Details

Time bar (total: 5.0s)

analyze590.0ms (11.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
6.2%79.6%14.2%8
7.8%75.7%16.5%9
11.7%68.6%19.6%10
20.3%49.3%30.4%11
22.2%44.4%33.4%12
25.2%37.3%37.5%13
28%27.3%44.7%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.5s (29.1%)

Results
925.0ms8256×body128valid
462.0ms4451×body128invalid
Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify86.0ms (1.7%)

Algorithm
egg-herbie
Rules
1052×fma-def_binary64
423×fabs-mul_binary64
333×distribute-rgt-in_binary64
319×div-sub_binary64
307×*-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11912
24512
310512
421912
536012
661712
7169812
8203712
9262912
10343712
11390912
12455712
13503912

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
9.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
9.0b
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(cosh.f64 x)
0.0b
(*.f64 (cosh.f64 x) (/.f64 y x))
8.4b
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series92.0ms (1.8%)

Counts
3 → 72
Calls

3 calls:

56.0ms
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
28.0ms
(*.f64 (cosh.f64 x) (/.f64 y x))
8.0ms
(cosh.f64 x)

rewrite13.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
13×associate-*r*_binary64
13×*-un-lft-identity_binary64
Counts
3 → 74
Calls

3 calls:

5.0ms
(*.f64 (cosh.f64 x) (/.f64 y x))
5.0ms
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
1.0ms
(cosh.f64 x)

simplify86.0ms (1.7%)

Algorithm
egg-herbie
Rules
935×times-frac_binary64
578×fma-def_binary64
493×associate-*l*_binary64
378×associate-/r*_binary64
349×associate-/r/_binary64
Counts
146 → 140
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01902514
14722226
215912222
344812216
449652216

prune112.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New12911140
Fresh000
Picked101
Done000
Total13011141
Error
0.0b
Counts
141 → 11
Alt Table
StatusErrorProgram
6.6b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))) (cbrt.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x)))) (cbrt.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
5.7b
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) (*.f64 z x))
9.0b
(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
9.3b
(*.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
9.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z))) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
37.7b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x)) 3))
32.1b
(/.f64 (*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 x)) (/.f64 y (sqrt.f64 x))) z)
9.2b
(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))
9.8b
(/.f64 (*.f64 (*.f64 (cosh.f64 x) (*.f64 (cbrt.f64 (/.f64 y x)) (cbrt.f64 (/.f64 y x)))) (cbrt.f64 (/.f64 y x))) z)
34.2b
(/.f64 (*.f64 (*.f64 (cosh.f64 x) (sqrt.f64 y)) (/.f64 (sqrt.f64 y) x)) z)
36.2b
(*.f64 (sqrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)) (sqrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
Compiler

Compiled 2435 to 850 computations (65.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
0.0b
(*.f64 (exp.f64 x) y)
0.0b
(/.f64 y (exp.f64 x))
5.4b
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) (*.f64 z x))

series101.0ms (2%)

Counts
4 → 64
Calls

4 calls:

60.0ms
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) (*.f64 z x))
22.0ms
(+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
13.0ms
(/.f64 y (exp.f64 x))
5.0ms
(*.f64 (exp.f64 x) y)

rewrite23.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
13×times-frac_binary64
13×add-cbrt-cube_binary64
Counts
4 → 91
Calls

4 calls:

8.0ms
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) (*.f64 z x))
5.0ms
(+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
3.0ms
(*.f64 (exp.f64 x) y)
3.0ms
(/.f64 y (exp.f64 x))

simplify74.0ms (1.5%)

Algorithm
egg-herbie
Rules
734×associate-/l*_binary64
620×fma-def_binary64
230×distribute-rgt-in_binary64
206×distribute-lft-in_binary64
196×associate-/l/_binary64
Counts
155 → 163
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992868
15312628
218182609
352442609

prune124.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1585163
Fresh7310
Picked101
Done000
Total1668174
Error
0b
Counts
174 → 8
Alt Table
StatusErrorProgram
9.0b
(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
9.3b
(*.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
8.3b
(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
5.6b
(/.f64 (*.f64 (/.f64 1/2 z) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))) x)
37.7b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x)) 3))
5.5b
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
6.8b
(*.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
32.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) z) (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) x))
Compiler

Compiled 4265 to 1846 computations (56.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (exp.f64 x) y)
0.0b
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)
0.0b
(/.f64 y (exp.f64 x))
5.5b
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)

series109.0ms (2.2%)

Counts
2 → 64
Calls

2 calls:

61.0ms
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
48.0ms
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)

rewrite27.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64
60×*-un-lft-identity_binary64
60×add-sqr-sqrt_binary64
60×add-cube-cbrt_binary64
20×associate-/l*_binary64
Counts
2 → 119
Calls

2 calls:

8.0ms
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
7.0ms
(/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)

simplify120.0ms (2.4%)

Algorithm
egg-herbie
Rules
705×associate-/l*_binary64
563×associate-/r*_binary64
543×associate-/l/_binary64
307×fma-def_binary64
265×associate-/r/_binary64
Counts
183 → 238
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02565498
16215280
216995270
350445270

prune213.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3102312
Fresh257
Picked011
Done000
Total3128320
Error
0b
Counts
320 → 8
Alt Table
StatusErrorProgram
9.0b
(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
8.3b
(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
6.8b
(*.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
32.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) z) (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) x))
5.6b
(/.f64 (*.f64 (/.f64 1/2 z) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))) x)
37.7b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x)) 3))
5.5b
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
5.5b
(/.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) x)
Compiler

Compiled 9087 to 3949 computations (56.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))
0.0b
(*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))
0.0b
(/.f64 1/2 (exp.f64 x))
5.5b
(/.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) x)

series128.0ms (2.6%)

Counts
4 → 88
Calls

4 calls:

61.0ms
(/.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) x)
52.0ms
(*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))
7.0ms
(fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))
7.0ms
(/.f64 1/2 (exp.f64 x))

rewrite22.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
22×times-frac_binary64
22×add-cube-cbrt_binary64
20×add-cbrt-cube_binary64
Counts
4 → 101
Calls

4 calls:

9.0ms
(*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))
5.0ms
(/.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) x)
2.0ms
(/.f64 1/2 (exp.f64 x))
0.0ms
(fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))

simplify117.0ms (2.3%)

Algorithm
egg-herbie
Rules
580×associate-/r*_binary64
413×associate-/r/_binary64
308×distribute-rgt-in_binary64
302×distribute-lft-in_binary64
289×fma-def_binary64
Counts
189 → 179
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02443829
15603477
219363466
349423462
450643462

prune136.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1790179
Fresh066
Picked011
Done011
Total1798187
Error
0b
Counts
187 → 8
Alt Table
StatusErrorProgram
9.0b
(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
8.3b
(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
6.8b
(*.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
32.8b
(*.f64 (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) z) (/.f64 (sqrt.f64 (*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) x))
5.6b
(/.f64 (*.f64 (/.f64 1/2 z) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))) x)
37.7b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x)) 3))
5.5b
(/.f64 (/.f64 (+.f64 (*.f64 1/2 (*.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
5.5b
(/.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) x)
Compiler

Compiled 3866 to 1882 computations (51.3% saved)

regimes1.2s (23.4%)

Accuracy

Total 0.5b remaining (85.4%)

Threshold costs 0.5b (85.4%)

Counts
108 → 3
Compiler

Compiled 10280 to 6167 computations (40% saved)

bsearch46.0ms (0.9%)

Steps
ItersRangePoint
8
3.0365501221063844e+39
3.248223830002184e+42
3.30371938788329e+39
5
-5.567908362602903e+34
-2.0054564965010831e+34
-3.443166066450671e+34
Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043104
157104
259104
360104
460104

end120.0ms (2.4%)

Compiler

Compiled 293 to 185 computations (36.9% saved)

Profiling

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