.0ms (0.5%)

Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 (PI.f64) #s(literal -4/3 binary64))
✓cost-diff0
(*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff128
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓cost-diff0
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
✓cost-diff0
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
✓cost-diff0
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓cost-diff0
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
✓cost-diff0
(sqrt.f64 #s(literal 2 binary64))
✓cost-diff0
(PI.f64)
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓cost-diff0
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓cost-diff0
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓cost-diff0
(PI.f64)
✓cost-diff0
(*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓cost-diff0
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
Rules
576×fma-define
390×sum3-define
224×fmsub-define
220×fma-lowering-fma.f32
220×fma-lowering-fma.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
025216
140201
258201
371201
494201
5121201
6149201
7188201
8245201
9305201
10394201
11529201
12686201
13931201
141266201
151287201
161289201
01289201
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt (+ 2 (* v (* v -6))))))
4/3
(* (PI) (sqrt (+ 2 (* v (* v -6)))))
(PI)
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
(/ (/ 4/3 (PI)) (sqrt 2))
(/ 4/3 (PI))
4/3
(PI)
(sqrt 2)
2
(/ (/ 4/3 (sqrt (+ 2 (* v (* v -6))))) (PI))
(/ 4/3 (sqrt (+ 2 (* v (* v -6)))))
4/3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
(PI)
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(pow (+ 2 (* v (* v -6))) -1/2)
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
-1/2
(/ (PI) 4/3)
(PI)
4/3
(/ -1 (* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6))))))
-1
(* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))
(/ (PI) -4/3)
(PI)
-4/3
(sqrt (+ 2 (* v (* v -6))))
(+ 2 (* v (* v -6)))
2
(* v (* v -6))
v
(* v -6)
-6
Outputs
(/ 4/3 (* (PI) (sqrt (+ 2 (* v (* v -6))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
4/3
#s(literal 4/3 binary64)
(* (PI) (sqrt (+ 2 (* v (* v -6)))))
(*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
(PI)
(PI.f64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(/ (/ 4/3 (PI)) (sqrt 2))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/ 4/3 (PI))
(/.f64 #s(literal 4/3 binary64) (PI.f64))
4/3
#s(literal 4/3 binary64)
(PI)
(PI.f64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ (/ 4/3 (sqrt (+ 2 (* v (* v -6))))) (PI))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
(/ 4/3 (sqrt (+ 2 (* v (* v -6)))))
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
4/3
#s(literal 4/3 binary64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
(PI)
(PI.f64)
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(pow (+ 2 (* v (* v -6))) -1/2)
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))) #s(literal -1/2 binary64))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)
-1/2
#s(literal -1/2 binary64)
(/ (PI) 4/3)
(/.f64 (PI.f64) #s(literal 4/3 binary64))
(PI)
(PI.f64)
4/3
#s(literal 4/3 binary64)
(/ -1 (* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))))
-1
#s(literal -1 binary64)
(* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))) (/.f64 (PI.f64) #s(literal -4/3 binary64)))
(/ (PI) -4/3)
(/.f64 (PI.f64) #s(literal -4/3 binary64))
(PI)
(PI.f64)
-4/3
#s(literal -4/3 binary64)
(sqrt (+ 2 (* v (* v -6))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v))))
(+ 2 (* v (* v -6)))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal -6 binary64) (*.f64 v v)))
2
#s(literal 2 binary64)
(* v (* v -6))
(*.f64 #s(literal -6 binary64) (*.f64 v v))
v
(* v -6)
(*.f64 v #s(literal -6 binary64))
-6
#s(literal -6 binary64)

localize170.0ms (2%)

Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy100.0%
(*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓accuracy100.0%
(PI.f64)
✓accuracy100.0%
(pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
✓accuracy98.5%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
✓accuracy98.5%
(/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy100.0%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓accuracy100.0%
(sqrt.f64 #s(literal 2 binary64))
✓accuracy100.0%
(PI.f64)
✓accuracy98.4%
(/.f64 #s(literal 4/3 binary64) (PI.f64))
✓accuracy100.0%
(*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓accuracy100.0%
(sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓accuracy99.8%
(*.f64 v (*.f64 v #s(literal -6 binary64)))
Results
110.0ms256×0valid
Compiler

Compiled 220 to 26 computations (88.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 63.0ms
...c/correct-round.rkt:119:19: 27.0ms (42.6% of total)
ival-div: 14.0ms (22.1% of total)
ival-mult: 8.0ms (12.6% of total)
ival-pow: 6.0ms (9.5% of total)
ival-sqrt: 4.0ms (6.3% of total)
ival-pi: 2.0ms (3.2% of total)
ival-add: 1.0ms (1.6% of total)
const: 1.0ms (1.6% of total)
backward-pass: 0.0ms (0% of total)

series9.0ms (0.1%)

Counts
16 → 132
Calls
Call 1
Inputs
#<alt (/ 4/3 (* (PI) (sqrt (+ 2 (* v (* v -6))))))>
#<alt (* (PI) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (PI)>
#<alt (sqrt (+ 2 (* v (* v -6))))>
#<alt (/ (/ 4/3 (PI)) (sqrt 2))>
#<alt (/ 4/3 (PI))>
#<alt (sqrt 2)>
#<alt (/ (/ 4/3 (sqrt (+ 2 (* v (* v -6))))) (PI))>
#<alt (/ 4/3 (sqrt (+ 2 (* v (* v -6)))))>
#<alt (+ 2 (* v (* v -6)))>
#<alt (/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))>
#<alt (pow (+ 2 (* v (* v -6))) -1/2)>
#<alt (* v (* v -6))>
#<alt (/ -1 (* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6))))))>
#<alt (* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))>
#<alt (/ (PI) -4/3)>
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 (* (PI) (sqrt 2))>
#<alt (+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))>
#<alt (* v (* (PI) (sqrt -6)))>
#<alt (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))>
#<alt (* v (sqrt -6))>
#<alt (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))>
#<alt (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))>
#<alt (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (sqrt -6)))>
#<alt (* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))>
#<alt (* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* 4/3 (sqrt 1/2))>
#<alt (+ (* 4/3 (sqrt 1/2)) (/ (pow v 2) (sqrt 1/2)))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (/ 1 (sqrt 1/2)))))>
#<alt (+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (/ 1 (sqrt 1/2)))))>
#<alt (* 4/3 (/ (sqrt -1/6) v))>
#<alt (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) v))>
#<alt (* -1 (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt 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 (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))>
#<alt (/ (sqrt -1/6) v)>
#<alt (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)>
#<alt (* -1 (/ (sqrt -1/6) v))>
#<alt (* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* -6 (pow v 2))>
#<alt (* 4/3 (/ (sqrt 1/2) (PI)))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))>
#<alt (* 4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)>
#<alt (* -4/3 (/ (sqrt -1/6) (* v (PI))))>
#<alt (* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))>
#<alt (* -3/4 (* (PI) (sqrt 2)))>
#<alt (+ (* -3/4 (* (PI) (sqrt 2))) (* 9/4 (/ (* (pow v 2) (PI)) (sqrt 2))))>
#<alt (+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* 27/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))))))>
#<alt (+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* 27/8 (/ (PI) (pow (sqrt 2) 3))) (* 81/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))))))))>
#<alt (* -3/4 (* v (* (PI) (sqrt -6))))>
#<alt (* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))>
#<alt (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))>
#<alt (* 3/4 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))>
#<alt (* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))))>
Calls

33 calls:

TimeVariablePointExpression
2.0ms
v
@inf
(* (PI) (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@inf
(/ 4/3 (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@inf
(pow (+ 2 (* v (* v -6))) -1/2)
0.0ms
v
@inf
(* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))
0.0ms
v
@0
(* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))

rewrite420.0ms (5%)

Algorithm
1×batch-egg-rewrite
Rules
4950×*-lowering-*.f32
4950×*-lowering-*.f64
3144×/-lowering-/.f32
3144×/-lowering-/.f64
1104×sum5-define
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
025124
1139113
2871113
37387113
08352113
Stop Event
1×iter limit
1×node limit
Counts
16 → 1403
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt (+ 2 (* v (* v -6))))))
(* (PI) (sqrt (+ 2 (* v (* v -6)))))
(PI)
(sqrt (+ 2 (* v (* v -6))))
(/ (/ 4/3 (PI)) (sqrt 2))
(/ 4/3 (PI))
(sqrt 2)
(/ (/ 4/3 (sqrt (+ 2 (* v (* v -6))))) (PI))
(/ 4/3 (sqrt (+ 2 (* v (* v -6)))))
(+ 2 (* v (* v -6)))
(/ (pow (+ 2 (* v (* v -6))) -1/2) (/ (PI) 4/3))
(pow (+ 2 (* v (* v -6))) -1/2)
(* v (* v -6))
(/ -1 (* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6))))))
(* (/ (PI) -4/3) (sqrt (+ 2 (* v (* v -6)))))
(/ (PI) -4/3)
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal 4/3 binary64) (PI.f64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (PI.f64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal -4/3 binary64))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(neg.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))))
(/.f64 #s(literal 4/3 binary64) (/.f64 (PI.f64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal -4/3 binary64) (PI.f64))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (/.f64 #s(literal 4/3 binary64) (PI.f64))))
(/.f64 #s(literal 1 binary64) (/.f64 (cbrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (PI.f64)) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))) (/.f64 (PI.f64) #s(literal -4/3 binary64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (PI.f64)) #s(literal 3/4 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64)))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal -4/3 binary64))) #s(literal -1 binary64))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64)) (PI.f64)) (/.f64 #s(literal 3/4 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/4 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal -4/3 binary64)))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (PI.f64))) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (sqrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (*.f64 (PI.f64) (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))) #s(literal 4/3 binary64)) (cbrt.f64 (PI.f64))))
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(/.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal 4/3 binary64))
(/.f64 #s(literal 3/4 binary64) (/.f64 #s(literal -1 binary64) (PI.f64)))
(/.f64 #s(literal -3/4 binary64) (/.f64 #s(literal 1 binary64) (PI.f64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (*.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))) (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 4/3 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal -4/3 binary64))
(pow.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal -1 binary64))
(*.f64 (PI.f64) #s(literal -3/4 binary64))
(*.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal -4/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -4/3 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal -3/4 binary64)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -4/3 binary64))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal -4/3 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (cbrt.f64 (PI.f64))) #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4/3 binary64)))
(*.f64 (sqrt.f64 (PI.f64)) (neg.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4/3 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) #s(literal 3/4 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal 3/4 binary64))
(*.f64 #s(literal 3/4 binary64) (-.f64 #s(literal 0 binary64) (PI.f64)))
(*.f64 #s(literal 3/4 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (PI.f64)) #s(literal -1 binary64)))
(*.f64 #s(literal -3/4 binary64) (PI.f64))
(*.f64 #s(literal -3/4 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4/3 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 4/3 binary64)))
(*.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal -4/3 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(*.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal -4/3 binary64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal -3/4 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (PI.f64))) #s(literal 3/4 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (PI.f64))) #s(literal -3/4 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64)))) (sqrt.f64 (PI.f64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))

simplify398.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
5186×*-lowering-*.f32
5186×*-lowering-*.f64
3580×+-lowering-+.f64
3580×+-lowering-+.f32
2504×/-lowering-/.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03033042
110262375
238042314
086592314
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))
(* (PI) (sqrt 2))
(+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))
(* v (* (PI) (sqrt -6)))
(* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (* (PI) (sqrt -6))))
(* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))
(sqrt 2)
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(* v (sqrt -6))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (sqrt -6)))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* 4/3 (sqrt 1/2))
(+ (* 4/3 (sqrt 1/2)) (/ (pow v 2) (sqrt 1/2)))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (/ 1 (sqrt 1/2)))))
(+ (* 4/3 (sqrt 1/2)) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (/ 1 (sqrt 1/2)))))
(* 4/3 (/ (sqrt -1/6) v))
(/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v)
(* -4/3 (/ (sqrt -1/6) v))
(* -1 (/ (- (* 4/3 (sqrt -1/6)) (* 1/27 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))) (* 4/3 (sqrt -1/6)))) (/ 1/27 (* (pow v 2) (sqrt -1/6)))) v))
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))
(sqrt 1/2)
(+ (sqrt 1/2) (* 3/4 (/ (pow v 2) (sqrt 1/2))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 3/4 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* (pow v 2) (+ (* (pow v 2) (+ (* 1/2 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 3/4 (/ 1 (sqrt 1/2))))))
(/ (sqrt -1/6) v)
(/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v)
(/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v)
(* -1 (/ (sqrt -1/6) v))
(* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* -6 (pow v 2))
(* 4/3 (/ (sqrt 1/2) (PI)))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(* -3/4 (* (PI) (sqrt 2)))
(+ (* -3/4 (* (PI) (sqrt 2))) (* 9/4 (/ (* (pow v 2) (PI)) (sqrt 2))))
(+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* 27/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))))))
(+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* 27/8 (/ (PI) (pow (sqrt 2) 3))) (* 81/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))))))))
(* -3/4 (* v (* (PI) (sqrt -6))))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6))))))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(* 3/4 (* v (* (PI) (sqrt -6))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (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 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64)))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) v)
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 #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 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) v) (PI.f64))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.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))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (PI.f64) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 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 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 #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))
(* (PI) (sqrt 2))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal -3 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 #s(literal -9/4 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal 2 binary64))) (*.f64 #s(literal -3 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (*.f64 #s(literal -3 binary64) (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 v v)) #s(literal -27/2 binary64)) (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)))))))
(* v (* (PI) (sqrt -6)))
(*.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))))
(* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(*.f64 v (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(*.f64 v (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (PI.f64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))))
(* -1 (* v (* (PI) (sqrt -6))))
(-.f64 #s(literal 0 binary64) (*.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(*.f64 (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(*.f64 (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))
(*.f64 (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal 1/12 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (PI.f64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal -3 binary64) (*.f64 v (/.f64 v (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 #s(literal -9/4 binary64) (*.f64 v v)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 v (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))))
(* -1 (* v (sqrt -6)))
(*.f64 v (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64))))))))
(* -1 (* v (- (+ (sqrt -6) (+ (/ 1 (* (pow v 2) (sqrt -6))) (* 1/2 (/ 1 (* (pow v 6) (pow (sqrt -6) 5)))))) (* 1/2 (/ 1 (* (pow v 4) (pow (sqrt -6) 3)))))))
(*.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 v #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (*.f64 #s(literal 6 binary64) (sqrt.f64 #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64)))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
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(-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal -1/6 binary64)) v))
(* -1 (/ (- (sqrt -1/6) (* 1/36 (/ 1 (* (pow v 2) (sqrt -1/6))))) v))
(/.f64 (+.f64 (/.f64 #s(literal 1/36 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))) v)
(* -1 (/ (- (+ (sqrt -1/6) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(/.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -1/36 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) (/.f64 #s(literal -1/144 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (/ (- (+ (sqrt -1/6) (+ (* -1/2 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (sqrt -1/6)))) (* -1/2 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (sqrt -1/6)))))) (/ 1/36 (* (pow v 2) (sqrt -1/6)))) v))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (+.f64 (sqrt.f64 #s(literal -1/6 binary64)) (/.f64 #s(literal -1/36 binary64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64)))))) (*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) v))
(* -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))
(* 4/3 (/ (sqrt 1/2) (PI)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (/ (pow v 2) (* (PI) (sqrt 1/2))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (/.f64 (*.f64 v v) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (/.f64 (*.f64 #s(literal 9/4 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 v (*.f64 v (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 binary64) (PI.f64)))))))))
(* 4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) v)
(/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v)
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 #s(literal 1/27 binary64) (*.f64 (PI.f64) (*.f64 v (*.f64 v (sqrt.f64 #s(literal -1/6 binary64))))))) (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 (*.f64 v v) (*.f64 v v)))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 #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 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) v) (PI.f64))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.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))
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/108 binary64) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (*.f64 (PI.f64) (*.f64 (*.f64 v v) (*.f64 v v))))) (-.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 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 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (+.f64 (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64))))) (/.f64 #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))
(* -3/4 (* (PI) (sqrt 2)))
(*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -3/4 binary64))
(+ (* -3/4 (* (PI) (sqrt 2))) (* 9/4 (/ (* (pow v 2) (PI)) (sqrt 2))))
(+.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -3/4 binary64)) (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 v v)) #s(literal 9/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* 27/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))))))
(+.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -3/4 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/4 binary64)) (/.f64 (*.f64 #s(literal 27/16 binary64) (*.f64 (PI.f64) (*.f64 v v))) (sqrt.f64 #s(literal 2 binary64))))))
(+ (* -3/4 (* (PI) (sqrt 2))) (* (pow v 2) (+ (* 9/4 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* 27/8 (/ (PI) (pow (sqrt 2) 3))) (* 81/8 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))))))))
(+.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -3/4 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 9/4 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 27/16 binary64)) (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 v v)) #s(literal 81/8 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))))))))
(* -3/4 (* v (* (PI) (sqrt -6))))
(*.f64 (*.f64 (PI.f64) v) (*.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal -3/4 binary64)))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6))))))
(*.f64 (*.f64 v #s(literal -3/4 binary64)) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))
(*.f64 v (+.f64 (*.f64 (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal -3/4 binary64)) (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal -1/16 binary64)) (*.f64 (*.f64 v v) (*.f64 v v)))))
(* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(*.f64 v (+.f64 (*.f64 (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal -3/4 binary64)) (+.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal -1/16 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 (*.f64 #s(literal -3/8 binary64) (/.f64 (PI.f64) (pow.f64 v #s(literal 6 binary64)))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))))
(* 3/4 (* v (* (PI) (sqrt -6))))
(*.f64 #s(literal 3/4 binary64) (*.f64 v (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))))))
(*.f64 v (*.f64 #s(literal 3/4 binary64) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3))))))))
(*.f64 v (+.f64 (*.f64 #s(literal 3/4 binary64) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))) (neg.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal -1/16 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))))))
(* -1 (* v (+ (* -3/4 (* (PI) (sqrt -6))) (+ (* -3/4 (/ (PI) (* (pow v 2) (sqrt -6)))) (+ (* -3/8 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (* 3/8 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))))))))
(*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) #s(literal -3/4 binary64)) (+.f64 (/.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) #s(literal -1/16 binary64)) (*.f64 (*.f64 v v) (*.f64 v v))) (/.f64 (*.f64 #s(literal -3/8 binary64) (/.f64 (PI.f64) (pow.f64 v #s(literal 6 binary64)))) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64))))) (-.f64 #s(literal 0 binary64) v))

eval300.0ms (3.6%)

Compiler

Compiled 46222 to 3876 computations (91.6% saved)

prune197.0ms (2.3%)

Pruning

9 alts after pruning (1 fresh and 8 done)

PrunedKeptTotal
New219412195
Fresh000
Picked055
Done033
Total219492203
Accuracy
100.0%
Counts
2203 → 9
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓97.3%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
✓98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.3%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
✓98.8%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
▶49.7%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))))
✓97.3%
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
Compiler

Compiled 124 to 103 computations (16.9% saved)

simplify384.0ms (4.6%)

Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓cost-diff256
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
✓cost-diff256
(sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
✓cost-diff256
(*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))))
✓cost-diff256
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))))
Rules
5958×*-lowering-*.f32
5958×*-lowering-*.f64
3198×pow-lowering-pow.f64
3198×pow-lowering-pow.f32
3140×cube-prod
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01273
12773
25773
310053
414653
516653
621853
758653
8162953
9189153
10235753
11264253
12303453
13353153
14415653
15444153
16464053
17474053
18485153
19497353
20574853
21686953
22737253
23746953
24756653
25766353
26777853
27788353
0817953
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))
4/3
(* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v))))))
(PI)
(sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))
(* (* v v) (+ -6 (/ 2 (* v v))))
(* v v)
v
(+ -6 (/ 2 (* v v)))
-6
(/ 2 (* v v))
2
Outputs
(/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))))
4/3
#s(literal 4/3 binary64)
(* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v))))))
(*.f64 (PI.f64) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))))
(PI)
(PI.f64)
(sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))
(sqrt.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64)))
(* (* v v) (+ -6 (/ 2 (* v v))))
(+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal 2 binary64))
(* v v)
(*.f64 v v)
v
(+ -6 (/ 2 (* v v)))
(+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))
-6
#s(literal -6 binary64)
(/ 2 (* v v))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
2
#s(literal 2 binary64)

localize49.0ms (0.6%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
✓accuracy100.0%
(sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))
✓accuracy100.0%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))))
✓accuracy99.8%
(/.f64 #s(literal 2 binary64) (*.f64 v v))
✓accuracy52.1%
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
Results
34.0ms256×0valid
Compiler

Compiled 75 to 13 computations (82.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 5.0ms (25.9% of total)
...c/correct-round.rkt:119:19: 5.0ms (25.9% of total)
ival-div: 3.0ms (15.6% of total)
ival-sqrt: 2.0ms (10.4% of total)
ival-pi: 1.0ms (5.2% of total)
ival-add: 1.0ms (5.2% of total)
const: 1.0ms (5.2% of total)
backward-pass: 0.0ms (0% of total)

series29.0ms (0.4%)

Counts
5 → 60
Calls
Call 1
Inputs
#<alt (/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))>
#<alt (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v))))))>
#<alt (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))>
#<alt (* (* v v) (+ -6 (/ 2 (* v v))))>
#<alt (/ 2 (* 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 (* (PI) (sqrt 2))>
#<alt (+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))>
#<alt (+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))>
#<alt (* v (* (PI) (sqrt -6)))>
#<alt (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (* (PI) (sqrt -6))))>
#<alt (* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))>
#<alt (* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))>
#<alt (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 (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
#<alt (/ 2 (pow v 2))>
Calls

15 calls:

TimeVariablePointExpression
17.0ms
v
@0
(/ 2 (* v v))
10.0ms
v
@inf
(* (* v v) (+ -6 (/ 2 (* v v))))
0.0ms
v
@0
(/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))
0.0ms
v
@0
(sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))
0.0ms
v
@inf
(/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))

rewrite252.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
3584×*-lowering-*.f32
3584×*-lowering-*.f64
2436×/-lowering-/.f32
2436×/-lowering-/.f64
1572×fma-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01258
18351
261738
3625638
0835038
Stop Event
1×iter limit
1×node limit
Counts
5 → 227
Calls
Call 1
Inputs
(/ 4/3 (* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))))
(* (PI) (sqrt (* (* v v) (+ -6 (/ 2 (* v v))))))
(sqrt (* (* v v) (+ -6 (/ 2 (* v v)))))
(* (* v v) (+ -6 (/ 2 (* v v))))
(/ 2 (* v v))
Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(neg.f64 (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (PI.f64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) v))))
(/.f64 #s(literal -4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) (PI.f64))))
(/.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (PI.f64)) #s(literal 3/4 binary64))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal -4/3 binary64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 4/3 binary64)))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (cbrt.f64 (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (sqrt.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) (PI.f64))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (PI.f64))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) v)) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (neg.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) v))) (neg.f64 (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) v) (*.f64 (PI.f64) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -4/3 binary64) (PI.f64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))) (PI.f64))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) v))) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))
(/.f64 (*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) #s(literal 4/3 binary64)) (PI.f64))
(/.f64 (*.f64 #s(literal -4/3 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (PI.f64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal -4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (-.f64 #s(literal 0 binary64) (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 v)) (sqrt.f64 (*.f64 v (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (*.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) (PI.f64)))) (sqrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))) v)
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 1 binary64)) (PI.f64))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) #s(literal 2/3 binary64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))
(pow.f64 (/.f64 (/.f64 (PI.f64) #s(literal 4/3 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 4/3 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (PI.f64)))
(*.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(*.f64 #s(literal -4/3 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))))
(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (PI.f64)) #s(literal 4/3 binary64))
(*.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))))
(*.f64 (/.f64 #s(literal -4/3 binary64) (PI.f64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))))))
(*.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64)))) #s(literal 4/3 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (PI.f64))) #s(literal -4/3 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal -1/2 binary64)) (/.f64 #s(literal 4/3 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (/.f64 #s(literal 1 binary64) (PI.f64)))
(*.f64 (/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) v)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 v)) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (sqrt.f64 (*.f64 v (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))))
(*.f64 (/.f64 #s(literal 4/3 binary64) v) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) v))
(*.f64 (/.f64 #s(literal 4/3 binary64) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))) #s(literal 1/4 binary64))))
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(/.f64 (*.f64 v v) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) #s(literal -12 binary64))) (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 8 binary64) (*.f64 #s(literal -216 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)) (+.f64 (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))) (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))) (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v))))))))
(/.f64 (+.f64 #s(literal 8 binary64) (*.f64 #s(literal -216 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) #s(literal -12 binary64))) (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v))))))
(/.f64 (+.f64 #s(literal 8 binary64) (*.f64 #s(literal -216 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 4 binary64) (-.f64 (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (*.f64 (*.f64 v v) #s(literal -12 binary64)))))
(/.f64 (+.f64 (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -4 binary64)) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64)))
(/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))))
(/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))
(/.f64 (neg.f64 (+.f64 #s(literal 8 binary64) (*.f64 #s(literal -216 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v))))))) (neg.f64 (+.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) #s(literal -12 binary64))) (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))))
(/.f64 (neg.f64 (+.f64 (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -4 binary64))) (neg.f64 (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))
(/.f64 (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))) #s(literal -36 binary64)))
(/.f64 (neg.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v))))))) (+.f64 #s(literal 6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(/.f64 (-.f64 #s(literal 4 binary64) (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (-.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))
(/.f64 (*.f64 (*.f64 v v) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))))) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))) #s(literal -36 binary64)))
(/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -36 binary64) (/.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(/.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -36 binary64))) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 v v)) #s(literal 6 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (*.f64 v v)) (+.f64 (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))) #s(literal -36 binary64)))
(/.f64 (*.f64 (+.f64 #s(literal -36 binary64) (/.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 v v)) (+.f64 #s(literal 6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -36 binary64)) (*.f64 v v)) (+.f64 (/.f64 #s(literal 2 binary64) (*.f64 v v)) #s(literal 6 binary64)))
(*.f64 v (*.f64 v (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(*.f64 (*.f64 v v) (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))
(*.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))) (*.f64 v v))
(*.f64 (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)))) (*.f64 v v)))
(*.f64 (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v)))) (/.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)))))
(*.f64 (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))) (*.f64 v v)))
(*.f64 (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v))))) (/.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(*.f64 (*.f64 v (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))) v)
(*.f64 (+.f64 #s(literal 8 binary64) (*.f64 #s(literal -216 binary64) (*.f64 (*.f64 v v) (*.f64 v (*.f64 v (*.f64 v v)))))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 4 binary64) (*.f64 (*.f64 v v) #s(literal -12 binary64))) (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))))
(*.f64 (+.f64 (*.f64 #s(literal 36 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (*.f64 v v) #s(literal -6 binary64)) #s(literal -2 binary64))))
(*.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)))))
(*.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))))
(*.f64 (/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 46656 binary64) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)))))) (+.f64 #s(literal 1296 binary64) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)) #s(literal 36 binary64)))))
(*.f64 (/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (-.f64 #s(literal 1296 binary64) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v)) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))))) (-.f64 #s(literal 36 binary64) (/.f64 (-.f64 (/.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -12 binary64)) (*.f64 v v))))
(*.f64 (/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))
(*.f64 (/.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal 36 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal -216 binary64) (/.f64 (/.f64 #s(literal 8 binary64) (*.f64 v (*.f64 v v))) (*.f64 v (*.f64 v v))))) (+.f64 #s(literal 36 binary64) (*.f64 (/.f64 #s(literal 2 binary64) (*.f64 v v)) (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(exp.f64 (*.f64 (log.f64 (/.f64 v (/.f64 #s(literal 2 binary64) v))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))
(neg.f64 (/.f64 #s(literal -2 binary64) (*.f64 v v)))
(neg.f64 (*.f64 (/.f64 #s(literal -2 binary64) (*.f64 v v)) #s(literal 1 binary64)))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/.f64 #s(literal 1 binary64) (/.f64 v (/.f64 #s(literal 2 binary64) v)))
(/.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 2 binary64) v) v)
(/.f64 (/.f64 #s(literal 2 binary64) v) (neg.f64 (-.f64 #s(literal 0 binary64) v)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 v v) #s(literal -2 binary64)))
(/.f64 (/.f64 #s(literal -2 binary64) v) (-.f64 #s(literal 0 binary64) v))
(/.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 v #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) v)) (-.f64 #s(literal 0 binary64) v))
(/.f64 (*.f64 (/.f64 #s(literal -2 binary64) v) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) v))
(pow.f64 (/.f64 v (/.f64 #s(literal 2 binary64) v)) #s(literal -1 binary64))
(*.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 v v)))
(*.f64 (/.f64 #s(literal 2 binary64) (*.f64 v v)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))
(*.f64 #s(literal -2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 v v)))
(*.f64 #s(literal -2 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (*.f64 v v)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 2 binary64) v) (/.f64 #s(literal 1 binary64) v))
(*.f64 (/.f64 #s(literal 2 binary64) v) (*.f64 (/.f64 #s(literal 1 binary64) v) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v)))
(*.f64 (/.f64 #s(literal -2 binary64) v) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) v)))
(*.f64 (/.f64 #s(literal 1 binary64) v) (/.f64 #s(literal 2 binary64) v))
(*.f64 (/.f64 #s(literal -1 binary64) (*.f64 v v)) #s(literal -2 binary64))
(*.f64 (pow.f64 (/.f64 v (/.f64 #s(literal 2 binary64) v)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 v (/.f64 #s(literal 2 binary64) v)) #s(literal -1/2 binary64)))

simplify259.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
4806×*-lowering-*.f32
4806×*-lowering-*.f64
1972×/-lowering-/.f32
1972×/-lowering-/.f64
1466×fma-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01911005
1602883
22195846
37360846
08113846
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
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))
(* (PI) (sqrt 2))
(+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))
(* v (* (PI) (sqrt -6)))
(* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (* (PI) (sqrt -6))))
(* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))
(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))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 2 (pow v 2))
(/ 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))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 v (/.f64 v (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64)))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 #s(literal 9/4 binary64) (*.f64 v (/.f64 v (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))))))))
(+ (* 4/3 (/ (sqrt 1/2) (PI))) (* (pow v 2) (+ (* (pow v 2) (+ (* 2/3 (/ (* (pow v 2) (- 27/2 (* 3/4 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (* (PI) (sqrt 1/2)))) (* 2/3 (/ (- 9/2 (* 9/16 (/ 1 (pow (sqrt 1/2) 2)))) (* (PI) (sqrt 1/2)))))) (/ 1 (* (PI) (sqrt 1/2))))))
(+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (PI.f64))) (*.f64 (*.f64 v v) (*.f64 (/.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal 135/16 binary64)) (PI.f64)) (/.f64 #s(literal 27/8 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)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (+.f64 (/.f64 (/.f64 #s(literal -1/108 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))) v)
(/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v)
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) v)
(* -4/3 (/ (sqrt -1/6) (* v (PI))))
(/.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) v) (PI.f64))
(* -1 (/ (- (* 4/3 (/ (sqrt -1/6) (PI))) (* 1/27 (/ 1 (* (pow v 2) (* (PI) (sqrt -1/6)))))) v))
(/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal -4/3 binary64)) (PI.f64))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI)))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (-.f64 (/.f64 #s(literal 1/108 binary64) (*.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))) (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))))) v)
(* -1 (/ (- (+ (* -2/3 (/ (+ 1/162 (* 1/36 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (pow (sqrt -1/6) 2)))) (* (pow v 6) (* (PI) (sqrt -1/6))))) (+ (* -2/3 (/ (+ 1/54 (* 1/1296 (/ 1 (pow (sqrt -1/6) 2)))) (* (pow v 4) (* (PI) (sqrt -1/6))))) (* 4/3 (/ (sqrt -1/6) (PI))))) (/ 1/27 (* (pow v 2) (* (PI) (sqrt -1/6))))) v))
(/.f64 (+.f64 (+.f64 (/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal -1/6 binary64))) (PI.f64)) (/.f64 (/.f64 #s(literal -1/27 binary64) (*.f64 v v)) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64))))) (*.f64 (/.f64 #s(literal -2/3 binary64) (*.f64 (PI.f64) (sqrt.f64 #s(literal -1/6 binary64)))) (+.f64 (/.f64 #s(literal 1/72 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 5/1296 binary64) (pow.f64 v #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) v))
(* (PI) (sqrt 2))
(*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* -3 (/ (* (pow v 2) (PI)) (sqrt 2))) (* (PI) (sqrt 2)))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -3 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -9/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 3))) (* -3 (/ (PI) (sqrt 2))))))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (PI.f64) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 v v)) #s(literal -9/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(+ (* (PI) (sqrt 2)) (* (pow v 2) (+ (* -3 (/ (PI) (sqrt 2))) (* (pow v 2) (+ (* -27/2 (/ (* (pow v 2) (PI)) (pow (sqrt 2) 5))) (* -9/2 (/ (PI) (pow (sqrt 2) 3))))))))
(+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (PI.f64) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (*.f64 v v) #s(literal -27/2 binary64))) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 (*.f64 (PI.f64) #s(literal -9/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))))))
(* v (* (PI) (sqrt -6)))
(*.f64 (PI.f64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(*.f64 v (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))))
(* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(*.f64 v (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v))))))))
(* -1 (* v (* (PI) (sqrt -6))))
(-.f64 #s(literal 0 binary64) (*.f64 (PI.f64) (*.f64 v (sqrt.f64 #s(literal -6 binary64)))))
(* -1 (* v (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))))))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6)))))))
(*.f64 (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (+ (* -1/2 (/ (PI) (* (pow v 4) (pow (sqrt -6) 3)))) (+ (* 1/2 (/ (PI) (* (pow v 6) (pow (sqrt -6) 5)))) (+ (* (PI) (sqrt -6)) (/ (PI) (* (pow v 2) (sqrt -6))))))))
(-.f64 #s(literal 0 binary64) (*.f64 v (+.f64 (/.f64 (/.f64 (PI.f64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) (*.f64 (pow.f64 v #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -6 binary64)) #s(literal 5 binary64)))) (+.f64 (*.f64 (PI.f64) (sqrt.f64 #s(literal -6 binary64))) (/.f64 (*.f64 (PI.f64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64)))) (*.f64 v (*.f64 v (*.f64 v v)))))))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* -3 (/ (pow v 2) (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* (pow v 2) (- (* -9/2 (/ (pow v 2) (pow (sqrt 2) 3))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal -9/4 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* (pow v 2) (- (* (pow v 2) (- (* -27/2 (/ (pow v 2) (pow (sqrt 2) 5))) (* 9/2 (/ 1 (pow (sqrt 2) 3))))) (* 3 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 v v) (+.f64 (*.f64 (*.f64 v v) (+.f64 (/.f64 (*.f64 (*.f64 v v) #s(literal -27/2 binary64)) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -9/4 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal -3 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(* v (sqrt -6))
(*.f64 v (sqrt.f64 #s(literal -6 binary64)))
(* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))))
(*.f64 v (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))))
(* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3)))))
(*.f64 v (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (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 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 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v))))))))
(* -1 (* v (sqrt -6)))
(-.f64 #s(literal 0 binary64) (*.f64 v (sqrt.f64 #s(literal -6 binary64))))
(* -1 (* v (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6))))))
(*.f64 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64)))) (-.f64 #s(literal 0 binary64) v))
(* -1 (* v (- (+ (sqrt -6) (/ 1 (* (pow v 2) (sqrt -6)))) (/ 1/2 (* (pow v 4) (pow (sqrt -6) 3))))))
(*.f64 (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) (sqrt.f64 #s(literal -6 binary64))) (+.f64 (sqrt.f64 #s(literal -6 binary64)) (/.f64 (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal -6 binary64))) (*.f64 v (*.f64 v (*.f64 v v)))))) (-.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 (+.f64 (sqrt.f64 #s(literal -6 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.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 (/.f64 #s(literal 1/12 binary64) (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)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(+ 2 (* -6 (pow v 2)))
(+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* -6 (pow v 2))
(*.f64 v (*.f64 v #s(literal -6 binary64)))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(* (pow v 2) (- (* 2 (/ 1 (pow v 2))) 6))
(*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v))))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))
(/ 2 (pow v 2))
(/.f64 #s(literal 2 binary64) (*.f64 v v))

eval34.0ms (0.4%)

Compiler

Compiled 5825 to 1087 computations (81.3% saved)

prune38.0ms (0.5%)

Pruning

11 alts after pruning (2 fresh and 9 done)

PrunedKeptTotal
New2852287
Fresh000
Picked011
Done088
Total28511296
Accuracy
100.0%
Counts
296 → 11
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓97.3%
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓100.0%
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
✓98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
✓98.8%
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
✓97.3%
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
51.1%
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) v) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
✓98.8%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
✓49.7%
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))))
✓97.3%
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
50.8%
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) v))
Compiler

Compiled 334 to 194 computations (41.9% saved)

regimes17.0ms (0.2%)

Counts
13 → 1
Calls
Call 1
Inputs
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))) (PI.f64))
(/.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))) #s(literal -1/2 binary64)) (/.f64 (PI.f64) #s(literal 4/3 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (PI.f64) #s(literal -4/3 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (*.f64 (PI.f64) v) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))))
(*.f64 (/.f64 #s(literal 4/3 binary64) (sqrt.f64 (-.f64 #s(literal -6 binary64) (/.f64 #s(literal -2 binary64) (*.f64 v v))))) (/.f64 (/.f64 #s(literal 1 binary64) (PI.f64)) v))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (*.f64 (*.f64 v v) (+.f64 #s(literal -6 binary64) (/.f64 #s(literal 2 binary64) (*.f64 v v)))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (PI.f64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
Outputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
Calls

4 calls:

4.0ms
v
3.0ms
(*.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)))))
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))))))
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(/.f64 #s(literal 4 binary64) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v))))))
100.0%1(*.f64 (*.f64 (*.f64 #s(literal 3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (-.f64 #s(literal 2 binary64) (*.f64 #s(literal 6 binary64) (*.f64 v v)))))
100.0%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes9.0ms (0.1%)

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

2 calls:

5.0ms
(*.f64 v v)
3.0ms
v
Results
AccuracySegmentsBranch
98.8%1v
98.8%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes2.0ms (0%)

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

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
98.8%1v
Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

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

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
97.3%1v
Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02342
13642
24342
34742
44942
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))
Outputs
(/.f64 (/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64))))))
(/.f64 #s(literal 4/3 binary64) (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 v (*.f64 v #s(literal -6 binary64)))))))
(/.f64 (/.f64 #s(literal 4/3 binary64) (PI.f64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 4/3 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (PI.f64))

soundness1.2s (14.8%)

Rules
5724×*-lowering-*.f32
5724×*-lowering-*.f64
5110×*-lowering-*.f32
5110×*-lowering-*.f64
4490×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02180
112477
293973
0847973
01861116
1601949
22351890
08324890
02541715
18451419
232791341
089201341
01620
14118
210816
333116
499416
5186716
6469216
0810416
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
Compiler

Compiled 172 to 130 computations (24.4% saved)

preprocess34.0ms (0.4%)

Remove

(abs v)

Compiler

Compiled 204 to 138 computations (32.4% saved)

end0.0ms (0%)

Profiling

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