Details

Time bar (total: 4.9s)

analyze1.6s (33.3%)

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
0%99.8%0.2%9
0%99.8%0.2%10
0%99.8%0.2%11
0%99.8%0.2%12
3.7%96.1%0.2%13
4.2%94.5%1.3%14
Compiler

Compiled 22 to 16 computations (27.3% saved)

sample33.0ms (0.7%)

Algorithm
1×intervals
Results
14.0ms256×body128valid
4.0ms71×body128invalid
Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify91.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
649×neg-mul-1_binary64
622×times-frac_binary64
416×div-sub_binary64
398×unsub-neg_binary64
378×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 7 (0.0ms)

IterNodesCost
01525
12825
25225
39225
417825
531725
663322
7149819
8316019
9396119
10488219
11488919

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Alt Table
StatusErrorProgram
▶0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t)))
8.4b
(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
Compiler

Compiled 93 to 69 computations (25.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 2 (/.f64 2 z))
0.0b
(+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t))
0.1b
(/.f64 (+.f64 2 (/.f64 2 z)) t)

rewrite72.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
24×*-un-lft-identity_binary64
12×times-frac_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
7×add-log-exp_binary64
Counts
3 → 57
Calls

3 calls:

8.0ms
(+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t))
6.0ms
(/.f64 (+.f64 2 (/.f64 2 z)) t)
4.0ms
(+.f64 2 (/.f64 2 z))
Compiler

Compiled 1120 to 777 computations (30.6% saved)

series53.0ms (1.1%)

Error
0.0b
Counts
3 → 27
Calls

3 calls:

20.0ms
(+.f64 -2 (/.f64 (+.f64 2 (/.f64 2 z)) t))
18.0ms
(/.f64 (+.f64 2 (/.f64 2 z)) t)
6.0ms
(+.f64 2 (/.f64 2 z))
Compiler

Compiled 928 to 702 computations (24.4% saved)

simplify87.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
635×times-frac_binary64
619×associate-/l*_binary64
495×div-sub_binary64
385×distribute-rgt-in_binary64
327×distribute-lft-in_binary64
Counts
84 → 41
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061209
12481165
25731159
315421159
448531159
558381159

prune39.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New35641
Fresh101
Picked101
Done000
Total37643
Error
0.0b
Counts
43 → 6
Alt Table
StatusErrorProgram
▶0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))))
12.6b
(+.f64 (/.f64 x y) (+.f64 -2 (/.f64 (/.f64 (-.f64 4 (/.f64 4 (*.f64 z z))) (-.f64 2 (/.f64 2 z))) t)))
26.9b
(+.f64 (/.f64 x y) (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 3) -8) (+.f64 4 (*.f64 (+.f64 2 (/.f64 2 z)) (/.f64 (+.f64 2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) t)))))
1.0b
(+.f64 (/.f64 x y) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))))
14.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) (/.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) t))))
0.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
Compiler

Compiled 828 to 608 computations (26.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t)))
0.0b
(+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))
0.5b
(/.f64 2 (*.f64 t z))

rewrite79.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
12×*-un-lft-identity_binary64
10×add-log-exp_binary64
8×add-cbrt-cube_binary64
8×add-exp-log_binary64
5×distribute-lft-out_binary64
Counts
3 → 50
Calls

3 calls:

9.0ms
(+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t)))
8.0ms
(+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))
3.0ms
(/.f64 2 (*.f64 t z))
Compiler

Compiled 1075 to 652 computations (39.3% saved)

series59.0ms (1.2%)

Error
0.0b
Counts
3 → 27
Calls

3 calls:

23.0ms
(+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t)))
17.0ms
(+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))
13.0ms
(/.f64 2 (*.f64 t z))
Compiler

Compiled 1005 to 751 computations (25.3% saved)

simplify84.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
517×cancel-sign-sub-inv_binary64
372×associate-*l*_binary64
313×div-sub_binary64
281×associate-*r*_binary64
256×distribute-rgt-in_binary64
Counts
77 → 43
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01071094
12691049
28141046
332691046
446381046
552831046

prune34.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New43043
Fresh055
Picked011
Done000
Total43649
Error
0.0b
Counts
49 → 6
Alt Table
StatusErrorProgram
✓0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))))
12.6b
(+.f64 (/.f64 x y) (+.f64 -2 (/.f64 (/.f64 (-.f64 4 (/.f64 4 (*.f64 z z))) (-.f64 2 (/.f64 2 z))) t)))
26.9b
(+.f64 (/.f64 x y) (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 3) -8) (+.f64 4 (*.f64 (+.f64 2 (/.f64 2 z)) (/.f64 (+.f64 2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) t)))))
1.0b
(+.f64 (/.f64 x y) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))))
14.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) (/.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) t))))
▶0.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
Compiler

Compiled 893 to 600 computations (32.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))
0.8b
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
0.8b
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
0.8b
(cbrt.f64 (+.f64 2 (/.f64 2 z)))

rewrite190.0ms (3.9%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
33×*-un-lft-identity_binary64
30×cbrt-div_binary64
26×add-sqr-sqrt_binary64
25×associate-*r*_binary64
25×cbrt-prod_binary64
Counts
4 → 106
Calls

4 calls:

24.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))
4.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
4.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
4.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
Compiler

Compiled 4084 to 3172 computations (22.3% saved)

series105.0ms (2.1%)

Error
0.0b
Counts
4 → 42
Calls

4 calls:

20.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
19.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
18.0ms
(cbrt.f64 (+.f64 2 (/.f64 2 z)))
17.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))
Compiler

Compiled 2994 to 2440 computations (18.5% saved)

simplify122.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
587×distribute-rgt-in_binary64
517×associate-/l*_binary64
333×associate-*r/_binary64
315×times-frac_binary64
297×*-commutative_binary64
Counts
148 → 105
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01833831
14593546
213853381
336083279
451433279

prune80.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1032105
Fresh134
Picked011
Done011
Total1047111
Error
0b
Counts
111 → 7
Alt Table
StatusErrorProgram
▶0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 1)))
✓0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))))
12.9b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (/.f64 (cbrt.f64 (-.f64 4 (/.f64 4 (*.f64 z z)))) (cbrt.f64 (-.f64 2 (/.f64 2 z)))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
26.9b
(+.f64 (/.f64 x y) (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 3) -8) (+.f64 4 (*.f64 (+.f64 2 (/.f64 2 z)) (/.f64 (+.f64 2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) t)))))
1.0b
(+.f64 (/.f64 x y) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))))
14.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) (/.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) t))))
✓0.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
Compiler

Compiled 2483 to 1879 computations (24.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 2 (/.f64 2 z))
0.0b
(+.f64 -2 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 1))
0.1b
(/.f64 (+.f64 2 (/.f64 2 z)) t)

rewrite88.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
24×*-un-lft-identity_binary64
12×times-frac_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
7×add-log-exp_binary64
Counts
3 → 57
Calls

3 calls:

10.0ms
(+.f64 -2 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 1))
6.0ms
(/.f64 (+.f64 2 (/.f64 2 z)) t)
4.0ms
(+.f64 2 (/.f64 2 z))
Compiler

Compiled 1240 to 897 computations (27.7% saved)

series57.0ms (1.2%)

Error
0b
Counts
3 → 27
Calls

3 calls:

23.0ms
(+.f64 -2 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 1))
17.0ms
(/.f64 (+.f64 2 (/.f64 2 z)) t)
6.0ms
(+.f64 2 (/.f64 2 z))
Compiler

Compiled 986 to 760 computations (22.9% saved)

simplify110.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
841×times-frac_binary64
500×distribute-rgt-in_binary64
443×distribute-lft-in_binary64
189×associate-*l*_binary64
155×distribute-rgt-out_binary64
Counts
84 → 41
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01091200
12471156
26211150
318151150
448991150
549941150
649111150

prune30.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New41041
Fresh044
Picked011
Done022
Total41748
Error
0b
Counts
48 → 7
Alt Table
StatusErrorProgram
0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 1)))
0.1b
(+.f64 (/.f64 x y) (+.f64 -2 (+.f64 (/.f64 2 (*.f64 t z)) (/.f64 2 t))))
12.9b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (/.f64 (cbrt.f64 (-.f64 4 (/.f64 4 (*.f64 z z)))) (cbrt.f64 (-.f64 2 (/.f64 2 z)))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
26.9b
(+.f64 (/.f64 x y) (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) 3) -8) (+.f64 4 (*.f64 (+.f64 2 (/.f64 2 z)) (/.f64 (+.f64 2 (/.f64 (+.f64 2 (/.f64 2 z)) t)) t)))))
1.0b
(+.f64 (/.f64 x y) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2)) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))) (cbrt.f64 (+.f64 (/.f64 (+.f64 2 (/.f64 2 z)) t) -2))))
14.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) (/.f64 (sqrt.f64 (+.f64 2 (/.f64 2 z))) t))))
0.8b
(+.f64 (/.f64 x y) (+.f64 -2 (*.f64 (*.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) (cbrt.f64 (+.f64 2 (/.f64 2 z)))) (/.f64 (cbrt.f64 (+.f64 2 (/.f64 2 z))) t))))
Compiler

Compiled 703 to 517 computations (26.5% saved)

regimes510.0ms (10.5%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Compiler

Compiled 11940 to 9232 computations (22.7% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01422
11822
21822

end1.0ms (0%)

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.3s (26.3%)

Algorithm
1×intervals
Results
525.0ms8000×body128valid
141.0ms2361×body128invalid
Compiler

Compiled 260 to 205 computations (21.2% saved)

Profiling

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