Details

analyze487.0ms (17.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (60.2%)

Results

853.0ms	2694×	body	1024	valid
297.0ms	1340×	body	512	valid
266.0ms	3230×	body	128	valid
118.0ms	306×	body	2048	valid
98.0ms	686×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune3.0ms (0.1%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

series8.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

simplify66.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

41 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune25.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Error

0.2b

Counts

41 → 3

Alt Table

Status	Error	Program
	23.1b	(+.f64 1/2 (/.f64 1 x))
▶	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
	27.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))))

Compiler

Compiled 503 to 182 computations (63.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))

series16.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
7.0ms	(/.f64 1 (expm1.f64 x))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 71

Calls

2 calls:

7.0ms	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
2.0ms	(/.f64 1 (expm1.f64 x))

simplify85.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-neg_binary64`
461×	`fma-def_binary64`
435×	`associate-/l*_binary64`
309×	`associate-/l/_binary64`
278×	`distribute-rgt-in_binary64`

Counts

95 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1002
1	180	897
2	435	895
3	857	895
4	2060	895
5	4338	895
6	4886	895

prune48.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

0.2b

Counts

109 → 3

Alt Table

Status	Error	Program
▶	23.1b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
	27.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))))

Compiler

Compiled 1370 to 676 computations (50.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 3

Calls

1 calls:

1.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

4.0ms

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

simplify83.0ms (3%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
425×	`unswap-sqr_binary64`
403×	`distribute-rgt-in_binary64`
330×	`associate-r_binary64`
260×	`fma-neg_binary64`

Counts

21 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	183
1	84	163
2	170	162
3	357	162
4	797	162
5	1860	162
6	3117	162
7	4800	162
8	4821	162
9	4911	162

prune15.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	28	3	31

Error

0.2b

Counts

31 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
▶	23.1b	(fma.f64 (sqrt.f64 1/2) (sqrt.f64 1/2) (/.f64 1 x))
	27.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))))

Compiler

Compiled 350 to 282 computations (19.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(fma.f64 (sqrt.f64 1/2) (sqrt.f64 1/2) (/.f64 1 x))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (sqrt.f64 1/2) (sqrt.f64 1/2) (/.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (sqrt.f64 1/2) (sqrt.f64 1/2) (/.f64 1 x))

simplify103.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

644×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
419×	`distribute-rgt-in_binary64`
370×	`fabs-mul_binary64`
353×	`*-commutative_binary64`

Counts

22 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	178
1	27	163
2	51	163
3	105	163
4	233	163
5	595	163
6	1522	163
7	2566	163
8	3548	163
9	4197	163
10	4736	163
11	4904	163
12	4893	163

prune11.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	23	3	26

Error

0.2b

Counts

26 → 3

Alt Table

Status	Error	Program
✓	0.3b	(*.f64 (exp.f64 x) (/.f64 1 (expm1.f64 x)))
✓	23.1b	(fma.f64 (sqrt.f64 1/2) (sqrt.f64 1/2) (/.f64 1 x))
	27.6b	(cbrt.f64 (/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))))

Compiler

Compiled 276 to 234 computations (15.2% saved)

regimes49.0ms (1.8%)

Accuracy

Total 0.1b remaining (20.4%)

Threshold costs 0.1b (20.4%)

Counts

24 → 1

Compiler

Compiled 761 to 502 computations (34% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	9	11

end48.0ms (1.7%)

Compiler: Compiled 52 to 35 computations (32.7% saved)

Details

analyze487.0ms (17.6%)

sample1.7s (60.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series8.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify66.0ms (2.4%)

prune25.0ms (0.9%)

localize4.0ms (0.2%)

series16.0ms (0.6%)

rewrite13.0ms (0.5%)

simplify85.0ms (3.1%)

prune48.0ms (1.7%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite5.0ms (0.2%)

simplify83.0ms (3%)

prune15.0ms (0.6%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite1.0ms (0%)

simplify103.0ms (3.7%)

prune11.0ms (0.4%)

regimes49.0ms (1.8%)

simplify2.0ms (0.1%)

end48.0ms (1.7%)

Profiling