Falkner and Boettcher, Equation (22+)

Time bar (total: 6.0s)

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
Operation ival-mult, time spent: 1.0ms, 36.0% of total-time
Operation ival-sqrt, time spent: 1.0ms, 36.0% of total-time
Operation ival-div, time spent: 0.0ms, 0.0% of total-time
Operation ival-sub, time spent: 0.0ms, 0.0% of total-time
Operation const, time spent: 0.0ms, 0.0% of total-time
Operation ival-pi, time spent: 0.0ms, 0.0% of total-time

sample1.6s (26.8%)

Results
1.4s8255×0valid
6.0ms11×0invalid
0.0ms1×0valid
Precisions
Click to see histograms. Total time spent on operations: 857.0ms
Operation ival-sub, time spent: 306.0ms, 36.0% of total-time
Operation ival-mult, time spent: 281.0ms, 33.0% of total-time
Operation ival-sqrt, time spent: 122.0ms, 14.0% of total-time
Operation ival-div, time spent: 68.0ms, 8.0% of total-time
Operation ival-pi, time spent: 42.0ms, 5.0% of total-time
Operation const, time spent: 37.0ms, 4.0% of total-time
Bogosity

preprocess1.7s (28%)

Algorithm
1×egg-herbie
Rules
1624×fma-neg
1462×div-sub
954×fma-def
768×associate-/r*
646×times-frac
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
2560-256(1.138201457127527e-232)(PI.f64)
00-0-(*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v)))
00-0-(-.f64 1 (*.f64 v v))
00-0-(*.f64 6 (*.f64 v v))
00-0-v
00-0-(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
00-0-(-.f64 2 (*.f64 6 (*.f64 v v)))
00-0-6
00-0-(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
00-0-(sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))
00-0-4
00-0-3
00-0-(*.f64 v v)
00-0-(*.f64 3 (PI.f64))
00-0-2
00-0-1
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
031292
189272
2195252
3555252
41597252
53618236
66322236
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 (neg.f64 v) (neg.f64 v)))))))
(neg.f64 (/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 (neg.f64 v) (neg.f64 v))))))))
Outputs
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 4/3 (neg.f64 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
(/.f64 4 (*.f64 (*.f64 3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 4/3 (neg.f64 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 (neg.f64 v) (neg.f64 v)))))))
(/.f64 4 (*.f64 (*.f64 3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 4/3 (neg.f64 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(neg.f64 (/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 (neg.f64 v) (neg.f64 v))))))))
(/.f64 -4 (*.f64 (*.f64 3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 -6 (*.f64 v v))))))
(neg.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6)))))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 -4/3 (neg.f64 (*.f64 (PI.f64) (fma.f64 v v -1)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
Symmetry

(abs v)

Compiler

Compiled 195 to 122 computations (37.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 940.0ms
Operation ival-sub, time spent: 405.0ms, 43.0% of total-time
Operation ival-mult, time spent: 319.0ms, 34.0% of total-time
Operation ival-sqrt, time spent: 131.0ms, 14.0% of total-time
Operation const, time spent: 45.0ms, 5.0% of total-time
Operation ival-div, time spent: 23.0ms, 2.0% of total-time
Operation ival-pi, time spent: 18.0ms, 2.0% of total-time

eval2.0ms (0%)

Compiler

Compiled 106 to 71 computations (33% saved)

prune2.0ms (0%)

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

Compiled 40 to 30 computations (25% saved)

localize1.2s (20%)

Localize:

Found 2 expressions with local error:

NewAccuracyProgram
✓3.1%
(PI.f64)
✓3.1%
(PI.f64)
Compiler

Compiled 155 to 89 computations (42.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 932.0ms
Operation ival-sub, time spent: 372.0ms, 40.0% of total-time
Operation ival-mult, time spent: 281.0ms, 30.0% of total-time
Operation ival-sqrt, time spent: 111.0ms, 12.0% of total-time
Operation ival-add, time spent: 77.0ms, 8.0% of total-time
Operation ival-div, time spent: 44.0ms, 5.0% of total-time
Operation const, time spent: 38.0ms, 4.0% of total-time
Operation ival-pi, time spent: 9.0ms, 1.0% of total-time

series0.0ms (0%)

Counts
2 → 0

rewrite219.0ms (3.7%)

Algorithm
1×batch-egg-rewrite
Rules
1294×prod-diff
922×log-prod
737×log1p-expm1-u
737×expm1-log1p-u
564×fma-def
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036
1246
22346
323806
Stop Event
1×node limit
Counts
2 → 126
Calls
Call 1
Inputs
(PI.f64)
(PI.f64)
Outputs
(+.f64 (PI.f64) 0)
(+.f64 (+.f64 (PI.f64) 1) -1)
(+.f64 0 (PI.f64))
(+.f64 (*.f64 2 (*.f64 1/3 (PI.f64))) (*.f64 1/3 (PI.f64)))
(+.f64 (*.f64 1/3 (PI.f64)) (*.f64 2 (*.f64 1/3 (PI.f64))))
(+.f64 (*.f64 1/2 (PI.f64)) (*.f64 1/2 (PI.f64)))
(-.f64 (+.f64 (PI.f64) 1) 1)
(-.f64 (+.f64 (PI.f64) 1) (log.f64 (E.f64)))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64))))))
(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(*.f64 (PI.f64) 1)
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 1 (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 2 (*.f64 1/2 (PI.f64)))
(*.f64 1/3 (*.f64 3 (PI.f64)))
(*.f64 3 (*.f64 1/3 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (pow.f64 (PI.f64) 3/2)))
(*.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/4) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/4))))
(*.f64 (log.f64 (E.f64)) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/6))
(*.f64 (pow.f64 1 1/3) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) 5/2) 1/3) (pow.f64 (PI.f64) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) 5/2)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) 3/2)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 5)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (PI.f64) 1/6)) (pow.f64 (PI.f64) 1/6))
(/.f64 (-.f64 (pow.f64 (+.f64 (PI.f64) 1) 3) 1) (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) (+.f64 1 (+.f64 (PI.f64) 1))))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (+.f64 (PI.f64) 1) 1))
(pow.f64 (PI.f64) 1)
(pow.f64 (cbrt.f64 (PI.f64)) 3)
(pow.f64 (pow.f64 (PI.f64) 2) 1/2)
(pow.f64 (pow.f64 (PI.f64) 3) 1/3)
(pow.f64 (sqrt.f64 (PI.f64)) 2)
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (PI.f64))) 2)) (cbrt.f64 (log.f64 (PI.f64))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (PI.f64)))) (sqrt.f64 (log.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) 2))
(fabs.f64 (PI.f64))
(log.f64 (exp.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (PI.f64) 3))
(expm1.f64 (log1p.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(fma.f64 1 (+.f64 (PI.f64) 1) -1)
(fma.f64 (+.f64 (PI.f64) 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (PI.f64) 1)) (cbrt.f64 (+.f64 (PI.f64) 1))) (cbrt.f64 (+.f64 (PI.f64) 1)) -1)
(fma.f64 (sqrt.f64 (+.f64 (PI.f64) 1)) (sqrt.f64 (+.f64 (PI.f64) 1)) -1)
(+.f64 (PI.f64) 0)
(+.f64 (+.f64 (PI.f64) 1) -1)
(+.f64 0 (PI.f64))
(+.f64 (*.f64 2 (*.f64 1/3 (PI.f64))) (*.f64 1/3 (PI.f64)))
(+.f64 (*.f64 1/3 (PI.f64)) (*.f64 2 (*.f64 1/3 (PI.f64))))
(+.f64 (*.f64 1/2 (PI.f64)) (*.f64 1/2 (PI.f64)))
(-.f64 (+.f64 (PI.f64) 1) 1)
(-.f64 (+.f64 (PI.f64) 1) (log.f64 (E.f64)))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64))))))
(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(*.f64 (PI.f64) 1)
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 1 (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 2 (*.f64 1/2 (PI.f64)))
(*.f64 1/3 (*.f64 3 (PI.f64)))
(*.f64 3 (*.f64 1/3 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (pow.f64 (PI.f64) 3/2)))
(*.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/4) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/4))))
(*.f64 (log.f64 (E.f64)) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/6))
(*.f64 (pow.f64 1 1/3) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) 5/2) 1/3) (pow.f64 (PI.f64) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) 5/2)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) 3/2)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 5)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (PI.f64) 1/6)) (pow.f64 (PI.f64) 1/6))
(/.f64 (-.f64 (pow.f64 (+.f64 (PI.f64) 1) 3) 1) (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) (+.f64 1 (+.f64 (PI.f64) 1))))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (+.f64 (PI.f64) 1) 1))
(pow.f64 (PI.f64) 1)
(pow.f64 (cbrt.f64 (PI.f64)) 3)
(pow.f64 (pow.f64 (PI.f64) 2) 1/2)
(pow.f64 (pow.f64 (PI.f64) 3) 1/3)
(pow.f64 (sqrt.f64 (PI.f64)) 2)
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (PI.f64))) 2)) (cbrt.f64 (log.f64 (PI.f64))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (PI.f64)))) (sqrt.f64 (log.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) 2))
(fabs.f64 (PI.f64))
(log.f64 (exp.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (PI.f64) 3))
(expm1.f64 (log1p.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(fma.f64 1 (+.f64 (PI.f64) 1) -1)
(fma.f64 (+.f64 (PI.f64) 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (PI.f64) 1)) (cbrt.f64 (+.f64 (PI.f64) 1))) (cbrt.f64 (+.f64 (PI.f64) 1)) -1)
(fma.f64 (sqrt.f64 (+.f64 (PI.f64) 1)) (sqrt.f64 (+.f64 (PI.f64) 1)) -1)

simplify84.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
1654×log-prod
1012×associate-+l+
978×associate-+r+
514×unswap-sqr
446×*-commutative
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01601602
13591522
214151490
369031490
Stop Event
1×node limit
Counts
126 → 85
Calls
Call 1
Inputs
(+.f64 (PI.f64) 0)
(+.f64 (+.f64 (PI.f64) 1) -1)
(+.f64 0 (PI.f64))
(+.f64 (*.f64 2 (*.f64 1/3 (PI.f64))) (*.f64 1/3 (PI.f64)))
(+.f64 (*.f64 1/3 (PI.f64)) (*.f64 2 (*.f64 1/3 (PI.f64))))
(+.f64 (*.f64 1/2 (PI.f64)) (*.f64 1/2 (PI.f64)))
(-.f64 (+.f64 (PI.f64) 1) 1)
(-.f64 (+.f64 (PI.f64) 1) (log.f64 (E.f64)))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64))))))
(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(*.f64 (PI.f64) 1)
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 1 (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 2 (*.f64 1/2 (PI.f64)))
(*.f64 1/3 (*.f64 3 (PI.f64)))
(*.f64 3 (*.f64 1/3 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (pow.f64 (PI.f64) 3/2)))
(*.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/4) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/4))))
(*.f64 (log.f64 (E.f64)) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/6))
(*.f64 (pow.f64 1 1/3) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) 5/2) 1/3) (pow.f64 (PI.f64) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) 5/2)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) 3/2)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 5)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (PI.f64) 1/6)) (pow.f64 (PI.f64) 1/6))
(/.f64 (-.f64 (pow.f64 (+.f64 (PI.f64) 1) 3) 1) (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) (+.f64 1 (+.f64 (PI.f64) 1))))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (+.f64 (PI.f64) 1) 1))
(pow.f64 (PI.f64) 1)
(pow.f64 (cbrt.f64 (PI.f64)) 3)
(pow.f64 (pow.f64 (PI.f64) 2) 1/2)
(pow.f64 (pow.f64 (PI.f64) 3) 1/3)
(pow.f64 (sqrt.f64 (PI.f64)) 2)
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (PI.f64))) 2)) (cbrt.f64 (log.f64 (PI.f64))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (PI.f64)))) (sqrt.f64 (log.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) 2))
(fabs.f64 (PI.f64))
(log.f64 (exp.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (PI.f64) 3))
(expm1.f64 (log1p.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(fma.f64 1 (+.f64 (PI.f64) 1) -1)
(fma.f64 (+.f64 (PI.f64) 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (PI.f64) 1)) (cbrt.f64 (+.f64 (PI.f64) 1))) (cbrt.f64 (+.f64 (PI.f64) 1)) -1)
(fma.f64 (sqrt.f64 (+.f64 (PI.f64) 1)) (sqrt.f64 (+.f64 (PI.f64) 1)) -1)
(+.f64 (PI.f64) 0)
(+.f64 (+.f64 (PI.f64) 1) -1)
(+.f64 0 (PI.f64))
(+.f64 (*.f64 2 (*.f64 1/3 (PI.f64))) (*.f64 1/3 (PI.f64)))
(+.f64 (*.f64 1/3 (PI.f64)) (*.f64 2 (*.f64 1/3 (PI.f64))))
(+.f64 (*.f64 1/2 (PI.f64)) (*.f64 1/2 (PI.f64)))
(-.f64 (+.f64 (PI.f64) 1) 1)
(-.f64 (+.f64 (PI.f64) 1) (log.f64 (E.f64)))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64))))))
(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(*.f64 (PI.f64) 1)
(*.f64 (PI.f64) (log.f64 (E.f64)))
(*.f64 1 (PI.f64))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 2 (*.f64 1/2 (PI.f64)))
(*.f64 1/3 (*.f64 3 (PI.f64)))
(*.f64 3 (*.f64 1/3 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (pow.f64 (PI.f64) 3/2)))
(*.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) 1/4) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/4))))
(*.f64 (log.f64 (E.f64)) (PI.f64))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/6))
(*.f64 (pow.f64 1 1/3) (PI.f64))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) 5/2) 1/3) (pow.f64 (PI.f64) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) 5/2)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/4)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) 3/2)) (pow.f64 (PI.f64) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 5)) (pow.f64 (PI.f64) 1/6))
(*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (pow.f64 (PI.f64) 1/6)) (pow.f64 (PI.f64) 1/6))
(/.f64 (-.f64 (pow.f64 (+.f64 (PI.f64) 1) 3) 1) (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) (+.f64 1 (+.f64 (PI.f64) 1))))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (+.f64 (PI.f64) 1) 1))
(pow.f64 (PI.f64) 1)
(pow.f64 (cbrt.f64 (PI.f64)) 3)
(pow.f64 (pow.f64 (PI.f64) 2) 1/2)
(pow.f64 (pow.f64 (PI.f64) 3) 1/3)
(pow.f64 (sqrt.f64 (PI.f64)) 2)
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (PI.f64))) 2)) (cbrt.f64 (log.f64 (PI.f64))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (PI.f64)))) (sqrt.f64 (log.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) 2))
(fabs.f64 (PI.f64))
(log.f64 (exp.f64 (PI.f64)))
(cbrt.f64 (pow.f64 (PI.f64) 3))
(expm1.f64 (log1p.f64 (PI.f64)))
(exp.f64 (log.f64 (PI.f64)))
(log1p.f64 (expm1.f64 (PI.f64)))
(fma.f64 1 (+.f64 (PI.f64) 1) -1)
(fma.f64 (+.f64 (PI.f64) 1) 1 -1)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (PI.f64) 1)) (cbrt.f64 (+.f64 (PI.f64) 1))) (cbrt.f64 (+.f64 (PI.f64) 1)) -1)
(fma.f64 (sqrt.f64 (+.f64 (PI.f64) 1)) (sqrt.f64 (+.f64 (PI.f64) 1)) -1)
Outputs
(+.f64 (PI.f64) 0)
(PI.f64)
(+.f64 (+.f64 (PI.f64) 1) -1)
(PI.f64)
(+.f64 0 (PI.f64))
(PI.f64)
(+.f64 (*.f64 2 (*.f64 1/3 (PI.f64))) (*.f64 1/3 (PI.f64)))
(PI.f64)
(+.f64 (*.f64 1/3 (PI.f64)) (*.f64 2 (*.f64 1/3 (PI.f64))))
(PI.f64)
(+.f64 (*.f64 1/2 (PI.f64)) (*.f64 1/2 (PI.f64)))
(PI.f64)
(-.f64 (+.f64 (PI.f64) 1) 1)
(PI.f64)
(-.f64 (+.f64 (PI.f64) 1) (log.f64 (E.f64)))
(PI.f64)
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64))))))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log1p.f64 (-.f64 (pow.f64 (expm1.f64 (PI.f64)) 2) (expm1.f64 (PI.f64)))))
(-.f64 (log1p.f64 (pow.f64 (expm1.f64 (PI.f64)) 3)) (log1p.f64 (*.f64 (expm1.f64 (PI.f64)) (+.f64 -1 (expm1.f64 (PI.f64))))))
(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(PI.f64)
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(-.f64 (log1p.f64 (neg.f64 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log1p.f64 (neg.f64 (expm1.f64 (PI.f64)))))
(*.f64 (PI.f64) 1)
(PI.f64)
(*.f64 (PI.f64) (log.f64 (E.f64)))
(PI.f64)
(*.f64 1 (PI.f64))
(PI.f64)
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) 2))
(PI.f64)
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(PI.f64)
(*.f64 2 (*.f64 1/2 (PI.f64)))
(PI.f64)
(*.f64 1/3 (*.f64 3 (PI.f64)))
(PI.f64)
(*.f64 3 (*.f64 1/3 (PI.f64)))
(PI.f64)
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(PI.f64)
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(PI.f64)
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2)))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(PI.f64)
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(PI.f64)
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (cbrt.f64 (PI.f64)))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/6)))
(*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (pow.f64 (PI.f64) 3/2)))
(*.f64 (pow.f64 (PI.f64) 1/4) (fabs.f64 (pow.f64 (PI.f64) 3/4)))
(*.f64 (pow.f64 (PI.f64) 1/4) (pow.f64 (PI.f64) 3/4))
(*.f64 (pow.f64 (PI.f64) 1/4) (*.f64 (pow.f64 (PI.f64) 1/4) (sqrt.f64 (PI.f64))))
(PI.f64)
(*.f64 (pow.f64 (PI.f64) 1/4) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (PI.f64))) (pow.f64 (PI.f64) 1/4))))
(PI.f64)
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(-.f64 (log.f64 (pow.f64 (E.f64) (+.f64 (PI.f64) 1))) (log.f64 (E.f64)))
(PI.f64)
(-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log.f64 (-.f64 1 (expm1.f64 (PI.f64)))))
(-.f64 (log1p.f64 (neg.f64 (pow.f64 (expm1.f64 (PI.f64)) 2))) (log1p.f64 (neg.f64 (expm1.f64 (PI.f64)))))
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(PI.f64)
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(PI.f64)
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(PI.f64)
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2) (cbrt.f64 (PI.f64)))
(PI.f64)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(PI.f64)
(*.f64 2 (*.f64 1/2 (PI.f64)))
(PI.f64)
(*.f64 1/3 (*.f64 3 (PI.f64)))
(PI.f64)
(*.f64 3 (*.f64 1/3 (PI.f64)))
(PI.f64)
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(PI.f64)
(*.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2))))
(PI.f64)
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (PI.f64))))
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(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))))
(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (pow.f64 (PI.f64) 1/6) (pow.f64 (cbrt.f64 (PI.f64)) 2)))
(PI.f64)
(*.f64 (pow.f64 (PI.f64) 1/6) (log.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (PI.f64) 1/6))))
(PI.f64)
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(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/6)))
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(PI.f64)
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(*.f64 (pow.f64 (PI.f64) 1/6) (*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64))))))
(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) (pow.f64 (PI.f64) 1/6)))
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(PI.f64)
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (PI.f64))))
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(*.f64 (pow.f64 (PI.f64) 1/6) (cbrt.f64 (pow.f64 (PI.f64) 5/2)))
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(PI.f64)
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(*.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) 4))))
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(PI.f64)
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(/.f64 (+.f64 -1 (pow.f64 (+.f64 (PI.f64) 1) 3)) (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 (PI.f64) 1) 3)) (+.f64 1 (*.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 2))))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (+.f64 (PI.f64) 1) 1))
(/.f64 (fma.f64 (+.f64 (PI.f64) 1) (+.f64 (PI.f64) 1) -1) (+.f64 (PI.f64) 2))
(/.f64 (*.f64 (+.f64 (PI.f64) 2) (PI.f64)) (+.f64 (PI.f64) 2))
(/.f64 (+.f64 (PI.f64) 2) (/.f64 (+.f64 (PI.f64) 2) (PI.f64)))
(pow.f64 (PI.f64) 1)
(PI.f64)
(pow.f64 (cbrt.f64 (PI.f64)) 3)
(PI.f64)
(pow.f64 (pow.f64 (PI.f64) 2) 1/2)
(PI.f64)
(pow.f64 (pow.f64 (PI.f64) 3) 1/3)
(PI.f64)
(pow.f64 (sqrt.f64 (PI.f64)) 2)
(PI.f64)
(pow.f64 (E.f64) (log.f64 (PI.f64)))
(PI.f64)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (PI.f64))) 2)) (cbrt.f64 (log.f64 (PI.f64))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (PI.f64)))) (sqrt.f64 (log.f64 (PI.f64))))
(sqrt.f64 (pow.f64 (PI.f64) 2))
(PI.f64)
(fabs.f64 (PI.f64))
(PI.f64)
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)
(cbrt.f64 (pow.f64 (PI.f64) 3))
(PI.f64)
(expm1.f64 (log1p.f64 (PI.f64)))
(PI.f64)
(exp.f64 (log.f64 (PI.f64)))
(PI.f64)
(log1p.f64 (expm1.f64 (PI.f64)))
(PI.f64)
(fma.f64 1 (+.f64 (PI.f64) 1) -1)
(PI.f64)
(fma.f64 (+.f64 (PI.f64) 1) 1 -1)
(PI.f64)
(fma.f64 (*.f64 (cbrt.f64 (+.f64 (PI.f64) 1)) (cbrt.f64 (+.f64 (PI.f64) 1))) (cbrt.f64 (+.f64 (PI.f64) 1)) -1)
(PI.f64)
(fma.f64 (sqrt.f64 (+.f64 (PI.f64) 1)) (sqrt.f64 (+.f64 (PI.f64) 1)) -1)
(PI.f64)

eval94.0ms (1.6%)

Compiler

Compiled 4543 to 2959 computations (34.9% saved)

prune24.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1691170
Fresh000
Picked022
Done000
Total1693172
Accuracy
100.0%
Counts
172 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(/.f64 (/.f64 4/3 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
✓100.0%
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
✓98.5%
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Compiler

Compiled 62 to 47 computations (24.2% saved)

localize663.0ms (11.1%)

Localize:

Found 1 expressions with local error:

NewAccuracyProgram
3.1%
(PI.f64)
Compiler

Compiled 85 to 49 computations (42.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 510.0ms
Operation ival-sub, time spent: 127.0ms, 25.0% of total-time
Operation ival-mult, time spent: 98.0ms, 19.0% of total-time
Operation ival-pow, time spent: 76.0ms, 15.0% of total-time
Operation ival-add, time spent: 75.0ms, 15.0% of total-time
Operation ival-sqrt, time spent: 69.0ms, 14.0% of total-time
Operation ival-div, time spent: 35.0ms, 7.0% of total-time
Operation const, time spent: 22.0ms, 4.0% of total-time
Operation ival-pi, time spent: 8.0ms, 2.0% of total-time

eval45.0ms (0.8%)

Compiler

Compiled 2442 to 1665 computations (31.8% saved)

prune14.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New85085
Fresh000
Picked011
Done022
Total85388
Accuracy
100.0%
Counts
88 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(/.f64 (/.f64 4/3 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
✓100.0%
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
✓98.5%
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Compiler

Compiled 122 to 88 computations (27.9% saved)

regimes11.0ms (0.2%)

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

4 calls:

3.0ms
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
3.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
100.0%1(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
100.0%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes9.0ms (0.2%)

Accuracy

Total -1.0b remaining (-6250%)

Threshold costs -1b (-6250%)

Counts
2 → 1
Calls
Call 1
Inputs
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Outputs
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
Calls

4 calls:

3.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
2.0ms
(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
Results
AccuracySegmentsBranch
100.0%1v
100.0%1(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))
100.0%1(*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))))
100.0%1(*.f64 v v)
Compiler

Compiled 46 to 33 computations (28.3% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
10×*-commutative
8×+-commutative
6×sub-neg
4×neg-mul-1
4×neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
024144
138144
245144
349144
451144
Stop Event
1×done
1×saturated
Calls
Call 1
Inputs
(/.f64 (/.f64 4/3 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
Outputs
(/.f64 (/.f64 4/3 (*.f64 (pow.f64 (sqrt.f64 (PI.f64)) 2) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))
Compiler

Compiled 41 to 31 computations (24.4% saved)

soundness280.0ms (4.7%)

Rules
1624×fma-neg
1462×div-sub
1294×prod-diff
954×fma-def
922×log-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031292
189272
2195252
3555252
41597252
53618236
66322236
036
1246
22346
323806
Stop Event
1×node limit
1×node limit
Compiler

Compiled 324 to 203 computations (37.3% saved)

end0.0ms (0%)

preprocess51.0ms (0.9%)

Remove

(abs v)

Compiler

Compiled 254 to 190 computations (25.2% saved)

Profiling

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