Details

analyze371.0ms (6.2%)

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)

sample3.3s (56%)

Results

1.5s	2066×	body	1024	valid
800.0ms	4417×	body	128	valid
475.0ms	1020×	body	512	valid
230.0ms	219×	body	2048	valid
165.0ms	534×	body	256	valid
88.0ms	421×	body	128	invalid
11.0ms	17×	body	1024	invalid
4.0ms	7×	body	512	invalid
3.0ms	8×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify67.0ms (1.1%)

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

30.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	44.3b	(*.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

44.3b

(*.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 (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	2.7b	(-.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)))))

series56.0ms (0.9%)

Counts

4 → 92

Calls

4 calls:

40.0ms	(-.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)))))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
6.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(*.f64 (+.f64 1 eps) x)

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
74×	`exp-neg_binary64`
72×	`frac-times_binary64`
56×	`exp-diff_binary64`
56×	`neg-sub0_binary64`

Counts

4 → 158

Calls

4 calls:

14.0ms	(-.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)))))
4.0ms	(*.f64 (+.f64 1 eps) x)
2.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
2.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify217.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

523×	`fma-neg_binary64`
506×	`associate-r_binary64`
495×	`associate-l_binary64`
435×	`fma-def_binary64`
245×	`distribute-rgt-in_binary64`

Counts

250 → 285

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	517	10874
1	1352	9874
2	4807	9874
3	5140	9874

prune381.0ms (6.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	281	4	285
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	283	4	287

Error

0.0b

Counts

287 → 4

Alt Table

Status	Error	Program
	0.7b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
	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) (pow.f64 (E.f64) (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	44.3b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
▶	0.7b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 15043 to 11342 computations (24.6% saved)

localize7.0ms (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 (0.1%)

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 (1.1%)

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

prune58.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Error

0.0b

Counts

65 → 4

Alt Table

Status	Error	Program
	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) (pow.f64 (E.f64) (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	44.3b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
▶	0.7b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	0.7b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 1226 to 863 computations (29.6% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 2 x 2) (exp.f64 x))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(/.f64 (fma.f64 2 x 2) (exp.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 2 x 2) (exp.f64 x))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
303×	`associate-l_binary64`
273×	`fma-def_binary64`
268×	`associate-r_binary64`
253×	`div-sub_binary64`

Counts

41 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	693
1	152	641
2	358	641
3	854	635
4	2825	635
5	4582	635
6	5087	635

prune36.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	44	4	48

Error

0.0b

Counts

48 → 4

Alt Table

Status	Error	Program
▶	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) (pow.f64 (E.f64) (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	44.3b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
✓	0.7b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	0.7b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 840 to 585 computations (30.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 1 eps) x)
	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	0.0b	(pow.f64 (E.f64) (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	2.9b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (E.f64) (neg.f64 (.f64 (+.f64 1 eps) x)))))

series44.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

35.0ms

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

7.0ms

(pow.f64 (E.f64) (neg.f64 (*.f64 (+.f64 1 eps) x)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
72×	`frac-times_binary64`
55×	`neg-sub0_binary64`
37×	`pow-neg_binary64`
36×	`exp-neg_binary64`

Counts

2 → 122

Calls

2 calls:

14.0ms

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

2.0ms

(pow.f64 (E.f64) (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify299.0ms (5%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
510×	`associate-r_binary64`
455×	`associate-l_binary64`
348×	`fma-def_binary64`
239×	`*-commutative_binary64`

Counts

170 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	10542
1	1224	9756
2	4429	9472
3	4985	9472
4	4979	9472
5	4957	9472

prune389.0ms (6.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	301	4	305

Error

0.0b

Counts

305 → 4

Alt Table

Status	Error	Program
✓	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) (pow.f64 (E.f64) (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	44.3b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
✓	0.7b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	0.7b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 15912 to 11653 computations (26.8% saved)

regimes310.0ms (5.2%)

Accuracy

Total 0.7b remaining (98%)

Threshold costs 0.7b (98%)

Counts

71 → 1

Compiler

Compiled 7956 to 6108 computations (23.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-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	8	15
1	13	15
2	15	15
3	16	15
4	16	15

end82.0ms (1.4%)

Compiler: Compiled 118 to 91 computations (22.9% saved)

Details

analyze371.0ms (6.2%)

sample3.3s (56%)

simplify67.0ms (1.1%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series56.0ms (0.9%)

rewrite46.0ms (0.8%)

simplify217.0ms (3.7%)

prune381.0ms (6.4%)

localize7.0ms (0.1%)

series3.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify65.0ms (1.1%)

prune58.0ms (1%)

localize7.0ms (0.1%)

series6.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify71.0ms (1.2%)

prune36.0ms (0.6%)

localize17.0ms (0.3%)

series44.0ms (0.7%)

rewrite39.0ms (0.7%)

simplify299.0ms (5%)

prune389.0ms (6.6%)

regimes310.0ms (5.2%)

simplify2.0ms (0%)

end82.0ms (1.4%)

Profiling