Details

analyze3.9s (21%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample429.0ms (2.3%)

Algorithm

1×

intervals

Results

240.0ms	139×	body	2048	valid
75.0ms	75×	body	1024	valid
17.0ms	23×	body	512	valid
14.0ms	12×	body	2048	overflowed
14.0ms	19×	body	1024	overflowed
12.0ms	307×	pre	128	true
4.0ms	7×	body	512	overflowed
3.0ms	15×	body	128	valid
2.0ms	5×	body	256	overflowed
1.0ms	4×	body	256	valid
1.0ms	8×	body	128	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
372×	`fma-def_binary64`
126×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	254	28
4	897	28
5	5292	28

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

44.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (+.f64 a b))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.3b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	42.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series809.0ms (4.3%)

Counts

4 → 132

Calls

4 calls:

648.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
77.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
67.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
15.0ms	(*.f64 eps (+.f64 a b))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64`

Counts

4 → 88

Calls

4 calls:

11.0ms	(*.f64 eps (+.f64 a b))
9.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
6.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
5.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))

simplify267.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
257×	`*-commutative_binary64`
166×	`+-commutative_binary64`

Counts

220 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	638	8331
1	2107	7574
2	5317	7574

prune282.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	223	3	226
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	223	4	227

Error

0.1b

Counts

227 → 4

Alt Table

Status	Error	Program
	15.9b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	44.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	59.0b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (exp.f64 (.f64 eps b))) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2)) (+.f64 (/.f64 (.f64 eps (exp.f64 (.f64 eps b))) (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))) (/.f64 (.f64 (pow.f64 eps 2) (exp.f64 (.f64 eps b))) (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 eps b)) 2)) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (/.f64 eps (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))))))
▶	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 10938 to 3589 computations (67.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	4.6b	(.f64 b (.f64 eps eps))
✓	7.0b	(.f64 a (.f64 eps eps))

series131.0ms (0.7%)

Counts

4 → 120

Calls

4 calls:

53.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
40.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
21.0ms	(.f64 b (.f64 eps eps))
17.0ms	(.f64 a (.f64 eps eps))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
9.0ms	(.f64 a (.f64 eps eps))
9.0ms	(.f64 b (.f64 eps eps))
1.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify220.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-+l+_binary64`
523×	`associate-l_binary64`
384×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
220×	`unswap-sqr_binary64`

Counts

201 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2505
1	236	2362
2	656	2362
3	2257	2360
4	4524	2360
5	5001	2360

prune199.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	129	6	135

Error

0.1b

Counts

135 → 6

Alt Table

Status	Error	Program
▶	15.9b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	44.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	34.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
	20.9b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	59.0b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (exp.f64 (.f64 eps b))) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2)) (+.f64 (/.f64 (.f64 eps (exp.f64 (.f64 eps b))) (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))) (/.f64 (.f64 (pow.f64 eps 2) (exp.f64 (.f64 eps b))) (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 eps b)) 2)) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (/.f64 eps (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))))))
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 3948 to 1857 computations (53% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.6b	(/.f64 (+.f64 a b) (*.f64 a b))

series16.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(/.f64 (+.f64 a b) (*.f64 a b))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

10.0ms

(/.f64 (+.f64 a b) (*.f64 a b))

simplify121.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
450×	`sub-neg_binary64`
441×	`associate-/r/_binary64`
370×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`

Counts

51 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	613
1	152	550
2	469	550
3	1544	550
4	3494	550
5	3895	550
6	4902	550
7	5491	550

prune46.0ms (0.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	33	6	39

Error

0.1b

Counts

39 → 6

Alt Table

Status	Error	Program
✓	15.9b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	44.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	34.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
▶	20.9b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	59.0b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (exp.f64 (.f64 eps b))) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2)) (+.f64 (/.f64 (.f64 eps (exp.f64 (.f64 eps b))) (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))) (/.f64 (.f64 (pow.f64 eps 2) (exp.f64 (.f64 eps b))) (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 eps b)) 2)) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (/.f64 eps (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))))))
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 845 to 329 computations (61.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 b))
✓	0.1b	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	4.6b	(.f64 b (.f64 eps eps))
	7.0b	(.f64 a (.f64 eps eps))

series48.0ms (0.3%)

Counts

2 → 28

Calls

2 calls:

42.0ms	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
6.0ms	(sqrt.f64 (/.f64 1 b))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(sqrt.f64 (/.f64 1 b))
0.0ms	(fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))

simplify115.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary64`
618×	`distribute-lft-in_binary64`
451×	`associate-l_binary64`
386×	`associate-r_binary64`
372×	`distribute-rgt-out_binary64`

Counts

68 → 61

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	1013
1	81	965
2	150	965
3	507	965
4	3029	965
5	4994	965
6	4976	965

prune333.0ms (1.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	157	6	163

Error

0.1b

Counts

163 → 6

Alt Table

Status	Error	Program
✓	15.9b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	44.1b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	34.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))) (sqrt.f64 (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
✓	20.9b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (fma.f64 (sqrt.f64 (/.f64 1 b)) (sqrt.f64 (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	59.0b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (exp.f64 (.f64 eps b))) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2)) (+.f64 (/.f64 (.f64 eps (exp.f64 (.f64 eps b))) (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))) (/.f64 (.f64 (pow.f64 eps 2) (exp.f64 (.f64 eps b))) (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (exp.f64 (.f64 eps b)) 2)) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 eps 3) (pow.f64 (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps) 2))) (/.f64 eps (.f64 a (-.f64 (.f64 eps (exp.f64 (.f64 eps b))) eps))))))
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))

Compiler

Compiled 4985 to 2601 computations (47.8% saved)

regimes443.0ms (2.4%)

Accuracy

Total 0.1b remaining (70.6%)

Threshold costs 0.1b (70.6%)

Counts

63 → 3

Compiler

Compiled 5362 to 3192 computations (40.5% saved)

bsearch4.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	142
1	55	142
2	58	142
3	56	142

end20.0ms (0.1%)

Compiler: Compiled 288 to 162 computations (43.8% saved)

sample11.0s (59.1%)

Algorithm

1×

intervals

Results

5.9s	4111×	body	2048	valid
1.8s	2338×	body	1024	valid
397.0ms	800×	body	512	valid
395.0ms	603×	body	1024	overflowed
355.0ms	369×	body	2048	overflowed
321.0ms	9699×	pre	128	true
128.0ms	302×	body	512	overflowed
74.0ms	504×	body	128	valid
67.0ms	232×	body	256	valid
40.0ms	287×	body	128	overflowed
37.0ms	136×	body	256	overflowed
30.0ms	15×	body	4096	valid
4.0ms	2×	body	2048	invalid

Compiler

Compiled 370 to 201 computations (45.7% saved)

Details

analyze3.9s (21%)

sample429.0ms (2.3%)

simplify43.0ms (0.2%)

prune7.0ms (0%)

localize24.0ms (0.1%)

series809.0ms (4.3%)

rewrite42.0ms (0.2%)

simplify267.0ms (1.4%)

prune282.0ms (1.5%)

localize25.0ms (0.1%)

series131.0ms (0.7%)

rewrite39.0ms (0.2%)

simplify220.0ms (1.2%)

prune199.0ms (1.1%)

localize8.0ms (0%)

series16.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify121.0ms (0.7%)

prune46.0ms (0.2%)

localize14.0ms (0.1%)

series48.0ms (0.3%)

rewrite5.0ms (0%)

simplify115.0ms (0.6%)

prune333.0ms (1.8%)

regimes443.0ms (2.4%)

bsearch4.0ms (0%)

simplify10.0ms (0.1%)

end20.0ms (0.1%)

sample11.0s (59.1%)

Profiling