Details

analyze440.0ms (14.9%)

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)

sample42.0ms (1.4%)

Algorithm

1×

intervals

Results

19.0ms	93×	body	1024	valid
5.0ms	52×	body	512	valid
3.0ms	91×	body	128	valid
1.0ms	6×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

16×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
4×	`times-frac_binary64`
4×	`add-exp-log_binary64`
4×	`pow1_binary64`

Counts

1 → 46

Calls

1 calls:

15.0ms

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

Compiler

Compiled 457 to 102 computations (77.7% saved)

series11.0ms (0.4%)

Error

0.6b

Counts

1 → 6

Calls

1 calls:

8.0ms

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

Compiler

Compiled 108 to 79 computations (26.9% saved)

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
447×	`fma-def_binary64`
314×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`
246×	`associate-/l*_binary64`

Counts

52 → 20

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	492
1	133	444
2	426	442
3	2470	432
4	4959	432

prune10.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Error

0.6b

Counts

21 → 3

Alt Table

Status	Error	Program
	32.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
▶	19.7b	(+.f64 (/.f64 1 x) 1/2)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 173 to 78 computations (54.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 x) 1/2)

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`flip3-+_binary64`
4×	`pow1_binary64`

Counts

1 → 41

Calls

1 calls:

11.0ms

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

Compiler

Compiled 456 to 389 computations (14.7% saved)

series6.0ms (0.2%)

Error

0.6b

Counts

1 → 6

Calls

1 calls:

5.0ms

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

Compiler

Compiled 54 to 45 computations (16.7% saved)

simplify80.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

717×	`div-sub_binary64`
632×	`fma-neg_binary64`
620×	`fma-def_binary64`
343×	`cancel-sign-sub-inv_binary64`
224×	`times-frac_binary64`

Counts

47 → 17

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	422
1	120	403
2	359	400
3	1106	394
4	2675	388
5	4260	388
6	5331	388

prune8.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	17	3	20

Error

0.6b

Counts

20 → 3

Alt Table

Status	Error	Program
▶	32.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	19.7b	(+.f64 (/.f64 1 x) 1/2)
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 175 to 143 computations (18.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))
29.6b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

rewrite74.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

30×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`cube-div_binary64`
9×	`add-exp-log_binary64`

Counts

3 → 133

Calls

3 calls:

12.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
12.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
9.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))

Compiler

Compiled 1394 to 590 computations (57.7% saved)

series34.0ms (1.2%)

Error

0.6b

Counts

3 → 18

Calls

3 calls:

12.0ms	(pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3)
8.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
8.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 438 to 345 computations (21.2% saved)

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-/l*_binary64`
374×	`fma-def_binary64`
373×	`associate-*l/_binary64`
369×	`associate-/r*_binary64`
306×	`associate-*r/_binary64`

Counts

151 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1438
1	231	1285
2	859	1243
3	4633	1239
4	5008	1239

prune18.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	75	3	78

Error

0.6b

Counts

78 → 3

Alt Table

Status	Error	Program
▶	50.7b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
✓	32.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 555 to 277 computations (50.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (pow.f64 x 3))
0.3b	(/.f64 3/2 (*.f64 x x))
10.8b	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
29.7b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

rewrite192.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

40×	`add-cube-cbrt_binary64`
18×	`add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
12×	`add-log-exp_binary64`

Counts

4 → 176

Calls

4 calls:

14.0ms	(/.f64 1 (pow.f64 x 3))
14.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
13.0ms	(/.f64 3/2 (*.f64 x x))
11.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

Compiler

Compiled 3785 to 2783 computations (26.5% saved)

series37.0ms (1.3%)

Error

0.6b

Counts

4 → 19

Calls

4 calls:

10.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
10.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
7.0ms	(/.f64 1 (pow.f64 x 3))
5.0ms	(/.f64 3/2 (*.f64 x x))

Compiler

Compiled 631 to 533 computations (15.5% saved)

simplify110.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
350×	`fma-neg_binary64`
244×	`cancel-sign-sub-inv_binary64`
202×	`log-prod_binary64`

Counts

195 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2773
1	415	2639
2	1789	2234
3	4553	2234
4	4949	2234

prune65.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	113	5	118

Error

0.6b

Counts

118 → 5

Alt Table

Status	Error	Program
	32.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 x)) 3))
	60.1b	(/.f64 1 (/.f64 (cbrt.f64 (+.f64 9/64 (.f64 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (.f64 x x)))) (+.f64 -3/8 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (.f64 x x)))))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (.f64 x x)))) 3) 27/512))))
	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	50.8b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 3/8 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (.f64 x x))))))) (cbrt.f64 (cbrt.f64 (+.f64 3/8 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (.f64 x x)))))))) (cbrt.f64 (cbrt.f64 (+.f64 3/8 (+.f64 (/.f64 1 x) (+.f64 (pow.f64 x -3) (/.f64 3/2 (*.f64 x x))))))))
	50.7b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 1 (pow.f64 x -3)) (/.f64 3/2 (.f64 x x)))) 3/8))

Compiler

Compiled 2098 to 1512 computations (27.9% saved)

regimes531.0ms (18.1%)

Accuracy

Total 0.1b remaining (21.7%)

Threshold costs 0.1b (21.7%)

Compiler

Compiled 12929 to 9961 computations (23% saved)

simplify3.0ms (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

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample1.0s (35.5%)

Algorithm

1×

intervals

Results

426.0ms	2621×	body	1024	valid
127.0ms	1356×	body	512	valid
98.0ms	3141×	body	128	valid
48.0ms	247×	body	2048	valid
39.0ms	635×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 160 to 119 computations (25.6% saved)

Details

analyze440.0ms (14.9%)

sample42.0ms (1.4%)

simplify13.0ms (0.4%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

rewrite32.0ms (1.1%)

series11.0ms (0.4%)

simplify52.0ms (1.8%)

prune10.0ms (0.3%)

localize3.0ms (0.1%)

rewrite29.0ms (1%)

series6.0ms (0.2%)

simplify80.0ms (2.7%)

prune8.0ms (0.3%)

localize6.0ms (0.2%)

rewrite74.0ms (2.5%)

series34.0ms (1.2%)

simplify83.0ms (2.8%)

prune18.0ms (0.6%)

localize12.0ms (0.4%)

rewrite192.0ms (6.5%)

series37.0ms (1.3%)

simplify110.0ms (3.7%)

prune65.0ms (2.2%)

regimes531.0ms (18.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (35.5%)

Profiling