Details

analyze575.0ms (17.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
12.5%	75%	12.5%	4
18.7%	62.5%	18.8%	5
21.9%	56.2%	21.9%	6
23.4%	53.1%	23.5%	7
24.2%	51.5%	24.3%	8
24.6%	51.1%	24.3%	9
24.6%	51.1%	24.3%	10
24.7%	51%	24.3%	11
24.7%	51%	24.3%	12
24.8%	50.9%	24.3%	13
24.8%	50.9%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (51.9%)

Results

879.0ms	2705×	body	1024	valid
307.0ms	1412×	body	512	valid
268.0ms	3176×	body	128	valid
112.0ms	303×	body	2048	valid
104.0ms	660×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 17 to 11 computations (35.3% 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

0.5b

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 (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.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))

simplify69.0ms (2.1%)

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

prune20.0ms (0.6%)

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
	29.3b	(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))))
▶	21.8b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 493 to 174 computations (64.7% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.4b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	29.3b	(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))))
✓	21.8b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 50 to 27 computations (46% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (expm1.f64 x) (expm1.f64 x))
✓	0.1b	(.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))
✓	0.5b	(/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x)))
✓	27.0b	(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))))

series63.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

40.0ms	(/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x)))
11.0ms	(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))))
8.0ms	(.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))
4.0ms	(*.f64 (expm1.f64 x) (expm1.f64 x))

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary64`
35×	`add-exp-log_binary64`
30×	`pow1_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`

Counts

4 → 107

Calls

4 calls:

17.0ms	(/.f64 (.f64 (.f64 (exp.f64 x) (exp.f64 x)) (exp.f64 x)) (.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x)))
15.0ms	(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))))
5.0ms	(.f64 (.f64 (expm1.f64 x) (expm1.f64 x)) (expm1.f64 x))
3.0ms	(*.f64 (expm1.f64 x) (expm1.f64 x))

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-def_binary64`
452×	`associate-*l/_binary64`
359×	`associate-*r/_binary64`
279×	`associate-/l/_binary64`
174×	`distribute-rgt-in_binary64`

Counts

155 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	2195
1	347	1715
2	1331	1542
3	4587	1542
4	5090	1542

prune85.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	174	3	177

Error

0.4b

Counts

177 → 3

Alt Table

Status	Error	Program
▶	50.4b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
✓	29.3b	(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 3789 to 1053 computations (72.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 3/2 (*.f64 x x))
✓	0.1b	(/.f64 1 (pow.f64 x 3))
✓	9.3b	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
✓	27.1b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

series16.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
5.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
3.0ms	(/.f64 1 (pow.f64 x 3))
3.0ms	(/.f64 3/2 (*.f64 x x))

rewrite69.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

4 → 178

Calls

4 calls:

26.0ms	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
20.0ms	(+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))
7.0ms	(/.f64 1 (pow.f64 x 3))
4.0ms	(/.f64 3/2 (*.f64 x x))

simplify143.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-def_binary64`
372×	`unswap-sqr_binary64`
356×	`associate-/l/_binary64`
224×	`distribute-rgt-in_binary64`
217×	`fma-neg_binary64`

Counts

214 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	185	2668
1	401	2553
2	1551	2501
3	4536	2445
4	4701	2435
5	4947	2435
6	4954	2435

prune135.0ms (4.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	193	5	198

Error

0.4b

Counts

198 → 5

Alt Table

Status	Error	Program
✓	29.3b	(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))))
	62.5b	(+.f64 (.f64 8/9 (.f64 (/.f64 1 x) (pow.f64 3/8 1/3))) (+.f64 (.f64 44/81 (.f64 (/.f64 1 (pow.f64 x 2)) (pow.f64 3/8 1/3))) (pow.f64 3/8 1/3)))
✓	50.4b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	50.6b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (.f64 x x)))) 3/8))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (.f64 x x)))) 3/8)))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))))

Compiler

Compiled 5045 to 3754 computations (25.6% saved)

regimes106.0ms (3.2%)

Accuracy

Total 0.1b remaining (20.8%)

Threshold costs 0.1b (20.8%)

Counts

39 → 1

Compiler

Compiled 2000 to 1432 computations (28.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end100.0ms (3.1%)

Compiler: Compiled 142 to 106 computations (25.4% saved)

Details

analyze575.0ms (17.5%)

sample1.7s (51.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series9.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify69.0ms (2.1%)

prune20.0ms (0.6%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series63.0ms (1.9%)

rewrite50.0ms (1.5%)

simplify86.0ms (2.6%)

prune85.0ms (2.6%)

localize11.0ms (0.3%)

series16.0ms (0.5%)

rewrite69.0ms (2.1%)

simplify143.0ms (4.4%)

prune135.0ms (4.1%)

regimes106.0ms (3.2%)

simplify7.0ms (0.2%)

end100.0ms (3.1%)

Profiling