Details

analyze327.0ms (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)

sample3.2s (65.9%)

Results

1.4s	2037×	body	1024	valid
743.0ms	4453×	body	128	valid
454.0ms	996×	body	512	valid
229.0ms	221×	body	2048	valid
171.0ms	549×	body	256	valid
77.0ms	462×	body	128	invalid
18.0ms	19×	body	512	invalid
14.0ms	21×	body	1024	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
197×	`associate-/l/_binary64`
123×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	159	37
3	510	37
4	1660	37

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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

29.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.2b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 x) (+.f64 eps -1)) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))
▶	29.1b	(/.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

30.2b

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

▶

29.1b

(/.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)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.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)))
✓	2.2b	(-.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)))))

series61.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(-.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)))))
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

rewrite49.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
190×	`add-cbrt-cube_binary64`
188×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	84
1	415	72

Stop Event

1×	node limit

Counts

4 → 124

Calls

4 calls:

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

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

372×	`cancel-sign-sub-inv_binary64`
357×	`fma-def_binary64`
251×	`distribute-rgt-out_binary64`
245×	`associate-+r+_binary64`
212×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	2581
1	762	2498
2	2944	2382

Stop Event

1×	node limit

Counts

220 → 191

prune191.0ms (4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Error

0.0b

Counts

193 → 5

Alt Table

Status	Error	Program
	15.3b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)
▶	1.0b	(/.f64 (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))) 2)
	21.9b	(/.f64 (+.f64 2 (.f64 x (-.f64 (.f64 x (*.f64 eps eps)) x))) 2)
	60.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (+.f64 (/.f64 1 eps) -1) (pow.f64 (exp.f64 (+.f64 1 eps)) x)))) 3) 2)
	29.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 8429 to 6190 computations (26.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (exp.f64 x))
✓	0.0b	(*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x)))

series14.0ms (0.3%)

Counts

2 → 16

Calls

2 calls:

7.0ms	(/.f64 2 (exp.f64 x))
7.0ms	(*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x)))

rewrite41.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`log1p-expm1-u_binary64`
780×	`expm1-log1p-u_binary64`
93×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	169	18
2	2094	18

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

40.0ms	(/.f64 2 (exp.f64 x))
40.0ms	(*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x)))

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

354×	`distribute-rgt-neg-in_binary64`
351×	`fma-def_binary64`
297×	`distribute-lft-neg-in_binary64`
261×	`associate-l_binary64`
261×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	202
1	94	187
2	252	182
3	812	176
4	3029	158

Stop Event

1×	node limit

Counts

82 → 83

prune78.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Error

0.0b

Counts

88 → 4

Alt Table

Status	Error	Program
	15.3b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)
▶	1.0b	(/.f64 (/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2)) 2)
	60.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (+.f64 (/.f64 1 eps) -1) (pow.f64 (exp.f64 (+.f64 1 eps)) x)))) 3) 2)
	29.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 1369 to 1002 computations (26.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2))

series8.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2))

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

840×	`log1p-expm1-u_binary64`
840×	`expm1-log1p-u_binary64`
111×	`prod-diff_binary64`
81×	`add-sqr-sqrt_binary64`
77×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	168	11
2	2205	11

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

39.0ms

(/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2))

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
767×	`cancel-sign-sub-inv_binary64`
218×	`distribute-rgt-neg-in_binary64`
199×	`distribute-lft-neg-in_binary64`
179×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	161
1	67	151
2	160	151
3	490	147
4	1805	129

Stop Event

1×	node limit

Counts

52 → 49

prune48.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	49	4	53

Error

0.0b

Counts

53 → 4

Alt Table

Status	Error	Program
▶	15.3b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)
✓	1.0b	(/.f64 (/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2)) 2)
	60.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (+.f64 (/.f64 1 eps) -1) (pow.f64 (exp.f64 (+.f64 1 eps)) x)))) 3) 2)
	29.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 916 to 642 computations (29.9% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.6b	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
✓	7.8b	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
✓	8.9b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
✓	10.1b	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

series56.0ms (1.2%)

Counts

4 → 40

Calls

4 calls:

28.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
18.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
5.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
4.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`log-prod_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
195×	`log-pow_binary64`
142×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	295	47
2	3427	47

Stop Event

1×	node limit

Counts

4 → 76

Calls

4 calls:

49.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
49.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
49.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
49.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

653×	`unswap-sqr_binary64`
370×	`distribute-rgt-neg-in_binary64`
341×	`associate-l_binary64`
333×	`fma-def_binary64`
323×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	662
1	187	648
2	658	568
3	3211	568

Stop Event

1×	node limit

Counts

116 → 115

prune129.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	115	4	119

Error

0.0b

Counts

119 → 4

Alt Table

Status	Error	Program
✓	15.3b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)
✓	1.0b	(/.f64 (/.f64 (+.f64 x 1) (*.f64 (exp.f64 x) 1/2)) 2)
	60.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (+.f64 (/.f64 1 eps) -1) (pow.f64 (exp.f64 (+.f64 1 eps)) x)))) 3) 2)
	29.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 5239 to 3001 computations (42.7% saved)

regimes246.0ms (5.1%)

Accuracy

Total 0.7b remaining (98.2%)

Threshold costs 0.7b (98.2%)

Counts

60 → 1

Compiler

Compiled 6252 to 4664 computations (25.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	13	18
2	18	18
3	20	18
4	21	18

Stop Event

1×

saturated

end93.0ms (1.9%)

Compiler: Compiled 144 to 111 computations (22.9% saved)

Details

analyze327.0ms (6.8%)

sample3.2s (65.9%)

simplify19.0ms (0.4%)

prune6.0ms (0.1%)

localize16.0ms (0.3%)

series61.0ms (1.3%)

rewrite49.0ms (1%)

simplify57.0ms (1.2%)

prune191.0ms (4%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite41.0ms (0.8%)

simplify27.0ms (0.6%)

prune78.0ms (1.6%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite40.0ms (0.8%)

simplify22.0ms (0.5%)

prune48.0ms (1%)

localize19.0ms (0.4%)

series56.0ms (1.2%)

rewrite50.0ms (1%)

simplify34.0ms (0.7%)

prune129.0ms (2.7%)

regimes246.0ms (5.1%)

simplify3.0ms (0.1%)

end93.0ms (1.9%)

Profiling