Details

analyze1.3s (10.8%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (10.1%)

Results

1.0s	8254×	body	128	valid
98.0ms	786×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series56.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
15.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune107.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	5	136

Error

0.0b

Counts

136 → 5

Alt Table

Status	Error	Program
	1.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
▶	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	38.8b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
	3.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	10.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))

Compiler

Compiled 3465 to 1136 computations (67.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.7b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series64.0ms (0.5%)

Counts

3 → 132

Calls

3 calls:

33.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
17.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
15.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

12.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify242.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune267.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	336	5	341

Error

0.0b

Counts

341 → 5

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	38.8b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
	3.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	10.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))

Compiler

Compiled 8693 to 2804 computations (67.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 1 (-.f64 z t)))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
✓	1.7b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)

series71.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

33.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
29.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
7.0ms	(/.f64 1 (-.f64 z t))
3.0ms	(/.f64 1 (/.f64 1 (-.f64 z t)))

rewrite86.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

305×	`times-frac_binary64`
250×	`add-sqr-sqrt_binary64`
208×	`*-un-lft-identity_binary64`
172×	`add-exp-log_binary64`
130×	`add-cube-cbrt_binary64`

Counts

4 → 357

Calls

4 calls:

36.0ms	(*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t))))
8.0ms	(/.f64 1 (/.f64 1 (-.f64 z t)))
4.0ms	(/.f64 1 (-.f64 z t))
0.0ms	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)

simplify227.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

511×	`cancel-sign-sub-inv_binary64`
363×	`sub-neg_binary64`
331×	`fma-neg_binary64`
220×	`neg-mul-1_binary64`
190×	`+-commutative_binary64`

Counts

501 → 533

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	380	8373
1	875	7951
2	3065	7309
3	4394	7306
4	5020	7306

prune429.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	532	1	533
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	533	5	538

Error

0.0b

Counts

538 → 5

Alt Table

Status	Error	Program
✓	1.8b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
▶	3.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	10.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	26.1b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (-.f64 a t))))

Compiler

Compiled 13464 to 6474 computations (51.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
✓	0.6b	(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))
	1.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series2.0s (17%)

Counts

3 → 180

Calls

3 calls:

1.7s

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))

304.0ms

(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))

36.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))

1.0ms

(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))

simplify482.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
259×	`times-frac_binary64`
101×	`sub-neg_binary64`
48×	`unpow1/3_binary64`
14×	`unpow2_binary64`

Counts

273 → 311

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3470	53705
1	5133	53705

prune1.7s (14.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	686	1	687
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	687	5	692

Error

0.0b

Counts

692 → 5

Alt Table

Status	Error	Program
✓	1.8b	(fma.f64 y (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 1 (/.f64 1 (-.f64 z t)))) x)
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	3.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))))
	10.5b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	26.1b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (-.f64 a t))))

Compiler

Compiled 117889 to 54972 computations (53.4% saved)

regimes3.1s (26.5%)

Accuracy

Total 0.4b remaining (94.4%)

Threshold costs 0.4b (94.4%)

Counts

248 → 3

Compiler

Compiled 61216 to 28892 computations (52.8% saved)

bsearch30.0ms (0.3%)

Steps

Iters	Range		Point
7	4.141880323264373e-41	2.6142494871054056e-36	3.850809288581042e-38
1	-5.9874853621433135e-9	-4.764319425246092e-13	-5.3186352085026664e-11

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	65
1	41	65
2	53	65
3	66	65
4	73	65
5	76	65
6	77	65
7	74	65

end86.0ms (0.7%)

Compiler: Compiled 241 to 104 computations (56.8% saved)

Details

analyze1.3s (10.8%)

sample1.2s (10.1%)

simplify119.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series56.0ms (0.5%)

rewrite14.0ms (0.1%)

simplify84.0ms (0.7%)

prune107.0ms (0.9%)

localize8.0ms (0.1%)

series64.0ms (0.5%)

rewrite39.0ms (0.3%)

simplify242.0ms (2.1%)

prune267.0ms (2.3%)

localize10.0ms (0.1%)

series71.0ms (0.6%)

rewrite86.0ms (0.7%)

simplify227.0ms (1.9%)

prune429.0ms (3.7%)

localize12.0ms (0.1%)

series2.0s (17%)

rewrite20.0ms (0.2%)

simplify482.0ms (4.1%)

prune1.7s (14.6%)

regimes3.1s (26.5%)

bsearch30.0ms (0.3%)

simplify4.0ms (0%)

end86.0ms (0.7%)

Profiling