Details

Time bar (total: 7.6s)

analyze1.5s (19.3%)

Algorithm
1×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)

sample131.0ms (1.7%)

Algorithm
1×intervals
Symmetry

(sort y z)

Results
25.0ms324×body128nan
23.0ms256×body128valid
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify91.0ms (1.2%)

Algorithm
1×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

prune5.0ms (0.1%)

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
1.7b
(*.f64 1/3 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
▶1.3b
(*.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
✓0.3b
(*.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))))
✓2.4b
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
✓4.9b
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))

series87.0ms (1.1%)

Counts
4 → 144
Calls

4 calls:

42.0ms
(*.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))
16.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
9.0ms
(*.f64 3 (/.f64 x (*.f64 y 27)))

rewrite43.0ms (0.6%)

Algorithm
1×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 3 (/.f64 x (*.f64 y 27)))
9.0ms
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
7.0ms
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))
5.0ms
(*.f64 (/.f64 1 3) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

simplify180.0ms (2.4%)

Algorithm
1×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

prune169.0ms (2.2%)

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
▶0.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
Compiler

Compiled 5848 to 4191 computations (28.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.0b
(*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓1.0b
(/.f64 1 (cbrt.f64 3))
2.4b
(*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))
4.9b
(/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2))

series122.0ms (1.6%)

Counts
2 → 48
Calls

2 calls:

121.0ms
(*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
0.0ms
(/.f64 1 (cbrt.f64 3))

rewrite16.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
40×times-frac_binary64
33×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
23×cbrt-prod_binary64
Counts
2 → 94
Calls

2 calls:

6.0ms
(*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.0ms
(/.f64 1 (cbrt.f64 3))

simplify278.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
958×fabs-mul_binary64
446×unswap-sqr_binary64
434×associate-/l*_binary64
319×associate-/l/_binary64
314×associate-*l/_binary64
Counts
142 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0973282
11762929
24632797
39742775
425752775
526722775
628882775
732042775
842792775
948342775
1048032775
1150522775

prune342.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2361237
Fresh011
Picked011
Done000
Total2363239
Error
0b
Counts
239 → 3
Alt Table
StatusErrorProgram
✓0.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
1.0b
(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))
▶0.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
Compiler

Compiled 8726 to 6893 computations (21% saved)

localize16.0ms (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 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)))
✓2.4b
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
✓4.7b
(/.f64 x (*.f64 y z))

series312.0ms (4.1%)

Counts
4 → 48
Calls

4 calls:

213.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
46.0ms
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
36.0ms
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
16.0ms
(/.f64 x (*.f64 y z))

rewrite45.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
77×add-exp-log_binary64
51×add-sqr-sqrt_binary64
46×add-cbrt-cube_binary64
39×times-frac_binary64
33×prod-exp_binary64
Counts
4 → 153
Calls

4 calls:

13.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
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))
3.0ms
(/.f64 x (*.f64 y z))

simplify187.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
568×associate-/r*_binary64
545×*-commutative_binary64
466×associate-/r/_binary64
389×associate-/l/_binary64
203×associate-*r*_binary64
Counts
201 → 199
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02435527
15624409
219324408
337594408
447114408
549714408
649134408

prune197.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1981199
Fresh101
Picked011
Done011
Total1993202
Error
0b
Counts
202 → 3
Alt Table
StatusErrorProgram
✓0.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
▶1.0b
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) 3)
✓0.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
Compiler

Compiled 6504 to 4032 computations (38% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓1.0b
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) 3)
2.4b
(*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))
4.7b
(/.f64 x (*.f64 y z))

series18.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

18.0ms
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) 3)

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64
9×times-frac_binary64
9×add-sqr-sqrt_binary64
9×add-cube-cbrt_binary64
3×associate-/r*_binary64
Counts
1 → 30
Calls

1 calls:

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

simplify173.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
658×unswap-sqr_binary64
530×fma-neg_binary64
515×associate-/l/_binary64
498×associate-/l*_binary64
430×associate-/r/_binary64
Counts
78 → 44
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0731934
11181852
22171852
33891852
47051852
510071852
613891852
727591852
833121852
940321852
1042831852
1146181852
1249141852

prune66.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1350135
Fresh000
Picked011
Done022
Total1353138
Error
0b
Counts
138 → 3
Alt Table
StatusErrorProgram
✓0.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))
✓1.0b
(/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) 3)
✓0.0b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
Compiler

Compiled 2886 to 1297 computations (55.1% saved)

regimes1.1s (14.9%)

Accuracy

Total 0.2b remaining (98.1%)

Threshold costs 0.2b (98.1%)

Counts
64 → 1
Compiler

Compiled 27053 to 22561 computations (16.6% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02038
12738
22638

end7.0ms (0.1%)

Remove

(sort y z)

Compiler

Compiled 84 to 72 computations (14.3% saved)

sample2.4s (32.4%)

Algorithm
1×intervals
Results
918.0ms10391×body128nan
698.0ms8000×body128valid
Compiler

Compiled 131 to 111 computations (15.3% saved)

Profiling

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