Details

analyze554.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
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
37.4%	62.3%	0.2%	6
37.4%	62.3%	0.2%	7
37.4%	62.3%	0.2%	8
37.4%	62.3%	0.2%	9
43.6%	56.1%	0.2%	10
51.4%	48.3%	0.2%	11
51.4%	48.3%	0.2%	12
51.4%	48.3%	0.2%	13
55.3%	44.4%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample921.0ms (10.9%)

Infinites

92.1% of outputs are infinite.

Results

806.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify120.0ms (1.4%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

9.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.3b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 a z))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	9.2b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series86.0ms (1%)

Counts

3 → 78

Calls

3 calls:

73.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
7.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))
2.0ms	(-.f64 t (*.f64 a z))

simplify115.0ms (1.4%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	228	4118
1	671	3825
2	2454	3679
3	4965	3679
4	4935	3679

prune137.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Error

3.0b

Counts

164 → 8

Alt Table

Status	Error	Program
	9.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
▶	9.3b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	9.7b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	48.5b	(-.f64 (fma.f64 (/.f64 a t) (/.f64 (.f64 z x) t) (fma.f64 (/.f64 (.f64 a a) (pow.f64 t 3)) (.f64 z (.f64 z x)) (/.f64 x t))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y (.f64 z z)) t) (fma.f64 (/.f64 y t) z (/.f64 y (/.f64 (pow.f64 (/.f64 t z) 3) (*.f64 a a))))))
	10.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (cbrt.f64 (-.f64 t (*.f64 a z))))
	42.1b	(/.f64 y a)
	42.0b	(/.f64 x t)
	44.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (.f64 (-.f64 t (.f64 a z)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z))))))

Compiler

Compiled 4321 to 1245 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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))))
✓	3.4b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	8.7b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series177.0ms (2.1%)

Counts

3 → 114

Calls

3 calls:

91.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
48.0ms	(/.f64 x (-.f64 t (*.f64 a z)))
38.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

rewrite61.0ms (0.7%)

Algorithm

1×	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:

16.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
4.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
3.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

simplify371.0ms (4.4%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	436	21196
1	1104	16095
2	4152	15759
3	4952	15759
4	5052	15759

prune351.0ms (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	510	3	513
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	514	7	521

Error

0.0b

Counts

521 → 7

Alt Table

Status	Error	Program
▶	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	9.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
	18.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (.f64 (/.f64 y (fma.f64 z a t)) (/.f64 z (-.f64 t (.f64 z a)))) (+.f64 t (*.f64 a z))))
	44.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (.f64 (-.f64 t (.f64 a z)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z))))))
	9.7b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	10.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (cbrt.f64 (-.f64 t (*.f64 a z))))
	30.7b	(/.f64 (-.f64 y (/.f64 x z)) a)

Compiler

Compiled 23601 to 3758 computations (84.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
✓	3.0b	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
	3.4b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	9.4b	(/.f64 (-.f64 t (*.f64 a z)) z)

series140.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

81.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
50.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
9.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)

rewrite304.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1556×	`times-frac_binary64`
949×	`add-sqr-sqrt_binary64`
934×	`*-un-lft-identity_binary64`
928×	`add-cube-cbrt_binary64`
660×	`prod-diff_binary64`

Counts

3 → 845

Calls

3 calls:

46.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
7.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)
5.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))

simplify1.5s (17.7%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
600×	`fma-udef_binary64`
521×	`unsub-neg_binary64`
200×	`sub-neg_binary64`
176×	`distribute-neg-frac_binary64`

Counts

989 → 1424

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1154	97355
1	2883	70114
2	4679	68596
3	5859	68596

prune976.0ms (11.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1493	1	1494
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	1494	7	1501

Error

0.0b

Counts

1501 → 7

Alt Table

Status	Error	Program
✓	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	9.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
▶	9.7b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	10.0b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (cbrt.f64 (-.f64 t (*.f64 a z))))
	10.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y (-.f64 t (*.f64 a z))) z))
	30.7b	(/.f64 (-.f64 y (/.f64 x z)) a)
	18.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (.f64 (/.f64 y (fma.f64 z a t)) (/.f64 z (-.f64 t (.f64 z a)))) (+.f64 t (*.f64 a z))))

Compiler

Compiled 102207 to 12712 computations (87.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 a z))
	0.0b	(-.f64 x (*.f64 y z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	9.2b	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

series139.0ms (1.6%)

Counts

2 → 120

Calls

2 calls:

75.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))
63.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 120

Calls

2 calls:

10.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
5.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

simplify221.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

398×	`sub-neg_binary64`
351×	`times-frac_binary64`
310×	`fma-neg_binary64`
262×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

240 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	8921
1	1048	8344
2	4130	8272
3	4944	8272
4	4953	8272

prune258.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	323	2	325
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	326	6	332

Error

0.0b

Counts

332 → 6

Alt Table

Status	Error	Program
	31.9b	(/.f64 1 (.f64 (/.f64 (-.f64 t (.f64 a z)) (.f64 (-.f64 x (.f64 z y)) (fma.f64 z y x))) (+.f64 x (*.f64 y z))))
	10.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y (-.f64 t (*.f64 a z))) z))
	9.3b	(.f64 1 (/.f64 (-.f64 x (.f64 z y)) (-.f64 t (*.f64 a z))))
	30.7b	(/.f64 (-.f64 y (/.f64 x z)) a)
✓	7.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	18.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (.f64 (/.f64 y (fma.f64 z a t)) (/.f64 z (-.f64 t (.f64 z a)))) (+.f64 t (*.f64 a z))))

Compiler

Compiled 9355 to 2830 computations (69.7% saved)

regimes1.8s (21.2%)

Accuracy

Total 1.9b remaining (98.1%)

Threshold costs 0b (0%)

Counts

220 → 3

Compiler

Compiled 29728 to 17510 computations (41.1% saved)

bsearch36.0ms (0.4%)

Steps

Iters	Range		Point
4	3.484227177165801e-93	5.723636802121476e-93	3.727078275686462e-93
10	-9.279819197963796e+76	-1.6616865856765917e+59	-1.6905947623455013e+59

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	38	61
2	59	61
3	77	61
4	87	61
5	90	61
6	90	61

end88.0ms (1%)

Compiler: Compiled 228 to 120 computations (47.4% saved)

Details

analyze554.0ms (6.6%)

sample921.0ms (10.9%)

simplify120.0ms (1.4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series86.0ms (1%)

rewrite14.0ms (0.2%)

simplify115.0ms (1.4%)

prune137.0ms (1.6%)

localize9.0ms (0.1%)

series177.0ms (2.1%)

rewrite61.0ms (0.7%)

simplify371.0ms (4.4%)

prune351.0ms (4.2%)

localize10.0ms (0.1%)

series140.0ms (1.7%)

rewrite304.0ms (3.6%)

simplify1.5s (17.7%)

prune976.0ms (11.6%)

localize14.0ms (0.2%)

series139.0ms (1.6%)

rewrite28.0ms (0.3%)

simplify221.0ms (2.6%)

prune258.0ms (3.1%)

regimes1.8s (21.2%)

bsearch36.0ms (0.4%)

simplify6.0ms (0.1%)

end88.0ms (1%)

Profiling