Details

Time bar (total: 11.1s)

analyze2.0s (18%)

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
0%99.8%0.2%9
13.2%86.5%0.2%10
17%82.8%0.2%11
18.2%81.5%0.2%12
21.7%78.1%0.2%13
32.9%66.9%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample54.0ms (0.5%)

Algorithm
intervals
Results
24.0ms256×body128valid
2.0ms23×body128invalid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify161.0ms (1.5%)

Algorithm
egg-herbie
Rules
1539×fma-neg_binary64
1346×fma-def_binary64
1046×div-sub_binary64
750×associate-/r/_binary64
420×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01116
12616
24916
39616
418316
533916
665716
7172616
8283016
9268716
10295116
11317216
12325816
13429716
14521316

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
8.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
8.7b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
Compiler

Compiled 59 to 33 computations (44.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 t (*.f64 a z))
0.0b
(-.f64 x (*.f64 y z))
8.4b
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

series152.0ms (1.4%)

Counts
3 → 78
Calls

3 calls:

129.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
11.0ms
(-.f64 t (*.f64 a z))
11.0ms
(-.f64 x (*.f64 y z))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
times-frac_binary64
add-log-exp_binary64
Counts
3 → 74
Calls

3 calls:

13.0ms
(/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))
5.0ms
(-.f64 t (*.f64 a z))
5.0ms
(-.f64 x (*.f64 y z))

simplify223.0ms (2%)

Algorithm
egg-herbie
Rules
886×fma-def_binary64
731×cancel-sign-sub-inv_binary64
207×sub-neg_binary64
192×fma-neg_binary64
173×times-frac_binary64
Counts
152 → 163
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02284118
16713825
224543679
349653679
449353679

prune284.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15211163
Fresh000
Picked101
Done000
Total15311164
Error
3.9b
Counts
164 → 11
Alt Table
StatusErrorProgram
42.6b
(/.f64 x t)
38.6b
(/.f64 (-.f64 x (*.f64 y z)) (*.f64 (sqrt.f64 (-.f64 t (*.f64 a z))) (sqrt.f64 (-.f64 t (*.f64 a z)))))
32.7b
(*.f64 (/.f64 (-.f64 x (*.f64 y z)) (*.f64 (-.f64 t (*.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
8.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
38.0b
(*.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (*.f64 y z))) (-.f64 t (*.f64 z a))))
45.2b
(/.f64 y a)
9.6b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (-.f64 t (*.f64 z a))))
8.7b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 a z))))
38.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (sqrt.f64 (-.f64 t (*.f64 a z)))) (/.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (sqrt.f64 (-.f64 t (*.f64 a z)))))
9.2b
(/.f64 1 (/.f64 (-.f64 t (*.f64 a z)) (-.f64 x (*.f64 y z))))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (/.f64 (-.f64 t (*.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
Compiler

Compiled 4409 to 1281 computations (70.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 t (*.f64 a z))
0.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 a z))))
2.9b
(/.f64 x (-.f64 t (*.f64 a z)))
8.0b
(/.f64 (*.f64 y z) (-.f64 t (*.f64 a z)))

series231.0ms (2.1%)

Counts
3 → 114
Calls

3 calls:

121.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 a z))))
64.0ms
(/.f64 x (-.f64 t (*.f64 a z)))
45.0ms
(/.f64 (*.f64 y z) (-.f64 t (*.f64 a z)))

rewrite132.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
151×times-frac_binary64
135×prod-diff_binary64
120×add-sqr-sqrt_binary64
117×*-un-lft-identity_binary64
115×add-cube-cbrt_binary64
Counts
3 → 236
Calls

3 calls:

30.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 a z))))
9.0ms
(/.f64 (*.f64 y z) (-.f64 t (*.f64 a z)))
6.0ms
(/.f64 x (-.f64 t (*.f64 a z)))

simplify551.0ms (5%)

Algorithm
egg-herbie
Rules
441×fma-neg_binary64
243×unsub-neg_binary64
216×associate-/l*_binary64
216×times-frac_binary64
203×associate-*l*_binary64
Counts
350 → 439
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043621196
1110416095
2415215759
3495215759
4505215759

prune636.0ms (5.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New5076513
Fresh6410
Picked101
Done000
Total51410524
Error
0.0b
Counts
524 → 10
Alt Table
StatusErrorProgram
29.7b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (expm1.f64 (log1p.f64 (-.f64 t (*.f64 z a))))))
38.6b
(/.f64 (-.f64 x (*.f64 y z)) (*.f64 (sqrt.f64 (-.f64 t (*.f64 a z))) (sqrt.f64 (-.f64 t (*.f64 a z)))))
8.7b
(+.f64 (/.f64 x (-.f64 t (*.f64 a z))) (neg.f64 (/.f64 (*.f64 y z) (-.f64 t (*.f64 a z)))))
34.7b
(/.f64 (-.f64 y (/.f64 x z)) a)
8.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
6.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z)))
6.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
37.6b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 (/.f64 y (sqrt.f64 (-.f64 t (*.f64 a z)))) (/.f64 z (sqrt.f64 (-.f64 t (*.f64 a z))))))
9.2b
(/.f64 1 (/.f64 (-.f64 t (*.f64 a z)) (-.f64 x (*.f64 y z))))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (/.f64 (-.f64 t (*.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
Compiler

Compiled 23695 to 3812 computations (83.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
2.9b
(/.f64 x (-.f64 t (*.f64 a z)))
2.9b
(*.f64 y (/.f64 z (-.f64 t (*.f64 z a))))
5.9b
(/.f64 z (-.f64 t (*.f64 z a)))

series251.0ms (2.3%)

Counts
3 → 144
Calls

3 calls:

123.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
80.0ms
(*.f64 y (/.f64 z (-.f64 t (*.f64 z a))))
44.0ms
(/.f64 z (-.f64 t (*.f64 z a)))

rewrite49.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
37×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
15×fma-neg_binary64
Counts
3 → 112
Calls

3 calls:

15.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
11.0ms
(*.f64 y (/.f64 z (-.f64 t (*.f64 z a))))
6.0ms
(/.f64 z (-.f64 t (*.f64 z a)))

simplify414.0ms (3.7%)

Algorithm
egg-herbie
Rules
382×fma-neg_binary64
271×distribute-rgt-neg-in_binary64
245×sub-neg_binary64
210×associate-/l*_binary64
210×times-frac_binary64
Counts
256 → 254
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03278156
18927648
234216954
347956953
449996953
549286953

prune415.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3213324
Fresh369
Picked011
Done000
Total32410334
Error
0.0b
Counts
334 → 10
Alt Table
StatusErrorProgram
29.7b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (expm1.f64 (log1p.f64 (-.f64 t (*.f64 z a))))))
38.6b
(/.f64 (-.f64 x (*.f64 y z)) (*.f64 (sqrt.f64 (-.f64 t (*.f64 a z))) (sqrt.f64 (-.f64 t (*.f64 a z)))))
3.2b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
6.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
34.7b
(/.f64 (-.f64 y (/.f64 x z)) a)
8.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
9.2b
(/.f64 1 (/.f64 (-.f64 t (*.f64 a z)) (-.f64 x (*.f64 y z))))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (/.f64 (-.f64 t (*.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
8.7b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 z a))))
19.4b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (cbrt.f64 (pow.f64 (/.f64 y (-.f64 (/.f64 t z) a)) 3)))
Compiler

Compiled 9964 to 2315 computations (76.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (/.f64 t z) a)
0.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
2.9b
(/.f64 x (-.f64 t (*.f64 a z)))
3.4b
(/.f64 y (-.f64 (/.f64 t z) a))

series209.0ms (1.9%)

Counts
3 → 87
Calls

3 calls:

128.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
62.0ms
(/.f64 y (-.f64 (/.f64 t z) a))
19.0ms
(-.f64 (/.f64 t z) a)

rewrite267.0ms (2.4%)

Algorithm
rewrite-expression-head
Rules
668×add-sqr-sqrt_binary64
628×times-frac_binary64
508×*-un-lft-identity_binary64
399×prod-diff_binary64
391×add-cube-cbrt_binary64
Counts
3 → 534
Calls

3 calls:

47.0ms
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
11.0ms
(/.f64 y (-.f64 (/.f64 t z) a))
8.0ms
(-.f64 (/.f64 t z) a)

simplify1.1s (10.3%)

Algorithm
egg-herbie
Rules
772×fma-def_binary64
339×fma-udef_binary64
269×unsub-neg_binary64
237×associate-/l*_binary64
230×associate-*l*_binary64
Counts
621 → 664
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
076050504
1182230992
2446530846
3514130846

prune879.0ms (7.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New7331734
Fresh178
Picked011
Done011
Total73410744
Error
0.0b
Counts
744 → 10
Alt Table
StatusErrorProgram
3.2b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
6.0b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (*.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
9.2b
(/.f64 1 (/.f64 (-.f64 t (*.f64 a z)) (-.f64 x (*.f64 y z))))
3.4b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 1 (/.f64 (-.f64 (/.f64 t z) a) y)))
38.6b
(/.f64 (-.f64 x (*.f64 y z)) (*.f64 (sqrt.f64 (-.f64 t (*.f64 a z))) (sqrt.f64 (-.f64 t (*.f64 a z)))))
34.7b
(/.f64 (-.f64 y (/.f64 x z)) a)
8.8b
(*.f64 (-.f64 x (*.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
9.6b
(/.f64 (*.f64 (cbrt.f64 (-.f64 x (*.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z)))) (/.f64 (-.f64 t (*.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
8.7b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 (*.f64 y z) (-.f64 t (*.f64 z a))))
19.4b
(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (cbrt.f64 (pow.f64 (/.f64 y (-.f64 (/.f64 t z) a)) 3)))
Compiler

Compiled 40536 to 5809 computations (85.7% saved)

regimes1.3s (12%)

Accuracy

Total 2.1b remaining (99%)

Threshold costs 0b (0%)

Counts
119 → 3
Compiler

Compiled 15851 to 8989 computations (43.3% saved)

bsearch74.0ms (0.7%)

Steps
ItersRangePoint
9
1.5628054108905067e-159
1.2584746228911093e-152
3.936325700975888e-156
7
-3.988328107398728e+46
-4.173050405874695e+44
-4.264720045142372e+44
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×+-commutative_binary64
10×sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02552
14652
26752
37952
48652
58752
68652

end3.0ms (0%)

Compiler

Compiled 40 to 22 computations (45% saved)

sample1.5s (13.9%)

Algorithm
intervals
Results
687.0ms8000×body128valid
57.0ms724×body128invalid
Compiler

Compiled 274 to 162 computations (40.9% saved)

Profiling

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