Details

analyze1.1s (12.3%)

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
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)

sample102.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
3.0ms	22×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify119.0ms (1.3%)

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

prune2.0ms (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

11.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize7.0ms (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))
✓	11.3b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series82.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

70.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
6.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite13.0ms (0.1%)

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))

simplify118.0ms (1.3%)

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

prune136.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	156	7	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

3.1b

Counts

164 → 7

Alt Table

Status	Error	Program
	11.9b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	35.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
▶	11.7b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	12.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	44.5b	(-.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))))))
	41.1b	(/.f64 y a)
	30.5b	(/.f64 x (-.f64 t (*.f64 a z)))

Compiler

Compiled 4241 to 1205 computations (71.6% saved)

localize8.0ms (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))))
✓	1.7b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	12.1b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series150.0ms (1.6%)

Counts

3 → 114

Calls

3 calls:

78.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
37.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
35.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

rewrite65.0ms (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:

14.0ms	(-.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)))

simplify393.0ms (4.3%)

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

prune361.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	508	5	513
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	513	7	520

Error

0.1b

Counts

520 → 7

Alt Table

Status	Error	Program
	11.7b	(+.f64 (/.f64 x (-.f64 t (.f64 a z))) (neg.f64 (/.f64 (.f64 y z) (-.f64 t (*.f64 a z)))))
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.9b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	38.1b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (fma.f64 (sqrt.f64 t) (sqrt.f64 t) (neg.f64 (*.f64 z a)))))
	12.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
▶	7.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))

Compiler

Compiled 23529 to 3736 computations (84.1% saved)

localize8.0ms (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)))
	1.7b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	2.9b	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
✓	7.8b	(/.f64 (-.f64 t (*.f64 a z)) z)

series121.0ms (1.3%)

Counts

3 → 144

Calls

3 calls:

73.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
39.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
9.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)

rewrite304.0ms (3.3%)

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:

40.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
5.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
3.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)

simplify1.6s (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

prune991.0ms (10.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1491	3	1494
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	1494	7	1501

Error

Counts

1501 → 7

Alt Table

Status	Error	Program
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.9b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
▶	2.2b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	10.3b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y (-.f64 t (*.f64 a z))) z))
	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))

Compiler

Compiled 102179 to 12715 computations (87.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 t z) a)
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	1.7b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	2.9b	(/.f64 y (-.f64 (/.f64 t z) a))

series127.0ms (1.4%)

Counts

3 → 87

Calls

3 calls:

76.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
40.0ms	(/.f64 y (-.f64 (/.f64 t z) a))
10.0ms	(-.f64 (/.f64 t z) a)

rewrite175.0ms (1.9%)

Algorithm

1×	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:

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

simplify707.0ms (7.7%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	760	50504
1	1822	30992
2	4465	30846
3	5141	30846

prune507.0ms (5.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	733	1	734
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	734	7	741

Error

Counts

741 → 7

Alt Table

Status	Error	Program
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.9b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.1b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	2.2b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	2.2b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (fma.f64 t (/.f64 1 z) (neg.f64 a))))
	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	10.3b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y (-.f64 t (*.f64 a z))) z))

Compiler

Compiled 40458 to 5767 computations (85.7% saved)

regimes820.0ms (8.9%)

Accuracy

Total 1.3b remaining (98.5%)

Threshold costs 0b (0%)

Counts

111 → 3

Compiler

Compiled 15124 to 8444 computations (44.2% saved)

bsearch27.0ms (0.3%)

Steps

Iters	Range		Point
7	4.657415066172088e-32	1.0627287957331823e-29	6.9268633400870775e-31
3	-1.1533439929099623e-17	-4.611700629374892e-29	-8.396757719904244e-25

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	52
1	46	52
2	65	52
3	76	52
4	82	52
5	83	52
6	83	52

end1.0ms (0%)

Compiler: Compiled 40 to 22 computations (45% saved)

sample1.1s (12%)

Algorithm

1×

intervals

Results

532.0ms	8000×	body	128	valid
44.0ms	770×	body	128	invalid

Compiler

Compiled 196 to 120 computations (38.8% saved)

Details

analyze1.1s (12.3%)

sample102.0ms (1.1%)

simplify119.0ms (1.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series82.0ms (0.9%)

rewrite13.0ms (0.1%)

simplify118.0ms (1.3%)

prune136.0ms (1.5%)

localize8.0ms (0.1%)

series150.0ms (1.6%)

rewrite65.0ms (0.7%)

simplify393.0ms (4.3%)

prune361.0ms (3.9%)

localize8.0ms (0.1%)

series121.0ms (1.3%)

rewrite304.0ms (3.3%)

simplify1.6s (17.7%)

prune991.0ms (10.7%)

localize11.0ms (0.1%)

series127.0ms (1.4%)

rewrite175.0ms (1.9%)

simplify707.0ms (7.7%)

prune507.0ms (5.5%)

regimes820.0ms (8.9%)

bsearch27.0ms (0.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.1s (12%)

Profiling