Details

Time bar (total: 4.6s)

analyze617.0ms (13.5%)

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
7%92.8%0.2%8
19.1%80.7%0.2%9
29.8%70%0.2%10
31.3%68.5%0.2%11
42.3%57.2%0.6%12
53.3%45.5%1.2%13
59.2%39.3%1.5%14
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample23.0ms (0.5%)

Algorithm
intervals
Results
8.0ms256×body128valid
0.0ms17×body128invalid
Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify263.0ms (5.8%)

Algorithm
egg-herbie
Rules
986×div-sub_binary64
972×distribute-rgt-in_binary64
929×distribute-lft-in_binary64
786×sub-neg_binary64
582×times-frac_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11513
23413
37013
413113
521713
650713
7125313
8266413
9282913
10320013
11324113
12325313
13331413
14376313
15350313
16373913
17373113
18376913
19376913
20380713
21380713
22558013

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
13.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
13.1b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
Compiler

Compiled 26 to 16 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 x (-.f64 y z))
12.4b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

rewrite67.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
16×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64
cancel-sign-sub-inv_binary64
Counts
2 → 59
Calls

2 calls:

9.0ms
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
7.0ms
(*.f64 x (-.f64 y z))
Compiler

Compiled 893 to 225 computations (74.8% saved)

series115.0ms (2.5%)

Error
3.9b
Counts
2 → 42
Calls

2 calls:

68.0ms
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
27.0ms
(*.f64 x (-.f64 y z))
Compiler

Compiled 1688 to 972 computations (42.4% saved)

simplify94.0ms (2.1%)

Algorithm
egg-herbie
Rules
347×associate-/l/_binary64
342×distribute-rgt-in_binary64
322×div-sub_binary64
317×distribute-lft-in_binary64
301×associate-/r/_binary64
Counts
101 → 55
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01801849
14901684
219121573
345701573
454341573

prune33.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New49655
Fresh000
Picked011
Done000
Total49756
Error
0.0b
Counts
56 → 7
Alt Table
StatusErrorProgram
13.1b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
48.7b
(/.f64 (*.f64 (/.f64 x (+.f64 (sqrt.f64 t) (sqrt.f64 z))) (-.f64 y z)) (-.f64 (sqrt.f64 t) (sqrt.f64 z)))
2.9b
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
37.7b
(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
40.3b
(/.f64 (*.f64 (sqrt.f64 x) (*.f64 (-.f64 y z) (sqrt.f64 x))) (-.f64 t z))
11.1b
(/.f64 (*.f64 (/.f64 x (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (-.f64 t z)))
38.5b
(*.f64 (/.f64 x t) (+.f64 (/.f64 (*.f64 y z) t) (-.f64 y z)))
Compiler

Compiled 710 to 270 computations (62% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (-.f64 y z) (-.f64 t z))
2.8b
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

rewrite95.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
75×add-sqr-sqrt_binary64
70×*-un-lft-identity_binary64
51×times-frac_binary64
31×associate-*r*_binary64
26×add-cube-cbrt_binary64
Counts
2 → 102
Calls

2 calls:

14.0ms
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
8.0ms
(/.f64 (-.f64 y z) (-.f64 t z))
Compiler

Compiled 1542 to 306 computations (80.2% saved)

series145.0ms (3.2%)

Error
0.0b
Counts
2 → 51
Calls

2 calls:

67.0ms
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
49.0ms
(/.f64 (-.f64 y z) (-.f64 t z))
Compiler

Compiled 2405 to 1422 computations (40.9% saved)

simplify134.0ms (2.9%)

Algorithm
egg-herbie
Rules
845×times-frac_binary64
337×distribute-rgt-in_binary64
270×cancel-sign-sub-inv_binary64
235×sub-neg_binary64
200×div-sub_binary64
Counts
153 → 86
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02353423
16433273
222943066
345153054
450303054

prune46.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New82486
Fresh235
Picked011
Done011
Total84993
Error
0.0b
Counts
93 → 9
Alt Table
StatusErrorProgram
13.1b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
9.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))
3.9b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
35.4b
(*.f64 (sqrt.f64 x) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
2.9b
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
37.7b
(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
33.1b
(*.f64 x (*.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
11.1b
(/.f64 (*.f64 (/.f64 x (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (-.f64 t z)))
38.5b
(*.f64 (/.f64 x t) (+.f64 (/.f64 (*.f64 y z) t) (-.f64 y z)))
Compiler

Compiled 1345 to 440 computations (67.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)
1.4b
(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x))
1.7b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))

rewrite101.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
49×add-sqr-sqrt_binary64
39×*-un-lft-identity_binary64
32×associate-*l*_binary64
30×add-exp-log_binary64
27×times-frac_binary64
Counts
4 → 104
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
14.0ms
(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
Compiler

Compiled 2261 to 357 computations (84.2% saved)

series228.0ms (5%)

Error
0.0b
Counts
4 → 53
Calls

4 calls:

98.0ms
(*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x))
74.0ms
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
16.0ms
(cbrt.f64 x)
15.0ms
(cbrt.f64 x)
Compiler

Compiled 2978 to 1764 computations (40.8% saved)

simplify100.0ms (2.2%)

Algorithm
egg-herbie
Rules
377×distribute-rgt-in_binary64
350×distribute-lft-in_binary64
246×cancel-sign-sub-inv_binary64
238×associate-*l*_binary64
210×associate-*r*_binary64
Counts
157 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02463471
16742799
223062632
352282632

prune62.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1231124
Fresh066
Picked011
Done022
Total12310133
Error
0b
Counts
133 → 10
Alt Table
StatusErrorProgram
13.1b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
9.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))
3.9b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
19.7b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))) (*.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))))))
35.4b
(*.f64 (sqrt.f64 x) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
2.9b
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
37.7b
(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
33.1b
(*.f64 x (*.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
11.1b
(/.f64 (*.f64 (/.f64 x (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (-.f64 t z)))
38.5b
(*.f64 (/.f64 x t) (+.f64 (/.f64 (*.f64 y z) t) (-.f64 y z)))
Compiler

Compiled 2025 to 569 computations (71.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 y z))
0.6b
(cbrt.f64 (-.f64 y z))
0.6b
(cbrt.f64 (-.f64 y z))
8.2b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))

rewrite133.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
58×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
46×associate-*r*_binary64
40×times-frac_binary64 cbrt-prod_binary64
30×cbrt-div_binary64
26×add-cube-cbrt_binary64
Counts
4 → 132
Calls

4 calls:

30.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))
4.0ms
(cbrt.f64 (-.f64 y z))
3.0ms
(cbrt.f64 (-.f64 y z))
3.0ms
(cbrt.f64 (-.f64 y z))
Compiler

Compiled 3675 to 569 computations (84.5% saved)

series409.0ms (8.9%)

Error
0b
Counts
4 → 51
Calls

4 calls:

304.0ms
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))
27.0ms
(cbrt.f64 (-.f64 y z))
27.0ms
(cbrt.f64 (-.f64 y z))
25.0ms
(cbrt.f64 (-.f64 y z))
Compiler

Compiled 3225 to 1935 computations (40% saved)

simplify211.0ms (4.6%)

Algorithm
egg-herbie
Rules
886×times-frac_binary64
426×associate-*l*_binary64
331×associate-*r*_binary64
223×*-commutative_binary64
187×cancel-sign-sub-inv_binary64
Counts
183 → 127
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02894419
17744230
228914161
346584155
449874155
549604155

prune58.0ms (1.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New1270127
Fresh066
Picked011
Done033
Total12710137
Error
0b
Counts
137 → 10
Alt Table
StatusErrorProgram
13.1b
(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
9.5b
(*.f64 (*.f64 x (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 t z)))
3.9b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
19.7b
(*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))) (*.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 (-.f64 y z) (-.f64 t z))))))
35.4b
(*.f64 (sqrt.f64 x) (*.f64 (/.f64 (-.f64 y z) (-.f64 t z)) (sqrt.f64 x)))
2.9b
(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
37.7b
(/.f64 (*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (-.f64 y z)) (sqrt.f64 (-.f64 t z)))
33.1b
(*.f64 x (*.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
11.1b
(/.f64 (*.f64 (/.f64 x (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (-.f64 y z)) (cbrt.f64 (-.f64 t z)))
38.5b
(*.f64 (/.f64 x t) (+.f64 (/.f64 (*.f64 y z) t) (-.f64 y z)))
Compiler

Compiled 2017 to 518 computations (74.3% saved)

regimes820.0ms (18%)

Accuracy

Total 1.3b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 9041 to 4835 computations (46.5% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
sub-neg_binary64 +-commutative_binary64
*-commutative_binary64
if-if-or-not_binary64 neg-mul-1_binary64 neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02064
12564
23164
33364
43464
53464

end1.0ms (0%)

Compiler

Compiled 47 to 17 computations (63.8% saved)

sample768.0ms (16.8%)

Algorithm
intervals
Results
268.0ms8000×body128valid
19.0ms638×body128invalid
Compiler

Compiled 261 to 132 computations (49.4% saved)

Profiling

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