Details

analyze1.3s (12.1%)

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 (11.3%)

Results

1.0s	8255×	body	128	valid
98.0ms	789×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% 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))
✓	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series58.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
17.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite12.0ms (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 (0.8%)

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

prune112.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

0.0b

Counts

137 → 6

Alt Table

Status	Error	Program
	32.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	3.2b	(.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)))
	22.9b	(fma.f64 (/.f64 y a) t x)
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	2.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 3414 to 1111 computations (67.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series88.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

42.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
23.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
22.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite39.0ms (0.4%)

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:

9.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
8.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify172.0ms (1.7%)

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

prune220.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	336	6	342

Error

0.0b

Counts

342 → 6

Alt Table

Status	Error	Program
	32.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
▶	3.2b	(.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)))
	22.9b	(fma.f64 (/.f64 y a) t x)
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	2.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 8634 to 2771 computations (67.9% saved)

localize10.0ms (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	(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))
✓	0.6b	(*.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)))
	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series3.2s (30.6%)

Counts

3 → 180

Calls

3 calls:

2.7s

(*.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)))

496.0ms

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

38.0ms

(*.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)))

5.0ms

(*.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))

simplify470.0ms (4.5%)

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 → 309

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3470	53705
1	5133	53705

prune1.9s (18.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	685	0	685
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	685	6	691

Error

0.0b

Counts

691 → 6

Alt Table

Status	Error	Program
	32.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
▶	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
✓	3.2b	(.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)))
	22.9b	(fma.f64 (/.f64 y a) t x)
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	2.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 117855 to 55034 computations (53.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
✓	4.8b	(/.f64 (*.f64 y t) (-.f64 z a))
✓	9.9b	(/.f64 (*.f64 y z) (-.f64 z a))

series120.0ms (1.1%)

Counts

3 → 81

Calls

3 calls:

72.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
27.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
21.0ms	(/.f64 (*.f64 y z) (-.f64 z a))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
35×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 137

Calls

3 calls:

13.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
6.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
4.0ms	(/.f64 (*.f64 y z) (-.f64 z a))

simplify136.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

570×	`cancel-sign-sub-inv_binary64`
266×	`sub-neg_binary64`
221×	`associate-/l*_binary64`
212×	`fma-neg_binary64`
193×	`times-frac_binary64`

Counts

218 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	8392
1	1001	6278
2	3795	5703
3	5105	5703

prune222.0ms (2.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	236	9	245

Error

Counts

245 → 9

Alt Table

Status	Error	Program
	17.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 y t) (-.f64 z a)) (/.f64 (.f64 y t) (-.f64 z a))) (/.f64 (.f64 y t) (-.f64 z a)))))
✓	3.2b	(.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)))
	32.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
✓	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	10.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (/.f64 (.f64 y t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 1 (/.f64 (-.f64 z a) (.f64 y t))))
	22.9b	(fma.f64 (/.f64 y a) t x)
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	2.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 8308 to 1629 computations (80.4% saved)

regimes814.0ms (7.8%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Counts

82 → 3

Compiler

Compiled 12819 to 6960 computations (45.7% saved)

bsearch3.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	85
1	35	85
2	42	85
3	46	85
4	48	85
5	47	85

end110.0ms (1.1%)

Compiler: Compiled 348 to 152 computations (56.3% saved)

Details

analyze1.3s (12.1%)

sample1.2s (11.3%)

simplify118.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series58.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify84.0ms (0.8%)

prune112.0ms (1.1%)

localize8.0ms (0.1%)

series88.0ms (0.8%)

rewrite39.0ms (0.4%)

simplify172.0ms (1.7%)

prune220.0ms (2.1%)

localize10.0ms (0.1%)

series3.2s (30.6%)

rewrite20.0ms (0.2%)

simplify470.0ms (4.5%)

prune1.9s (18.3%)

localize9.0ms (0.1%)

series120.0ms (1.1%)

rewrite38.0ms (0.4%)

simplify136.0ms (1.3%)

prune222.0ms (2.1%)

regimes814.0ms (7.8%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end110.0ms (1.1%)

Profiling