Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.1s (44.1%)

Results

862.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify228.0ms (9%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series20.0ms (0.8%)

Counts

3 → 18

Calls

3 calls:

14.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
5.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
0.0ms	(fma.f64 6 x -6)

simplify85.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune59.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Error

Counts

66 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	37.7b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1)))
	37.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	0.2b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 1549 to 1126 computations (27.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1))
	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1)))

series20.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1)))
6.0ms	(+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

6.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1)))
5.0ms	(+.f64 (*.f64 4 (sqrt.f64 x)) (+.f64 x 1))

simplify86.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

569×	`div-sub_binary64`
450×	`sub-neg_binary64`
270×	`fma-neg_binary64`
262×	`distribute-rgt-in_binary64`
231×	`fma-def_binary64`

Counts

53 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1158
1	210	1040
2	630	1027
3	1996	1017
4	3601	1017
5	4560	1017
6	5336	1017

prune90.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Error

Counts

107 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	17.5b	(.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 (sqrt.f64 x) (.f64 x 64) (pow.f64 (+.f64 1 x) 3))) (+.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (-.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1)))))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
	37.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.2b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 2451 to 1776 computations (27.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

series20.0ms (0.8%)

Counts

2 → 5

Calls

2 calls:

15.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
0.0ms	(fma.f64 4 (sqrt.f64 x) x)

simplify96.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
546×	`fma-def_binary64`
541×	`distribute-lft-in_binary64`
440×	`associate-/l/_binary64`
337×	`associate-+l+_binary64`

Counts

50 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1070
1	144	996
2	351	996
3	971	994
4	4376	994
5	4871	994
6	4991	994
7	4917	994

prune61.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Error

Counts

72 → 6

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	17.5b	(.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 (sqrt.f64 x) (.f64 x 64) (pow.f64 (+.f64 1 x) 3))) (+.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (-.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1)))))
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
	37.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.2b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 1581 to 1130 computations (28.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

series25.0ms (1%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
11.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
2.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

simplify131.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

710×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
455×	`div-sub_binary64`
283×	`associate-/l*_binary64`
276×	`+-commutative_binary64`

Counts

113 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	3414
1	179	3099
2	493	3072
3	1384	3057
4	3517	3057
5	4145	3057
6	5164	3057

prune143.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	171	5	176

Error

Counts

176 → 5

Alt Table

Status	Error	Program
	1.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
	37.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	17.5b	(.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 (sqrt.f64 x) (.f64 x 64) (pow.f64 (+.f64 1 x) 3))) (+.f64 (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))) (-.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (.f64 (.f64 4 (sqrt.f64 x)) (+.f64 x 1)))))
	0.3b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))))

Compiler

Compiled 4415 to 3310 computations (25% saved)

regimes159.0ms (6.3%)

Accuracy

Total 0.1b remaining (38.9%)

Threshold costs 0.1b (38.9%)

Counts

86 → 1

Compiler

Compiled 3485 to 2712 computations (22.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	13	17
2	17	17
3	19	17
4	20	17
5	20	17

end102.0ms (4.1%)

Compiler: Compiled 151 to 115 computations (23.8% saved)

Details

analyze4.0ms (0.2%)

sample1.1s (44.1%)

simplify228.0ms (9%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series20.0ms (0.8%)

rewrite5.0ms (0.2%)

simplify85.0ms (3.4%)

prune59.0ms (2.3%)

localize7.0ms (0.3%)

series20.0ms (0.8%)

rewrite13.0ms (0.5%)

simplify86.0ms (3.4%)

prune90.0ms (3.6%)

localize8.0ms (0.3%)

series20.0ms (0.8%)

rewrite6.0ms (0.3%)

simplify96.0ms (3.8%)

prune61.0ms (2.4%)

localize8.0ms (0.3%)

series25.0ms (1%)

rewrite16.0ms (0.6%)

simplify131.0ms (5.2%)

prune143.0ms (5.7%)

regimes159.0ms (6.3%)

simplify3.0ms (0.1%)

end102.0ms (4.1%)

Profiling