Details

analyze429.0ms (21.1%)

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)

sample48.0ms (2.3%)

Algorithm

1×

intervals

Results

15.0ms	89×	body	1024	valid
5.0ms	45×	body	512	valid
3.0ms	91×	body	128	valid
2.0ms	11×	body	2048	valid
1.0ms	20×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify7.0ms (0.4%)

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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

series9.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

rewrite6.0ms (0.3%)

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:

4.0ms

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

simplify64.0ms (3.2%)

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

prune18.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

0.4b

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	19.6b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
	19.9b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 473 to 170 computations (64.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	0.1b	(fma.f64 x 1/12 (/.f64 1 x))

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x 1/12 (/.f64 1 x))
2.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
0.0ms	(fma.f64 x 1/12 (/.f64 1 x))

simplify52.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

930×	`distribute-rgt-in_binary64`
900×	`distribute-lft-in_binary64`
726×	`fma-def_binary64`
566×	`associate-+l+_binary64`
388×	`fma-neg_binary64`

Counts

52 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	547
1	94	516
2	242	516
3	989	514
4	4674	514
5	4932	514

prune27.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	3	52

Error

0.4b

Counts

52 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.6b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
▶	19.9b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 662 to 521 computations (21.3% 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 (0.1%)

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))

simplify89.0ms (4.4%)

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

prune17.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	28	3	31

Error

0.4b

Counts

31 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.6b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
▶	19.9b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))

Compiler

Compiled 325 to 275 computations (15.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

series12.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

12.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
0.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))

simplify68.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
384×	`associate-+l+_binary64`
316×	`associate-*r/_binary64`
304×	`associate-*l/_binary64`
300×	`*-commutative_binary64`

Counts

64 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	624
1	82	589
2	189	585
3	390	571
4	1061	495
5	1907	495
6	4077	495
7	4883	495

prune52.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	69	3	72

Error

0.4b

Counts

72 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	19.6b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
	19.9b	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))

Compiler

Compiled 1061 to 980 computations (7.6% saved)

regimes41.0ms (2%)

Accuracy

Total 0.1b remaining (20.3%)

Threshold costs 0.1b (20.3%)

Counts

17 → 1

Compiler

Compiled 527 to 451 computations (14.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

sample1.0s (51.6%)

Algorithm

1×

intervals

Results

441.0ms	2599×	body	1024	valid
119.0ms	1321×	body	512	valid
99.0ms	3138×	body	128	valid
53.0ms	286×	body	2048	valid
52.0ms	656×	body	256	valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

Details

analyze429.0ms (21.1%)

sample48.0ms (2.3%)

simplify7.0ms (0.4%)

prune3.0ms (0.1%)

localize3.0ms (0.2%)

series9.0ms (0.4%)

rewrite6.0ms (0.3%)

simplify64.0ms (3.2%)

prune18.0ms (0.9%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify52.0ms (2.5%)

prune27.0ms (1.3%)

localize3.0ms (0.1%)

series1.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify89.0ms (4.4%)

prune17.0ms (0.9%)

localize6.0ms (0.3%)

series12.0ms (0.6%)

rewrite7.0ms (0.3%)

simplify68.0ms (3.3%)

prune52.0ms (2.5%)

regimes41.0ms (2%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample1.0s (51.6%)

Profiling