tanhf (example 3.4)

Time bar (total: 5.3s)

analyze150.0ms (2.8%)

Algorithm
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
25%25%75%0%0%0%0%3
37.5%37.5%62.5%0%0%0%0%4
43.8%43.7%56.2%0%0%0%0%5
46.9%46.9%53.1%0%0%0%0%6
48.4%48.4%51.5%0%0%0%0%7
49.2%49.2%50.8%0%0%0%0%8
49.6%49.6%50.4%0%0%0%0%9
49.8%49.8%50.2%0%0%0%0%10
49.9%49.9%50.1%0%0%0%0%11
50%49.9%50%0%0%0%0%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample4.8s (90.9%)

Results
2.8s2134×body2048valid
1.3s3118×body1024valid
362.0ms1503×body512valid
232.0ms1413×body256valid
88.0ms86×body4096valid
4.0msbody8192valid
Bogosity

preprocess28.0ms (0.5%)

Algorithm
egg-herbie
Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify25.0ms (0.5%)

Algorithm
egg-herbie
Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))

eval1.0ms (0%)

Compiler

Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Accurracy
100.0%
Counts
3 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(tan.f64 (/.f64 x 2))
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 10 to 8 computations (20% saved)

localize39.0ms (0.7%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 11 to 8 computations (27.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(tan.f64 (/.f64 x 2))
0.0ms
x
@-inf
(tan.f64 (/.f64 x 2))
0.0ms
x
@0
(tan.f64 (/.f64 x 2))

rewrite49.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
1366×pow1
1262×add-exp-log
1262×log1p-expm1-u
1262×expm1-log1p-u
1234×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114811
2172411
Stop Event
node limit
Counts
1 → 20
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
Outputs
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))

simplify68.0ms (1.3%)

Algorithm
egg-herbie
Rules
1072×log-prod
980×fma-def
832×fma-neg
742×exp-prod
496×exp-sum
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
068804
1144708
2438612
32071612
44553612
56569612
Stop Event
node limit
Counts
32 → 36
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/2 x)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/240 (pow.f64 x 5)) (+.f64 (*.f64 17/40320 (pow.f64 x 7)) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 1 (tan.f64 (*.f64 x 1/2)))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(*.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval10.0ms (0.2%)

Compiler

Compiled 350 to 283 computations (19.1% saved)

prune5.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New35136
Fresh000
Picked011
Done000
Total35237
Accurracy
100.0%
Counts
37 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.1%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
51.1%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize15.0ms (0.3%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Accurracy
100.0%
Counts
2 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
51.1%
(*.f64 1/2 x)
100.0%
(tan.f64 (/.f64 x 2))
Compiler

Compiled 24 to 18 computations (25% saved)

regimes8.0ms (0.2%)

Counts
3 → 1
Calls
Call 1
Inputs
(*.f64 1/2 x)
(tan.f64 (/.f64 x 2))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Outputs
(tan.f64 (/.f64 x 2))
Calls

2 calls:

3.0ms
x
3.0ms
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Results
AccuracySegmentsBranch
100.0%1x
100.0%1(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
Compiler

Compiled 25 to 18 computations (28% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
Calls

1 calls:

2.0ms
x
Results
AccuracySegmentsBranch
51.1%1x
Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
11018
Stop Event
done
saturated
Calls
Call 1
Inputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
Outputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
(*.f64 x 1/2)
Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness40.0ms (0.7%)

Rules
472×fma-def
54×div-sub
48×associate-/l*
48×unsub-neg
44×sub-neg
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11911
22511
33611
45911
58211
612011
718911
833411
953511
1067711
1172511
Stop Event
saturated
Compiler

Compiled 12 to 9 computations (25% saved)

end38.0ms (0.7%)

Compiler

Compiled 42 to 32 computations (23.8% saved)

Profiling

Loading profile data...