Details

analyze321.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample143.0ms (3%)

Algorithm

1×

intervals

Results

37.0ms	74×	body	1024	valid
14.0ms	132×	body	128	valid
10.0ms	32×	body	512	valid
7.0ms	9×	body	2048	valid
2.0ms	9×	body	256	valid
1.0ms	6×	body	128	invalid
1.0ms	1×	body	1024	invalid
0.0ms	3×	body	128	overflowed
0.0ms	1×	body	256	invalid

Compiler

Compiled 65 to 53 computations (18.5% saved)

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
577×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
467×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	153	37
3	394	37
4	1347	37
5	4048	37
6	4614	37
7	5259	37

prune5.0ms (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

30.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	41.8b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))
▶	30.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

41.8b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

▶

30.1b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
✓	0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
✓	1.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series81.0ms (1.7%)

Counts

4 → 92

Calls

4 calls:

45.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
16.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
14.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
6.0ms	(*.f64 (+.f64 1 eps) x)

rewrite69.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
80×	`exp-neg_binary64`
80×	`frac-times_binary64`
60×	`exp-diff_binary64`
60×	`neg-sub0_binary64`

Counts

4 → 191

Calls

4 calls:

13.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
12.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
10.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(*.f64 (+.f64 1 eps) x)

simplify236.0ms (5%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-neg_binary64`
538×	`associate-l_binary64`
535×	`associate-r_binary64`
518×	`fma-def_binary64`
273×	`distribute-rgt-in_binary64`

Counts

283 → 340

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	12489
1	1523	11687
2	4721	11687
3	5065	11687

prune364.0ms (7.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	340	2	342

Error

Counts

342 → 2

Alt Table

Status	Error	Program
	15.1b	(/.f64 (+.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (.f64 2 x))) (fma.f64 1/3 (.f64 (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)
▶	0.1b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Status

Error

Program

15.1b

(/.f64 (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 2 x))) (fma.f64 1/3 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)

▶

0.1b

(/.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2)) 2)

Compiler

Compiled 17429 to 12997 computations (25.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`frac-times_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 30

Calls

1 calls:

7.0ms

(*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-neg_binary64`
438×	`associate-*l/_binary64`
360×	`associate-/l*_binary64`
273×	`fma-def_binary64`
266×	`distribute-rgt-in_binary64`

Counts

42 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	671
1	244	543
2	771	537
3	2084	533
4	4357	533
5	4922	533

prune59.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	61	2	63

Error

Counts

63 → 2

Alt Table

Status	Error	Program
▶	15.1b	(/.f64 (+.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (.f64 2 x))) (fma.f64 1/3 (.f64 (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)
✓	0.1b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Status

Error

Program

▶

15.1b

(/.f64 (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 2 x))) (fma.f64 1/3 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)

✓

0.1b

(/.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2)) 2)

Compiler

Compiled 1138 to 789 computations (30.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (*.f64 2 x)))
✓	5.4b	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
✓	12.1b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))
✓	15.2b	(.f64 (.f64 eps eps) (*.f64 x x))

series59.0ms (1.3%)

Counts

4 → 80

Calls

4 calls:

23.0ms	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
19.0ms	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (*.f64 2 x)))
12.0ms	(.f64 (.f64 eps eps) (*.f64 x x))
4.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64`
37×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
30×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`

Counts

4 → 124

Calls

4 calls:

12.0ms	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (*.f64 2 x)))
8.0ms	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
7.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))
6.0ms	(.f64 (.f64 eps eps) (*.f64 x x))

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
501×	`cancel-sign-sub-inv_binary64`
436×	`associate-r_binary64`
430×	`associate-l_binary64`
395×	`unswap-sqr_binary64`

Counts

204 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	3709
1	593	3078
2	2494	2980
3	4714	2980
4	5114	2980

prune190.0ms (4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	198	2	200

Error

Counts

200 → 2

Alt Table

Status	Error	Program
✓	15.1b	(/.f64 (+.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (.f64 2 x))) (fma.f64 1/3 (.f64 (.f64 eps eps) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)
✓	0.1b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Status

Error

Program

✓

15.1b

(/.f64 (+.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 (*.f64 eps eps) (*.f64 x x)) (*.f64 2 x))) (fma.f64 1/3 (*.f64 (*.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))) (/.f64 2 (exp.f64 x)))) 2)

✓

0.1b

(/.f64 (*.f64 (exp.f64 (neg.f64 x)) (+.f64 (*.f64 2 x) 2)) 2)

Compiler

Compiled 8369 to 3863 computations (53.8% saved)

regimes400.0ms (8.5%)

Accuracy

Total 0.1b remaining (13.7%)

Threshold costs 0.1b (13.7%)

Counts

92 → 1

Compiler

Compiled 10237 to 7739 computations (24.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	18	17
3	19	17
4	19	17

end1.0ms (0%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

sample2.4s (51.7%)

Algorithm

1×

intervals

Results

1.0s	2023×	body	1024	valid
445.0ms	4257×	body	128	valid
334.0ms	1018×	body	512	valid
175.0ms	230×	body	2048	valid
100.0ms	472×	body	256	valid
20.0ms	203×	body	128	invalid
15.0ms	163×	body	128	overflowed
7.0ms	16×	body	1024	invalid
4.0ms	12×	body	512	invalid
1.0ms	3×	body	256	invalid

Compiler

Compiled 97 to 73 computations (24.7% saved)

Details

analyze321.0ms (6.8%)

sample143.0ms (3%)

simplify66.0ms (1.4%)

prune5.0ms (0.1%)

localize18.0ms (0.4%)

series81.0ms (1.7%)

rewrite69.0ms (1.5%)

simplify236.0ms (5%)

prune364.0ms (7.7%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify65.0ms (1.4%)

prune59.0ms (1.3%)

localize18.0ms (0.4%)

series59.0ms (1.3%)

rewrite40.0ms (0.9%)

simplify119.0ms (2.5%)

prune190.0ms (4%)

regimes400.0ms (8.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.4s (51.7%)

Profiling