Details

Time bar (total: 25.3s)

analyze5.4s (21.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%99.6%0.4%8
0%99.6%0.4%9
0%99.6%0.4%10
0%99.6%0.4%11
0%99.6%0.4%12
0%99.6%0.4%13
0%99.6%0.4%14
Compiler

Compiled 39 to 24 computations (38.5% saved)

sample185.0ms (0.7%)

Algorithm
intervals
Results
72.0ms304×body128invalid
51.0ms256×body128valid
Compiler

Compiled 86 to 56 computations (34.9% saved)

simplify344.0ms (1.4%)

Algorithm
egg-herbie
Rules
802×unsub-neg_binary64
656×sub-neg_binary64
486×fma-neg_binary64
419×distribute-neg-in_binary64
395×+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02443
15941
213941
343839
4130239
5298239
6342039
7389839
8405639
9398639
10403139
11402739
12439339
13460039
14466539
15467039
16467039
17467239
18467439
19467439
20493439
21493139

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
14.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
14.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
Compiler

Compiled 137 to 74 computations (46% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 t c) (*.f64 y i))
4.4b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
5.9b
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
6.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))

series351.0ms (1.4%)

Counts
4 → 312
Calls

4 calls:

176.0ms
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
117.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
36.0ms
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
17.0ms
(-.f64 (*.f64 t c) (*.f64 y i))

rewrite22.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 64
Calls

4 calls:

10.0ms
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
5.0ms
(-.f64 (*.f64 t c) (*.f64 y i))
1.0ms
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
1.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))

simplify449.0ms (1.8%)

Algorithm
egg-herbie
Rules
395×sub-neg_binary64
365×exp-prod_binary64
338×cancel-sign-sub-inv_binary64
333×exp-sum_binary64
316×fma-neg_binary64
Counts
376 → 191
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02419330
15838944
217318621
333938366
444478366
551098366

prune413.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1838191
Fresh000
Picked101
Done000
Total1848192
Error
0.0b
Counts
192 → 8
Alt Table
StatusErrorProgram
26.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (/.f64 (*.f64 j (*.f64 (-.f64 (*.f64 c t) (*.f64 y i)) (fma.f64 c t (*.f64 y i)))) (+.f64 (*.f64 t c) (*.f64 y i)))))
22.0b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 c (*.f64 t j) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))
28.7b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
27.4b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 y i))))
12.4b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
28.4b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
25.2b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 j y))))
15.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))))
Compiler

Compiled 6318 to 1030 computations (83.7% saved)

localize51.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.2b
(*.f64 y (*.f64 i j))
5.2b
(*.f64 a (*.f64 i b))
5.4b
(*.f64 y (*.f64 z x))
6.9b
(*.f64 c (*.f64 t j))

series71.0ms (0.3%)

Counts
4 → 32
Calls

4 calls:

20.0ms
(*.f64 a (*.f64 i b))
17.0ms
(*.f64 y (*.f64 z x))
17.0ms
(*.f64 c (*.f64 t j))
17.0ms
(*.f64 y (*.f64 i j))

rewrite39.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×add-cbrt-cube_binary64
24×add-exp-log_binary64
24×pow1_binary64
12×associate-*l*_binary64
12×cbrt-unprod_binary64
Counts
4 → 80
Calls

4 calls:

10.0ms
(*.f64 c (*.f64 t j))
7.0ms
(*.f64 y (*.f64 z x))
7.0ms
(*.f64 y (*.f64 i j))
7.0ms
(*.f64 a (*.f64 i b))

simplify141.0ms (0.6%)

Algorithm
egg-herbie
Rules
626×*-commutative_binary64
545×associate-/l/_binary64
505×sqr-pow_binary64
484×unswap-sqr_binary64
281×associate-*l*_binary64
Counts
112 → 106
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01391100
1335920
21129920
31579920
42002920
52760920
63657920
74920920
84990920

prune193.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1042106
Fresh077
Picked101
Done000
Total1059114
Error
0.0b
Counts
114 → 9
Alt Table
StatusErrorProgram
26.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (/.f64 (*.f64 j (*.f64 (-.f64 (*.f64 c t) (*.f64 y i)) (fma.f64 c t (*.f64 y i)))) (+.f64 (*.f64 t c) (*.f64 y i)))))
22.0b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 c (*.f64 t j) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))
28.7b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
27.4b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 y i))))
12.5b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (*.f64 i j))) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
39.5b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (*.f64 t j))) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
28.4b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
25.2b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 j y))))
15.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))))
Compiler

Compiled 5023 to 966 computations (80.8% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.4b
(*.f64 a (*.f64 t x))
5.2b
(*.f64 a (*.f64 i b))
5.4b
(*.f64 y (*.f64 z x))
6.9b
(*.f64 c (*.f64 t j))

series23.0ms (0.1%)

Counts
1 → 0
Calls

1 calls:

23.0ms
(*.f64 a (*.f64 t x))

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*l*_binary64
cbrt-unprod_binary64
Counts
1 → 20
Calls

1 calls:

8.0ms
(*.f64 a (*.f64 t x))

simplify99.0ms (0.4%)

Algorithm
egg-herbie
Rules
580×log-div_binary64
514×associate-/l*_binary64
411×*-commutative_binary64
409×associate-*l*_binary64
339×cube-div_binary64
Counts
20 → 20
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038219
187174
2275174
3770174
4976174
51185174
61422174
71902174
83020174
94714174
104982174

prune343.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New96298
Fresh088
Picked101
Done000
Total9710107
Error
0.0b
Counts
107 → 10
Alt Table
StatusErrorProgram
26.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (/.f64 (*.f64 j (*.f64 (-.f64 (*.f64 c t) (*.f64 y i)) (fma.f64 c t (*.f64 y i)))) (+.f64 (*.f64 t c) (*.f64 y i)))))
22.0b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 c (*.f64 t j) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))
28.7b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
27.4b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 y i))))
32.0b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (*.f64 i j))) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 (sqrt.f64 (*.f64 a (*.f64 t x))) (sqrt.f64 (*.f64 a (*.f64 t x)))))))
39.5b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (*.f64 t j))) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
28.4b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
25.2b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 j y))))
12.7b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x)))) (cbrt.f64 (*.f64 y (*.f64 z x)))))) (+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (*.f64 i j))) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
15.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))))
Compiler

Compiled 5553 to 1022 computations (81.6% saved)

localize64.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.2b
(*.f64 a (*.f64 i b))
5.4b
(*.f64 y (*.f64 z x))
6.9b
(*.f64 c (*.f64 t j))
16.0b
(cbrt.f64 (*.f64 y (*.f64 z x)))

series1.3s (5.1%)

Counts
1 → 36
Calls

1 calls:

1.3s
(cbrt.f64 (*.f64 y (*.f64 z x)))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
cbrt-prod_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 11
Calls

1 calls:

5.0ms
(cbrt.f64 (*.f64 y (*.f64 z x)))

simplify113.0ms (0.4%)

Algorithm
egg-herbie
Rules
722×fma-def_binary64
496×exp-sum_binary64
426×fma-neg_binary64
407×exp-prod_binary64
272×exp-diff_binary64
Counts
47 → 22
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
072789
1149789
2239705
3700537
41671537
54042537
64953537

prune340.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1840184
Fresh099
Picked011
Done000
Total18410194
Error
0.0b
Counts
194 → 10
Alt Table
StatusErrorProgram
26.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (/.f64 (*.f64 j (*.f64 (-.f64 (*.f64 c t) (*.f64 y i)) (fma.f64 c t (*.f64 y i)))) (+.f64 (*.f64 t c) (*.f64 y i)))))
22.0b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 c (*.f64 t j) (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a)))))
28.7b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
27.4b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 y i))))
32.0b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (*.f64 i j))) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 (sqrt.f64 (*.f64 a (*.f64 t x))) (sqrt.f64 (*.f64 a (*.f64 t x)))))))
39.5b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 (sqrt.f64 c) (*.f64 (sqrt.f64 c) (*.f64 t j))) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
28.4b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
25.2b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 i (-.f64 (*.f64 a b) (*.f64 j y))))
12.7b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 z x))) (cbrt.f64 (*.f64 y (*.f64 z x)))) (cbrt.f64 (*.f64 y (*.f64 z x)))))) (+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (*.f64 i j))) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
15.6b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))))) (cbrt.f64 (fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))))
Compiler

Compiled 11915 to 1458 computations (87.8% saved)

regimes8.9s (35.1%)

Accuracy

Total 2.8b remaining (94.5%)

Threshold costs 0b (0%)

Counts
165 → 3
Compiler

Compiled 68746 to 38708 computations (43.7% saved)

bsearch22.0ms (0.1%)

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify74.0ms (0.3%)

Algorithm
egg-herbie
Rules
248×distribute-rgt-neg-in_binary64
204×cancel-sign-sub-inv_binary64
165×distribute-lft-neg-in_binary64
154×neg-sub0_binary64
154×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072254
1137254
2189254
3248254
4312254
5353254
6411254
7497254
8559254
9631254
10713254
11842254
12961254
131072254
141135254
151168254
161184254
171188254
181188254
191184254

end3.0ms (0%)

Compiler

Compiled 180 to 63 computations (65% saved)

sample6.3s (24.8%)

Algorithm
intervals
Results
2.2s11004×body128invalid
1.6s8000×body128valid
Compiler

Compiled 695 to 330 computations (52.5% saved)

Profiling

Loading profile data...