Details

analyze1.9s (12.6%)

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%	99.9%	0.1%	6
1.6%	96.8%	1.7%	7
2.3%	95.2%	2.4%	8
7.4%	86.6%	6%	9
10%	83.1%	6.9%	10
14.7%	76.3%	9%	11
16.5%	73.9%	9.6%	12
19.5%	69.8%	10.7%	13
19.8%	69.1%	11.1%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample10.5s (68.8%)

Results

7.0s	6040×	body	8192	exit
1.6s	2130×	body	1024	valid
824.0ms	4354×	body	128	valid
519.0ms	1038×	body	512	valid
233.0ms	214×	body	2048	valid
189.0ms	520×	body	256	valid
36.0ms	181×	body	128	invalid
13.0ms	18×	body	1024	invalid
6.0ms	9×	body	512	invalid
3.0ms	8×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify65.0ms (0.4%)

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%)

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

32.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	32.0b	(/.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)
	45.2b	(*.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

▶

32.0b

(/.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)

45.2b

(*.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)

localize19.0ms (0.1%)

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	(*.f64 (-.f64 1 eps) x)
✓	3.6b	(-.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)))))

series69.0ms (0.4%)

Counts

4 → 84

Calls

4 calls:

41.0ms	(-.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)))))
15.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
7.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
5.0ms	(*.f64 (-.f64 1 eps) x)

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
77×	`exp-neg_binary64`
76×	`frac-times_binary64`
58×	`exp-diff_binary64`
58×	`neg-sub0_binary64`

Counts

4 → 172

Calls

4 calls:

16.0ms	(-.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)))))
9.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
5.0ms	(*.f64 (-.f64 1 eps) x)
2.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify228.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-r_binary64`
538×	`associate-l_binary64`
519×	`fma-neg_binary64`
484×	`fma-def_binary64`
245×	`distribute-rgt-in_binary64`

Counts

256 → 308

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	11648
1	1468	10857
2	4600	10857
3	4970	10857

prune367.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	306	4	310

Error

Counts

310 → 4

Alt Table

Status	Error	Program
	46.5b	(/.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)
	14.9b	(/.f64 2 2)
▶	13.8b	(/.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)
	32.0b	(/.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 (fma.f64 x eps x)))) 2)

Compiler

Compiled 16173 to 12163 computations (24.8% saved)

localize20.0ms (0.1%)

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)))
✓	6.8b	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
✓	8.4b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))
✓	15.1b	(.f64 (.f64 eps eps) (*.f64 x x))

series64.0ms (0.4%)

Counts

4 → 80

Calls

4 calls:

27.0ms	(.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)))
13.0ms	(.f64 (.f64 eps eps) (*.f64 x x))
4.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))

rewrite51.0ms (0.3%)

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:

16.0ms	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
14.0ms	(.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (*.f64 2 x)))
7.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))
7.0ms	(.f64 (.f64 eps eps) (*.f64 x x))

simplify123.0ms (0.8%)

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

prune304.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	199	3	202

Error

Counts

202 → 3

Alt Table

Status	Error	Program
	46.5b	(/.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)
▶	13.8b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (.f64 eps x)) 2)) (exp.f64 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)
	32.0b	(/.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 (fma.f64 x eps x)))) 2)

Compiler

Compiled 8525 to 3973 computations (53.4% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))
✓	3.6b	(log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))))
	6.8b	(.f64 (.f64 eps eps) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3)))
	8.4b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 3))

series84.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

57.0ms	(log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))))
26.0ms	(/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`log-pow_binary64`
7×	`add-cbrt-cube_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`exp-prod_binary64`

Counts

2 → 46

Calls

2 calls:

12.0ms	(/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))
3.0ms	(log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (*.f64 eps x)) 2)) (exp.f64 x))))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-l_binary64`
455×	`fma-def_binary64`
442×	`associate-/l*_binary64`
373×	`unswap-sqr_binary64`
340×	`times-frac_binary64`

Counts

94 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	2187
1	302	1958
2	1087	1921
3	4359	1917
4	5395	1917

prune218.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
	46.5b	(/.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)
✓	13.8b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (.f64 eps x)) 2)) (exp.f64 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)
▶	32.0b	(/.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 (fma.f64 x eps x)))) 2)

Compiler

Compiled 7938 to 4101 computations (48.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))
	0.0b	(*.f64 (-.f64 1 eps) x)
✓	4.6b	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))

series71.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

63.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))
7.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`frac-add_binary64`
6×	`exp-prod_binary64`
6×	`add-log-exp_binary64`
5×	`exp-neg_binary64`
4×	`flip-+_binary64`

Counts

2 → 42

Calls

2 calls:

16.0ms	(+.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))
3.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify126.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

416×	`distribute-rgt-in_binary64`
381×	`fma-neg_binary64`
378×	`distribute-lft-in_binary64`
263×	`cancel-sign-sub-inv_binary64`
255×	`fma-def_binary64`

Counts

90 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	3182
1	729	2897
2	2530	2752
3	4947	2752
4	5145	2752

prune192.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	210	3	213

Error

Counts

213 → 3

Alt Table

Status	Error	Program
	46.5b	(/.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)
✓	13.8b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (.f64 x (+.f64 (.f64 eps (.f64 eps x)) 2)) (exp.f64 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)
✓	32.0b	(/.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 (fma.f64 x eps x)))) 2)

Compiler

Compiled 8164 to 5118 computations (37.3% saved)

regimes474.0ms (3.1%)

Accuracy

Total 0.3b remaining (55.1%)

Threshold costs 0.3b (55.1%)

Counts

101 → 1

Compiler

Compiled 13598 to 9770 computations (28.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	10	24
1	18	24
2	20	24
3	21	24
4	21	24

end133.0ms (0.9%)

Compiler: Compiled 137 to 96 computations (29.9% saved)

Details

analyze1.9s (12.6%)

sample10.5s (68.8%)

simplify65.0ms (0.4%)

prune5.0ms (0%)

localize19.0ms (0.1%)

series69.0ms (0.4%)

rewrite60.0ms (0.4%)

simplify228.0ms (1.5%)

prune367.0ms (2.4%)

localize20.0ms (0.1%)

series64.0ms (0.4%)

rewrite51.0ms (0.3%)

simplify123.0ms (0.8%)

prune304.0ms (2%)

localize25.0ms (0.2%)

series84.0ms (0.5%)

rewrite19.0ms (0.1%)

simplify90.0ms (0.6%)

prune218.0ms (1.4%)

localize18.0ms (0.1%)

series71.0ms (0.5%)

rewrite22.0ms (0.1%)

simplify126.0ms (0.8%)

prune192.0ms (1.3%)

regimes474.0ms (3.1%)

simplify2.0ms (0%)

end133.0ms (0.9%)

Profiling