Details

Time bar (total: 8.3s)

analyze1.4s (16.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
3.1%71.7%25.1%9
4.7%69.8%25.5%10
7%66.9%26.1%11
10.9%61.5%27.6%12
11.1%47%41.9%13
12.8%44.4%42.8%14
Compiler

Compiled 24 to 20 computations (16.7% saved)

sample97.0ms (1.2%)

Algorithm
intervals
Results
29.0ms340×body128nan
22.0ms256×body128valid
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify106.0ms (1.3%)

Algorithm
egg-herbie
Rules
2067×associate-/l*_binary64
1151×associate-/l/_binary64
961×associate-/r/_binary64
904×*-commutative_binary64
879×associate-*l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02026
14023
212120
344620
4175020
5300520
6300220
7300220
8375320
9407420
10421520
11422520
12422920
13423020
14539820

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.5b
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
2.2b
(*.f64 1/3 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
Compiler

Compiled 116 to 91 computations (21.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 3 (/.f64 x (*.f64 y 27)))
1.0b
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.3b
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
5.3b
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))

series93.0ms (1.1%)

Counts
4 → 144
Calls

4 calls:

43.0ms
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
22.0ms
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))
18.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
10.0ms
(*.f64 3 (/.f64 x (*.f64 y 27)))

rewrite45.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
96×add-exp-log_binary64
92×add-cbrt-cube_binary64
41×prod-exp_binary64
39×cbrt-unprod_binary64
31×add-sqr-sqrt_binary64
Counts
4 → 141
Calls

4 calls:

10.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
10.0ms
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
6.0ms
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))
5.0ms
(*.f64 3 (/.f64 x (*.f64 y 27)))

simplify187.0ms (2.3%)

Algorithm
egg-herbie
Rules
782×associate-/r/_binary64
291×times-frac_binary64
262×sub-neg_binary64
198×associate-*l*_binary64
191×log-prod_binary64
Counts
285 → 211
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02325969
15474670
224414667
340434667
447934667
549774667

prune201.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2092211
Fresh101
Picked101
Done000
Total2112213
Error
0.0b
Counts
213 → 2
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
1.0b
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 3 (*.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
Compiler

Compiled 5848 to 4191 computations (28.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
0.3b
(*.f64 1/9 (/.f64 x y))
3.3b
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.3b
(/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2))

series123.0ms (1.5%)

Counts
4 → 120
Calls

4 calls:

58.0ms
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
41.0ms
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
18.0ms
(/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2))
7.0ms
(*.f64 1/9 (/.f64 x y))

rewrite36.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
61×add-exp-log_binary64
60×add-cbrt-cube_binary64
39×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
30×times-frac_binary64
Counts
4 → 143
Calls

4 calls:

11.0ms
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
6.0ms
(/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2))
5.0ms
(*.f64 1/9 (/.f64 x y))
3.0ms
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))

simplify197.0ms (2.4%)

Algorithm
egg-herbie
Rules
722×associate-/r/_binary64
549×*-commutative_binary64
213×times-frac_binary64
183×associate--l+_binary64
173×log-prod_binary64
Counts
263 → 212
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02375748
15254830
219794830
333034826
447894826
549424826

prune290.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2102212
Fresh011
Picked011
Done000
Total2104214
Error
0b
Counts
214 → 4
Alt Table
StatusErrorProgram
0.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))
0.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
1.0b
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 3 (*.f64 (*.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))
1.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (sqrt.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) (/.f64 (sqrt.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) (cbrt.f64 3))))
Compiler

Compiled 7287 to 5079 computations (30.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))
0.2b
(*.f64 1/18 (/.f64 x (*.f64 y z)))
3.3b
(*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))
4.2b
(/.f64 x (*.f64 y z))

series343.0ms (4.1%)

Counts
4 → 84
Calls

4 calls:

262.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))
42.0ms
(*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))
20.0ms
(*.f64 1/18 (/.f64 x (*.f64 y z)))
19.0ms
(/.f64 x (*.f64 y z))

rewrite43.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
77×add-exp-log_binary64
49×add-sqr-sqrt_binary64
46×add-cbrt-cube_binary64
39×times-frac_binary64
33×prod-exp_binary64
Counts
4 → 152
Calls

4 calls:

14.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))
7.0ms
(*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))
5.0ms
(*.f64 1/18 (/.f64 x (*.f64 y z)))
3.0ms
(/.f64 x (*.f64 y z))

simplify180.0ms (2.2%)

Algorithm
egg-herbie
Rules
876×times-frac_binary64
552×associate-/r*_binary64
508×*-commutative_binary64
383×associate-/l/_binary64
210×sqr-pow_binary64
Counts
236 → 210
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02435981
15574866
218844865
343684865
447454865
551244865

prune266.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2082210
Fresh202
Picked101
Done011
Total2113214
Error
0b
Counts
214 → 3
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
1.3b
(expm1.f64 (log1p.f64 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))
0.4b
(/.f64 (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
Compiler

Compiled 6885 to 4497 computations (34.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
0.2b
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
3.4b
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
4.2b
(/.f64 x (*.f64 y z))

series139.0ms (1.7%)

Counts
3 → 0
Calls

3 calls:

60.0ms
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
42.0ms
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
36.0ms
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×add-exp-log_binary64
27×add-sqr-sqrt_binary64
27×add-cbrt-cube_binary64
23×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
Counts
3 → 100
Calls

3 calls:

7.0ms
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
7.0ms
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
3.0ms
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))

simplify150.0ms (1.8%)

Algorithm
egg-herbie
Rules
948×times-frac_binary64
502×associate-/l*_binary64
454×associate-/r*_binary64
307×*-commutative_binary64
211×fma-def_binary64
Counts
100 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01752662
13512392
211112392
337662388
446532388
548842388
650002388
749412388

prune155.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh011
Picked011
Done011
Total1723175
Error
0b
Counts
175 → 3
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
1.3b
(expm1.f64 (log1p.f64 (*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))
0.4b
(/.f64 (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)) (*.f64 (cbrt.f64 3) (cbrt.f64 3)))
Compiler

Compiled 5149 to 3050 computations (40.8% saved)

regimes1.3s (15.4%)

Accuracy

Total 0.3b remaining (99.5%)

Threshold costs 0.3b (99.5%)

Counts
69 → 1
Compiler

Compiled 27908 to 23050 computations (17.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01935
12335
22235

end7.0ms (0.1%)

Compiler

Compiled 78 to 66 computations (15.4% saved)

sample2.9s (34.7%)

Algorithm
intervals
Results
890.0ms10297×body128nan
734.0ms8000×body128valid
Compiler

Compiled 125 to 105 computations (16% saved)

Profiling

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