Details

Time bar (total: 6.3s)

analyze1.1s (18.1%)

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)

sample139.0ms (2.2%)

Algorithm
intervals
Symmetry

(sort y z)

Results
33.0ms372×body128nan
22.0ms256×body128valid
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify84.0ms (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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
2.3b
(*.f64 1/3 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
1.7b
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
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))))
3.8b
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
5.4b
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))

series88.0ms (1.4%)

Counts
4 → 144
Calls

4 calls:

45.0ms
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
19.0ms
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))
17.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
6.0ms
(*.f64 3 (/.f64 x (*.f64 y 27)))

rewrite41.0ms (0.7%)

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:

9.0ms
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
8.0ms
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))
5.0ms
(*.f64 3 (/.f64 x (*.f64 y 27)))
5.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

simplify162.0ms (2.5%)

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

prune155.0ms (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
0.8b
(*.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 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
Compiler

Compiled 5840 to 4183 computations (28.4% saved)

localize18.0ms (0.3%)

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))
3.8b
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.4b
(/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2))

series432.0ms (6.8%)

Counts
4 → 120
Calls

4 calls:

336.0ms
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
68.0ms
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
22.0ms
(/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2))
6.0ms
(*.f64 1/9 (/.f64 x y))

rewrite35.0ms (0.5%)

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:

10.0ms
(*.f64 (sqrt.f64 t) (/.f64 (*.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.0ms
(/.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))

simplify196.0ms (3.1%)

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

prune174.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2111212
Fresh011
Picked101
Done000
Total2122214
Error
0b
Counts
214 → 2
Alt Table
StatusErrorProgram
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)))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
Compiler

Compiled 7171 to 4991 computations (30.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3))
0.3b
(*.f64 1/18 (/.f64 x (*.f64 y z)))
3.8b
(*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))
6.9b
(/.f64 x (*.f64 y z))

series157.0ms (2.5%)

Counts
4 → 84
Calls

4 calls:

72.0ms
(/.f64 (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3))
49.0ms
(*.f64 (sqrt.f64 t) (*.f64 1/18 (/.f64 x (*.f64 y z))))
20.0ms
(*.f64 1/18 (/.f64 x (*.f64 y z)))
16.0ms
(/.f64 x (*.f64 y z))

rewrite54.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
34×add-exp-log_binary64
33×add-cbrt-cube_binary64
28×add-sqr-sqrt_binary64
26×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
Counts
4 → 122
Calls

4 calls:

32.0ms
(/.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))

simplify118.0ms (1.9%)

Algorithm
egg-herbie
Rules
687×associate-*r/_binary64
637×times-frac_binary64
583×associate-*l/_binary64
442×associate-/r*_binary64
364×associate-/l*_binary64
Counts
206 → 173
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01894425
13714123
211064123
348084123
450134123

prune132.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1730173
Fresh011
Picked011
Done000
Total1732175
Error
0b
Counts
175 → 2
Alt Table
StatusErrorProgram
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)))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
Compiler

Compiled 5493 to 3547 computations (35.4% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
3.6b
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
6.9b
(/.f64 x (*.f64 y z))

series102.0ms (1.6%)

Counts
3 → 0
Calls

3 calls:

44.0ms
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
40.0ms
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
19.0ms
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
28×add-cbrt-cube_binary64
28×add-exp-log_binary64
16×add-sqr-sqrt_binary64
13×associate-*l*_binary64
13×cbrt-unprod_binary64
Counts
3 → 78
Calls

3 calls:

6.0ms
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
6.0ms
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
4.0ms
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

simplify119.0ms (1.9%)

Algorithm
egg-herbie
Rules
934×times-frac_binary64
716×associate-*l/_binary64
600×associate-*r/_binary64
471×associate-/l*_binary64
423×associate-/r*_binary64
Counts
78 → 106
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01391602
13021346
210191345
353011345

prune49.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh000
Picked011
Done011
Total1322134
Error
0b
Counts
134 → 2
Alt Table
StatusErrorProgram
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)))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
Compiler

Compiled 2725 to 1199 computations (56% saved)

regimes478.0ms (7.5%)

Accuracy

Total 0.0b remaining (4.5%)

Threshold costs 0.0b (4.5%)

Counts
16 → 1
Compiler

Compiled 7972 to 6516 computations (18.3% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01935
12535
22435

end52.0ms (0.8%)

Remove

(sort y z)

Compiler

Compiled 78 to 66 computations (15.4% saved)

sample2.3s (36.7%)

Algorithm
intervals
Results
899.0ms10303×body128nan
733.0ms8000×body128valid
Compiler

Compiled 97 to 81 computations (16.5% saved)

Profiling

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