Details

analyze142.0ms (2.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample93.0ms (1.8%)

Algorithm

1×

intervals

Results

38.0ms	64×	body	2048	valid
17.0ms	50×	body	1024	valid
6.0ms	31×	body	512	valid
5.0ms	90×	body	128	valid
2.0ms	21×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify123.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

prune5.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series11.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

1.0ms

(expm1.f64 (*.f64 a x))

simplify115.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
785×	`fma-neg_binary64`
383×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`

Counts

35 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	382
1	96	369
2	262	363
3	966	347
4	2376	333
5	3696	333
6	4842	333
7	5375	333

prune20.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Error

0.0b

Counts

20 → 3

Alt Table

Status	Error	Program
▶	27.7b	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
✓	0.0b	(expm1.f64 (*.f64 a x))
	35.0b	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 259 to 131 computations (49.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (expm1.f64 (*.f64 a x)))
	0.0b	(expm1.f64 (*.f64 a x))
✓	4.2b	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))

series31.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(exp.f64 (expm1.f64 (*.f64 a x)))
12.0ms	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-pow_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
2.0ms	(exp.f64 (expm1.f64 (*.f64 a x)))

simplify178.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-neg_binary64`
492×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`
230×	`associate-l_binary64`
214×	`fma-def_binary64`

Counts

80 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	873
1	150	832
2	389	818
3	1394	814
4	2468	794
5	3637	794
6	4918	794
7	5097	794

prune63.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	80	3	83

Error

0.0b

Counts

83 → 3

Alt Table

Status	Error	Program
✓	27.7b	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	35.0b	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 1002 to 392 computations (60.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	1.4b	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
✓	12.9b	(log.f64 (expm1.f64 (*.f64 a x)))

series780.0ms (15.6%)

Counts

2 → 48

Calls

2 calls:

768.0ms	(log.f64 (expm1.f64 (*.f64 a x)))
12.0ms	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(log.f64 (expm1.f64 (*.f64 a x)))
3.0ms	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))

simplify160.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

843×	`fma-neg_binary64`
513×	`*-commutative_binary64`
379×	`distribute-rgt-neg-in_binary64`
370×	`cancel-sign-sub-inv_binary64`
362×	`distribute-lft-neg-in_binary64`

Counts

79 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	972
1	162	921
2	425	911
3	1545	891
4	3112	871
5	4905	871
6	5066	871

prune69.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.0b

Counts

78 → 3

Alt Table

Status	Error	Program
✓	27.7b	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
▶	42.2b	(cbrt.f64 (.f64 (.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1031 to 405 computations (60.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))))
	1.4b	(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
✓	8.2b	(cbrt.f64 (.f64 (.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))
	12.9b	(log.f64 (expm1.f64 (*.f64 a x)))

series39.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

25.0ms

(*.f64 (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))))

14.0ms

(cbrt.f64 (*.f64 (*.f64 (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`exp-prod_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`pow1_binary64`
16×	`exp-sum_binary64`

Counts

2 → 69

Calls

2 calls:

28.0ms

(cbrt.f64 (*.f64 (*.f64 (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))

15.0ms

(*.f64 (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x)))))

simplify183.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

632×	`unswap-sqr_binary64`
435×	`associate-l_binary64`
365×	`associate-r_binary64`
350×	`prod-exp_binary64`
305×	`fma-def_binary64`

Counts

117 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1738
1	230	1453
2	628	1337
3	2183	1289
4	4778	1289
5	4972	1289

prune225.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	270	4	274

Error

0.0b

Counts

274 → 4

Alt Table

Status	Error	Program
✓	27.7b	(log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))
	42.2b	(cbrt.f64 (.f64 (.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 a x)))) (pow.f64 (E.f64) (log.f64 (expm1.f64 (.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))
✓	42.2b	(cbrt.f64 (.f64 (.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 a x)))) (exp.f64 (log.f64 (expm1.f64 (.f64 a x))))) (exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 7343 to 1635 computations (77.7% saved)

regimes276.0ms (5.5%)

Accuracy

Total 0.0b remaining (16.8%)

Threshold costs 0.0b (16.8%)

Counts

27 → 1

Compiler

Compiled 2117 to 1280 computations (39.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end12.0ms (0.2%)

Remove: (sort a x)
Compiler: Compiled 18 to 12 computations (33.3% saved)

sample2.4s (47.1%)

Algorithm

1×

intervals

Results

879.0ms	1429×	body	2048	valid
539.0ms	1678×	body	1024	valid
204.0ms	1127×	body	512	valid
162.0ms	3121×	body	128	valid
73.0ms	645×	body	256	valid
7.0ms	132×	body	128	invalid

Compiler

Compiled 78 to 43 computations (44.9% saved)

Details

analyze142.0ms (2.8%)

sample93.0ms (1.8%)

simplify123.0ms (2.4%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite1.0ms (0%)

simplify115.0ms (2.3%)

prune20.0ms (0.4%)

localize11.0ms (0.2%)

series31.0ms (0.6%)

rewrite7.0ms (0.1%)

simplify178.0ms (3.6%)

prune63.0ms (1.3%)

localize11.0ms (0.2%)

series780.0ms (15.6%)

rewrite8.0ms (0.2%)

simplify160.0ms (3.2%)

prune69.0ms (1.4%)

localize17.0ms (0.3%)

series39.0ms (0.8%)

rewrite58.0ms (1.2%)

simplify183.0ms (3.7%)

prune225.0ms (4.5%)

regimes276.0ms (5.5%)

simplify4.0ms (0.1%)

end12.0ms (0.2%)

sample2.4s (47.1%)

Profiling