Details

analyze335.0ms (6.7%)

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)

sample3.5s (70.7%)

Results

1.6s	2050×	body	1024	valid
779.0ms	4416×	body	128	valid
488.0ms	987×	body	512	valid
249.0ms	230×	body	2048	valid
189.0ms	573×	body	256	valid
76.0ms	417×	body	128	invalid
15.0ms	22×	body	1024	invalid
4.0ms	8×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify65.0ms (1.3%)

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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.8b	(/.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)
	44.8b	(*.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)))))

Status

Error

Program

▶

28.8b

(/.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)

44.8b

(*.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)))))

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	0.0b	(*.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)))))

series54.0ms (1.1%)

Counts

3 → 56

Calls

3 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)))))

4.0ms

(*.f64 (-.f64 1 eps) x)

4.0ms

(*.f64 (+.f64 1 eps) x)

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 145

Calls

3 calls:

15.0ms

(-.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

(*.f64 (+.f64 1 eps) x)

5.0ms

(*.f64 (-.f64 1 eps) x)

simplify189.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

684×	`times-frac_binary64`
494×	`associate-l_binary64`
475×	`associate-r_binary64`
407×	`fma-neg_binary64`
299×	`fma-def_binary64`

Counts

201 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	10033
1	1152	9173
2	4013	9145
3	5346	9145

prune282.0ms (5.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	237	2	239

Error

0.0b

Counts

239 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)
✓	28.8b	(/.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

▶

0.5b

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

✓

28.8b

(/.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 13018 to 9757 computations (25% 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))

rewrite15.0ms (0.3%)

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:

8.0ms

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

simplify63.0ms (1.3%)

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

prune48.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	61	2	63

Error

Counts

63 → 2

Alt Table

Status	Error	Program
✓	28.8b	(/.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)
▶	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)

Status

Error

Program

✓

28.8b

(/.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)

▶

0.5b

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

Compiler

Compiled 1104 to 775 computations (29.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

6.0ms	(/.f64 (fma.f64 2 x 2) (exp.f64 x))
3.0ms	(exp.f64 x)

rewrite5.0ms (0.1%)

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`
4×	`add-cbrt-cube_binary64`

Counts

2 → 42

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 2 x 2) (exp.f64 x))
1.0ms	(exp.f64 x)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
445×	`fma-def_binary64`
365×	`associate-l_binary64`
313×	`associate-r_binary64`
253×	`div-sub_binary64`

Counts

58 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	800
1	187	741
2	436	741
3	1042	730
4	3253	730
5	4706	730
6	5186	730

prune41.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	66	2	68

Error

Counts

68 → 2

Alt Table

Status	Error	Program
✓	28.8b	(/.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)
✓	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)

Status

Error

Program

✓

28.8b

(/.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)

✓

0.5b

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

Compiler

Compiled 1001 to 695 computations (30.6% saved)

regimes126.0ms (2.5%)

Accuracy

Total 0.8b remaining (97.1%)

Threshold costs 0.8b (97.1%)

Counts

26 → 1

Compiler

Compiled 2304 to 1780 computations (22.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	23	25
2	37	25
3	45	25
4	49	25
5	50	25
6	50	25

end57.0ms (1.1%)

Compiler: Compiled 78 to 56 computations (28.2% saved)

Details

analyze335.0ms (6.7%)

sample3.5s (70.7%)

simplify65.0ms (1.3%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series54.0ms (1.1%)

rewrite51.0ms (1%)

simplify189.0ms (3.8%)

prune282.0ms (5.7%)

localize7.0ms (0.1%)

series3.0ms (0.1%)

rewrite15.0ms (0.3%)

simplify63.0ms (1.3%)

prune48.0ms (1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify73.0ms (1.5%)

prune41.0ms (0.8%)

regimes126.0ms (2.5%)

simplify3.0ms (0.1%)

end57.0ms (1.1%)

Profiling