Details

Time bar (total: 15.1s)

analyze5.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
99.6%0%0.4%1
Compiler

Compiled 39 to 24 computations (38.5% saved)

sample1.7s (11%)

Infinites
57.5% of outputs are infinite.
Results
1.5s8256×body128valid
Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify325.0ms (2.1%)

Algorithm
egg-herbie
Rules
800×unsub-neg_binary64
655×sub-neg_binary64
486×fma-neg_binary64
421×distribute-neg-in_binary64
393×+-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02443
15941
213941
343839
4130239
5297839
6343339
7390039
8405839
9398839
10403339
11402939
12439339
13460039
14466539
15467039
16467039
17467239
18467439
19467439
20493439
21493139

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
16.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
16.3b
(fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
17.3b
(+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))
Compiler

Compiled 213 to 118 computations (44.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (*.f64 y z) (*.f64 t a))
4.4b
(*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))
6.4b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))
7.9b
(fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))

series234.0ms (1.5%)

Counts
4 → 312
Calls

4 calls:

117.0ms
(fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
84.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))
23.0ms
(*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))
9.0ms
(-.f64 (*.f64 y z) (*.f64 t a))

rewrite11.0ms (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:

6.0ms
(*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))
2.0ms
(-.f64 (*.f64 y z) (*.f64 t a))
0.0ms
(fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
0.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))

simplify273.0ms (1.8%)

Algorithm
egg-herbie
Rules
410×sub-neg_binary64
370×cancel-sign-sub-inv_binary64
359×exp-prod_binary64
345×exp-sum_binary64
339×*-commutative_binary64
Counts
376 → 186
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02539332
16318944
219168621
338458366
443728366
549518366

prune211.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1779186
Fresh101
Picked101
Done000
Total1799188
Error
0.0b
Counts
188 → 9
Alt Table
StatusErrorProgram
25.0b
(-.f64 (+.f64 (*.f64 c (*.f64 a j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 a (*.f64 t x)) (*.f64 c (*.f64 z b))))
29.9b
(cbrt.f64 (pow.f64 (fma.f64 b (-.f64 (*.f64 i t) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 a t)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))) 3))
23.0b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
27.3b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))
35.5b
(*.f64 b (-.f64 (*.f64 i t) (*.f64 c z)))
27.1b
(-.f64 (+.f64 (*.f64 i (*.f64 t b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
24.9b
(+.f64 (*.f64 a (-.f64 (*.f64 c j) (*.f64 x t))) (*.f64 i (-.f64 (*.f64 t b) (*.f64 j y))))
37.4b
(*.f64 (sqrt.f64 (fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))) (sqrt.f64 (fma.f64 b (-.f64 (*.f64 t i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))))
16.8b
(+.f64 (*.f64 b (-.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
Compiler

Compiled 6086 to 1033 computations (83% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.5b
(+.f64 (*.f64 b (-.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
4.4b
(*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))
6.4b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i))))
8.0b
(*.f64 b (-.f64 (*.f64 t i) (*.f64 z c)))

series133.0ms (0.9%)

Counts
2 → 168
Calls

2 calls:

109.0ms
(+.f64 (*.f64 b (-.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
24.0ms
(*.f64 b (-.f64 (*.f64 t i) (*.f64 z c)))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
associate-+l+_binary64
distribute-lft-in_binary64
distribute-rgt-in_binary64
add-sqr-sqrt_binary64
cancel-sign-sub-inv_binary64
Counts
2 → 49
Calls

2 calls:

6.0ms
(*.f64 b (-.f64 (*.f64 t i) (*.f64 z c)))
5.0ms
(+.f64 (*.f64 b (-.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))

simplify153.0ms (1%)

Algorithm
egg-herbie
Rules
439×distribute-rgt-in_binary64
406×cancel-sign-sub-inv_binary64
377×distribute-lft-in_binary64
259×fma-neg_binary64
256×unsub-neg_binary64
Counts
217 → 137
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02166315
15856222
218176188
343815767
449555767

prune242.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2212223
Fresh178
Picked101
Done000
Total2239232
Error
0b
Counts
232 → 9
Alt Table
StatusErrorProgram
25.0b
(-.f64 (+.f64 (*.f64 c (*.f64 a j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 a (*.f64 t x)) (*.f64 c (*.f64 z b))))
29.9b
(cbrt.f64 (pow.f64 (fma.f64 b (-.f64 (*.f64 i t) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 a t)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))) 3))
23.0b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
27.3b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))
35.5b
(*.f64 b (-.f64 (*.f64 i t) (*.f64 c z)))
27.1b
(-.f64 (+.f64 (*.f64 i (*.f64 t b)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x))))
24.9b
(+.f64 (*.f64 a (-.f64 (*.f64 c j) (*.f64 x t))) (*.f64 i (-.f64 (*.f64 t b) (*.f64 j y))))
32.9b
(+.f64 (/.f64 (*.f64 b (*.f64 (-.f64 (*.f64 i t) (*.f64 c z)) (fma.f64 i t (*.f64 c z)))) (+.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
17.5b
(+.f64 (*.f64 (*.f64 t i) b) (-.f64 (fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))) (*.f64 b (*.f64 c z))))
Compiler

Compiled 7726 to 1165 computations (84.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.4b
(*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))
6.1b
(*.f64 b (*.f64 c z))
6.4b
(fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y))))
7.0b
(*.f64 (*.f64 t i) b)

series101.0ms (0.7%)

Counts
4 → 220
Calls

4 calls:

60.0ms
(fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y))))
21.0ms
(*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))
10.0ms
(*.f64 (*.f64 t i) b)
9.0ms
(*.f64 b (*.f64 c z))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
16×pow1_binary64
10×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
Counts
4 → 78
Calls

4 calls:

6.0ms
(*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))
4.0ms
(*.f64 b (*.f64 c z))
4.0ms
(*.f64 (*.f64 t i) b)
0.0ms
(fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y))))

simplify157.0ms (1%)

Algorithm
egg-herbie
Rules
614×fma-neg_binary64
514×fma-def_binary64
297×associate-*l*_binary64
277×exp-prod_binary64
257×cancel-sign-sub-inv_binary64
Counts
298 → 145
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02065062
15064629
216104401
331214395
445914395
549124395

prune161.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1441145
Fresh178
Picked011
Done000
Total1459154
Error
0b
Counts
154 → 9
Alt Table
StatusErrorProgram
25.0b
(-.f64 (+.f64 (*.f64 c (*.f64 a j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 a (*.f64 t x)) (*.f64 c (*.f64 z b))))
27.4b
(+.f64 (*.f64 (*.f64 t i) b) (-.f64 (*.f64 y (-.f64 (*.f64 z x) (*.f64 i j))) (*.f64 b (*.f64 c z))))
29.9b
(cbrt.f64 (pow.f64 (fma.f64 b (-.f64 (*.f64 i t) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 a t)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))) 3))
23.0b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
27.3b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))
35.5b
(*.f64 b (-.f64 (*.f64 i t) (*.f64 c z)))
24.9b
(+.f64 (*.f64 a (-.f64 (*.f64 c j) (*.f64 x t))) (*.f64 i (-.f64 (*.f64 t b) (*.f64 j y))))
32.9b
(+.f64 (/.f64 (*.f64 b (*.f64 (-.f64 (*.f64 i t) (*.f64 c z)) (fma.f64 i t (*.f64 c z)))) (+.f64 (*.f64 t i) (*.f64 z c))) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 a c) (*.f64 y i)))))
17.5b
(+.f64 (*.f64 (*.f64 t i) b) (-.f64 (fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))) (*.f64 b (*.f64 c z))))
Compiler

Compiled 5436 to 1029 computations (81.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(-.f64 (*.f64 i b) (*.f64 a x))
2.4b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
4.1b
(*.f64 c (-.f64 (*.f64 a j) (*.f64 z b)))
5.6b
(*.f64 t (-.f64 (*.f64 i b) (*.f64 a x)))

series114.0ms (0.8%)

Counts
4 → 208
Calls

4 calls:

65.0ms
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
20.0ms
(*.f64 t (-.f64 (*.f64 i b) (*.f64 a x)))
20.0ms
(*.f64 c (-.f64 (*.f64 a j) (*.f64 z b)))
9.0ms
(-.f64 (*.f64 i b) (*.f64 a x))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×associate-*r/_binary64
12×distribute-lft-in_binary64
12×distribute-rgt-in_binary64
12×add-sqr-sqrt_binary64
cancel-sign-sub-inv_binary64
Counts
4 → 102
Calls

4 calls:

7.0ms
(*.f64 c (-.f64 (*.f64 a j) (*.f64 z b)))
6.0ms
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))))
5.0ms
(*.f64 t (-.f64 (*.f64 i b) (*.f64 a x)))
3.0ms
(-.f64 (*.f64 i b) (*.f64 a x))

simplify180.0ms (1.2%)

Algorithm
egg-herbie
Rules
359×fma-neg_binary64
320×associate-*l*_binary64
279×associate-*r*_binary64
249×cancel-sign-sub-inv_binary64
224×associate-+l+_binary64
Counts
310 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02346273
16625810
225775762
347245762
449365762

prune287.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1882190
Fresh257
Picked101
Done011
Total1918199
Error
0b
Counts
199 → 8
Alt Table
StatusErrorProgram
25.0b
(-.f64 (+.f64 (*.f64 c (*.f64 a j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 a (*.f64 t x)) (*.f64 c (*.f64 z b))))
27.4b
(+.f64 (*.f64 (*.f64 t i) b) (-.f64 (*.f64 y (-.f64 (*.f64 z x) (*.f64 i j))) (*.f64 b (*.f64 c z))))
29.3b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (cbrt.f64 (pow.f64 (*.f64 t (-.f64 (*.f64 i b) (*.f64 a x))) 3)))
35.5b
(*.f64 b (-.f64 (*.f64 i t) (*.f64 c z)))
24.9b
(+.f64 (*.f64 a (-.f64 (*.f64 c j) (*.f64 x t))) (*.f64 i (-.f64 (*.f64 t b) (*.f64 j y))))
23.1b
(+.f64 (*.f64 c (-.f64 (*.f64 a j) (*.f64 z b))) (*.f64 t (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 i b) (*.f64 a x))) (cbrt.f64 (-.f64 (*.f64 i b) (*.f64 a x)))) (cbrt.f64 (-.f64 (*.f64 i b) (*.f64 a x))))))
17.5b
(+.f64 (*.f64 (*.f64 t i) b) (-.f64 (fma.f64 x (-.f64 (*.f64 z y) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 c a) (*.f64 i y)))) (*.f64 b (*.f64 c z))))
27.3b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))
Compiler

Compiled 5563 to 857 computations (84.6% saved)

regimes10.3s (68.3%)

Accuracy

Total 18.2b remaining (95.3%)

Threshold costs 0b (0%)

Counts
259 → 9
Compiler

Compiled 78496 to 49788 computations (36.6% saved)

bsearch214.0ms (1.4%)

Steps
ItersRangePoint
10
1.4094219898437142e-52
4.190715485667577e-39
1.4276677929317117e-52
9
1.1998112685168236e-86
1.0888570684396623e-79
1.0736222073065391e-79
6
3.395532635548053e-245
2.6144077161557448e-244
3.5212638255044147e-245
9
-2.2700899272169845e-131
-5.596842920117076e-137
-5.418483375313162e-135
10
-27551948906746.734
-579.6489308531277
-746741518026.9556
4
-7.053515577656262e+113
-4.117936282767277e+113
-6.587183720127357e+113
8
-2.7808052631861194e+169
-1.127415032737201e+166
-5.583327439550542e+166
7
-3.7983524192728697e+236
-3.132551912832575e+234
-3.4146347982611155e+236
Compiler

Compiled 10 to 9 computations (10% saved)

simplify13.0ms (0.1%)

Algorithm
egg-herbie
Rules
55×*-commutative_binary64
41×+-commutative_binary64
35×sub-neg_binary64
24×distribute-rgt-neg-in_binary64
23×neg-sub0_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0105348
1188346
2262346
3317346
4344346
5349346
6349346

end169.0ms (1.1%)

Compiler

Compiled 739 to 341 computations (53.9% saved)

Profiling

Loading profile data...