Details

Time bar (total: 12.8s)

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)

sample1.4s (11.2%)

Infinites
57.6% of outputs are infinite.
Results
1.3s8256×body128valid
Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify317.0ms (2.5%)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
15.3b
(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)))))
17.3b
(+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))
Compiler

Compiled 213 to 120 computations (43.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (*.f64 a i) (*.f64 z c))
5.0b
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
5.8b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
7.0b
(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)))))

series178.0ms (1.4%)

Counts
4 → 312
Calls

4 calls:

94.0ms
(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)))))
55.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
19.0ms
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
9.0ms
(-.f64 (*.f64 a i) (*.f64 z c))

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:

5.0ms
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
3.0ms
(-.f64 (*.f64 a i) (*.f64 z c))
0.0ms
(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)))))
0.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))

simplify227.0ms (1.8%)

Algorithm
egg-herbie
Rules
417×sub-neg_binary64
382×exp-prod_binary64
378×cancel-sign-sub-inv_binary64
342×*-commutative_binary64
340×fma-neg_binary64
Counts
376 → 193
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02609329
16388941
219358618
338658372
449768372
551398372

prune211.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1858193
Fresh101
Picked101
Done000
Total1878195
Error
0.0b
Counts
195 → 8
Alt Table
StatusErrorProgram
24.8b
(+.f64 (*.f64 z (-.f64 (*.f64 y x) (*.f64 c b))) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
15.5b
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
19.8b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (-.f64 (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))) (*.f64 i (*.f64 j y))))
40.2b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 (*.f64 j (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i)))) (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i))))))
36.1b
(*.f64 (-.f64 (*.f64 a i) (*.f64 c z)) b)
18.2b
(-.f64 (+.f64 (*.f64 i (*.f64 a b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 z b)) (*.f64 a (*.f64 t x)))))
15.3b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
40.1b
(*.f64 y (-.f64 (*.f64 z x) (*.f64 i j)))
Compiler

Compiled 6208 to 972 computations (84.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (*.f64 a i) (*.f64 c z))
5.0b
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
5.8b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
7.0b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))

series100.0ms (0.8%)

Counts
2 → 129
Calls

2 calls:

91.0ms
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
9.0ms
(-.f64 (*.f64 a i) (*.f64 c z))

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 26
Calls

2 calls:

3.0ms
(-.f64 (*.f64 a i) (*.f64 c z))
0.0ms
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))

simplify147.0ms (1.1%)

Algorithm
egg-herbie
Rules
918×fma-def_binary64
848×fma-neg_binary64
487×cancel-sign-sub-inv_binary64
348×sub-neg_binary64
277×associate-*l*_binary64
Counts
155 → 105
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01774985
14734882
213994702
332934435
445734435
550694435

prune187.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1882190
Fresh257
Picked011
Done000
Total1908198
Error
0.0b
Counts
198 → 8
Alt Table
StatusErrorProgram
24.3b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
36.1b
(*.f64 (-.f64 (*.f64 a i) (*.f64 c z)) b)
15.5b
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
40.2b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 (*.f64 j (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i)))) (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i))))))
18.2b
(-.f64 (+.f64 (*.f64 i (*.f64 a b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 z b)) (*.f64 a (*.f64 t x)))))
17.7b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (-.f64 (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x)))))
15.3b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
40.1b
(*.f64 y (-.f64 (*.f64 z x) (*.f64 i j)))
Compiler

Compiled 6096 to 953 computations (84.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
5.0b
(*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))
5.8b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i))))
7.0b
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
17.9b
(cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))

series222.0ms (1.7%)

Counts
2 → 156
Calls

2 calls:

126.0ms
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
96.0ms
(cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
cbrt-prod_binary64
add-cube-cbrt_binary64
cbrt-div_binary64
Counts
2 → 25
Calls

2 calls:

4.0ms
(cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))
0.0ms
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))

simplify121.0ms (0.9%)

Algorithm
egg-herbie
Rules
456×associate-/l*_binary64
449×associate-/r*_binary64
368×associate-*l*_binary64
326×fma-def_binary64
197×*-commutative_binary64
Counts
181 → 187
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05008309
115428131
253188131

prune496.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4811482
Fresh156
Picked011
Done011
Total4828490
Error
0.0b
Counts
490 → 8
Alt Table
StatusErrorProgram
24.3b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
36.1b
(*.f64 (-.f64 (*.f64 a i) (*.f64 c z)) b)
15.5b
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
40.2b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 (*.f64 j (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i)))) (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i))))))
17.7b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (-.f64 (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x)))))
17.5b
(-.f64 (fma.f64 i (*.f64 a b) (fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))) (fma.f64 c (*.f64 z b) (fma.f64 a (*.f64 t x) (*.f64 i (*.f64 j y)))))
15.3b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
40.1b
(*.f64 y (-.f64 (*.f64 z x) (*.f64 i j)))
Compiler

Compiled 32363 to 9136 computations (71.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.1b
(*.f64 y (*.f64 z x))
5.4b
(fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))
6.6b
(*.f64 i (*.f64 j y))
7.6b
(-.f64 (fma.f64 i (*.f64 a b) (fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))) (fma.f64 c (*.f64 z b) (fma.f64 a (*.f64 t x) (*.f64 i (*.f64 j y)))))

series138.0ms (1.1%)

Counts
4 → 216
Calls

4 calls:

100.0ms
(-.f64 (fma.f64 i (*.f64 a b) (fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))) (fma.f64 c (*.f64 z b) (fma.f64 a (*.f64 t x) (*.f64 i (*.f64 j y)))))
21.0ms
(fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))
9.0ms
(*.f64 y (*.f64 z x))
8.0ms
(*.f64 i (*.f64 j y))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity_binary64
16×add-sqr-sqrt_binary64
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
14×pow1_binary64
Counts
4 → 82
Calls

4 calls:

4.0ms
(*.f64 i (*.f64 j y))
4.0ms
(*.f64 y (*.f64 z x))
3.0ms
(-.f64 (fma.f64 i (*.f64 a b) (fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))) (fma.f64 c (*.f64 z b) (fma.f64 a (*.f64 t x) (*.f64 i (*.f64 j y)))))
0.0ms
(fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))

simplify169.0ms (1.3%)

Algorithm
egg-herbie
Rules
602×distribute-rgt-in_binary64
558×distribute-lft-in_binary64
408×cancel-sign-sub-inv_binary64
407×fma-neg_binary64
200×associate-*l*_binary64
Counts
298 → 178
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02547928
16327503
220237271
346607271
449177271

prune168.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1780178
Fresh055
Picked011
Done022
Total1788186
Error
0.0b
Counts
186 → 8
Alt Table
StatusErrorProgram
24.3b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 t (-.f64 (*.f64 c j) (*.f64 x a))))
36.1b
(*.f64 (-.f64 (*.f64 a i) (*.f64 c z)) b)
15.5b
(fma.f64 b (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c))) (cbrt.f64 (-.f64 (*.f64 a i) (*.f64 z c)))) (cbrt.f64 (-.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)))))
40.2b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 z c)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 (*.f64 j (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i)))) (sqrt.f64 (-.f64 (*.f64 t c) (*.f64 y i))))))
17.7b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (-.f64 (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x))) (+.f64 (*.f64 y (*.f64 i j)) (*.f64 a (*.f64 t x)))))
17.5b
(-.f64 (fma.f64 i (*.f64 a b) (fma.f64 c (*.f64 t j) (*.f64 y (*.f64 z x)))) (fma.f64 c (*.f64 z b) (fma.f64 a (*.f64 t x) (*.f64 i (*.f64 j y)))))
15.3b
(fma.f64 b (-.f64 (*.f64 a i) (*.f64 c z)) (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 j (-.f64 (*.f64 t c) (*.f64 y i)))))
40.1b
(*.f64 y (-.f64 (*.f64 z x) (*.f64 i j)))
Compiler

Compiled 7020 to 859 computations (87.8% saved)

regimes8.1s (63.4%)

Accuracy

Total 15.9b remaining (95.3%)

Threshold costs 0b (0%)

Counts
186 → 11
Compiler

Compiled 58126 to 34428 computations (40.8% saved)

bsearch251.0ms (2%)

Steps
ItersRangePoint
9
4.105606636655793e+141
6.083824152242256e+147
8.037968703008732e+144
4
0.00022557875623825422
0.0003747883064771832
0.00022820018466013974
8
1.2272045405386184e-61
6.284365003997549e-59
3.881933784725765e-61
9
4.3200036597530493e-156
3.548483827229496e-148
4.341747647585589e-155
6
6.843268701837262e-183
2.909416870609326e-182
9.762989677428703e-183
10
6.257604631507101e-205
7.561263192576724e-187
7.426429121366233e-187
4
-8.550487901031771e-283
-4.955749551073371e-283
-7.090125446361172e-283
9
-2.8494111628715396e-230
-6.620571328254982e-236
-2.4408582861360383e-231
9
-6.615316409357684e-69
-8.213910726591001e-75
-3.470786552764898e-71
9
-9.112084715240934e-18
-2.1601293664108792e-24
-2.4801242598556534e-24
Compiler

Compiled 10 to 9 computations (10% saved)

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Rules
51×*-commutative_binary64
34×sub-neg_binary64
33×+-commutative_binary64
21×neg-sub0_binary64
21×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107426
1171426
2235426
3287426
4313426
5318426
6316426

end179.0ms (1.4%)

Compiler

Compiled 885 to 347 computations (60.8% saved)

Profiling

Loading profile data...