Details

analyze987.0ms (7.8%)

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
37.4%	12.5%	50.1%	4
37.4%	12.5%	50.1%	5
37.4%	12.5%	50.1%	6
37.4%	12.5%	50.1%	7
37.4%	12.5%	50.1%	8
37.8%	12.1%	50.1%	9
37.8%	12.1%	50.1%	10
37.9%	12%	50.1%	11
38.1%	11.8%	50.1%	12
38.5%	11.4%	50.1%	13
38.6%	11.3%	50.1%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.8s (70.1%)

Symmetry

(sort a b)

Results

5.2s	4185×	body	2048	valid
1.9s	2523×	body	1024	valid
357.0ms	738×	body	512	valid
355.0ms	391×	body	2048	invalid
338.0ms	554×	body	1024	invalid
177.0ms	273×	body	512	invalid
105.0ms	554×	body	128	invalid
95.0ms	538×	body	128	valid
83.0ms	254×	body	256	valid
56.0ms	144×	body	256	invalid
29.0ms	18×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify23.0ms (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

prune4.0ms (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

37.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.7b	(/.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps a))
✓	0.0b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	37.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series369.0ms (2.9%)

Counts

4 → 132

Calls

4 calls:

302.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
31.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
29.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(expm1.f64 (*.f64 eps a))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

6.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
1.0ms	(expm1.f64 (*.f64 eps a))

simplify163.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
249×	`*-commutative_binary64`
163×	`+-commutative_binary64`

Counts

206 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	8300
1	2021	7554
2	5057	7554

prune243.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	210	4	214

Error

0.0b

Counts

214 → 4

Alt Table

Status	Error	Program
✓	37.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	14.0b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	8.1b	(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))))
	53.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 a eps))) 3)))

Compiler

Compiled 10530 to 3504 computations (66.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	5.5b	(.f64 b (.f64 eps eps))
✓	6.6b	(.f64 a (.f64 eps eps))

series135.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

58.0ms	(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))))
51.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
13.0ms	(.f64 a (.f64 eps eps))
12.0ms	(.f64 b (.f64 eps eps))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

4 → 62

Calls

4 calls:

8.0ms	(.f64 a (.f64 eps eps))
7.0ms	(.f64 b (.f64 eps eps))
1.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
1.0ms	(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))))

simplify191.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

766×	`unswap-sqr_binary64`
610×	`fma-def_binary64`
470×	`associate-l_binary64`
333×	`associate-r_binary64`
295×	`associate-+r+_binary64`

Counts

182 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2698
1	202	2339
2	549	2269
3	1651	2269
4	3788	2269
5	5058	2269

prune156.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	121	5	126

Error

Counts

126 → 5

Alt Table

Status	Error	Program
	51.4b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (sqrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (sqrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
	53.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 a eps))) 3)))
✓	37.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	14.0b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	4.8b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 3173 to 1551 computations (51.1% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

series13.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

14.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify209.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg_binary64`
421×	`div-sub_binary64`
357×	`fma-def_binary64`
329×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`

Counts

40 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	332
1	106	302
2	241	301
3	565	301
4	1313	301
5	2794	301
6	4202	301
7	4546	301
8	4845	301
9	4973	301
10	4870	301

prune50.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	37	5	42

Error

Counts

42 → 5

Alt Table

Status	Error	Program
	51.4b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (sqrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (sqrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
	53.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 a eps))) 3)))
✓	37.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
▶	14.0b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	4.8b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 690 to 493 computations (28.6% saved)

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.0b	(/.f64 (+.f64 a b) (*.f64 a b))

series16.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

16.0ms

(/.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))

simplify139.0ms (1.1%)

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

prune48.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
	12.2b	(/.f64 (/.f64 (+.f64 a b) a) b)
	53.0b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (cbrt.f64 (pow.f64 (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 a eps))) 3)))
✓	37.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	4.8b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 491 to 166 computations (66.2% saved)

regimes427.0ms (3.4%)

Accuracy

Total 0.4b remaining (96.8%)

Threshold costs 0.4b (96.8%)

Counts

43 → 3

Compiler

Compiled 3366 to 2132 computations (36.7% saved)

bsearch3.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	142
1	54	142
2	57	142
3	55	142

end455.0ms (3.6%)

Compiler: Compiled 449 to 259 computations (42.3% saved)

Details

analyze987.0ms (7.8%)

sample8.8s (70.1%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series369.0ms (2.9%)

rewrite21.0ms (0.2%)

simplify163.0ms (1.3%)

prune243.0ms (1.9%)

localize22.0ms (0.2%)

series135.0ms (1.1%)

rewrite20.0ms (0.2%)

simplify191.0ms (1.5%)

prune156.0ms (1.2%)

localize9.0ms (0.1%)

series13.0ms (0.1%)

rewrite18.0ms (0.1%)

simplify209.0ms (1.7%)

prune50.0ms (0.4%)

localize14.0ms (0.1%)

series16.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify139.0ms (1.1%)

prune48.0ms (0.4%)

regimes427.0ms (3.4%)

bsearch3.0ms (0%)

simplify8.0ms (0.1%)

end455.0ms (3.6%)

Profiling