Details

analyze58.0ms (0.9%)

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)

sample87.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort a x)

Results

13.0ms	39×	body	2048	valid
8.0ms	51×	body	1024	valid
3.0ms	35×	body	512	valid
3.0ms	106×	body	128	valid
2.0ms	25×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify73.0ms (1.1%)

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

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

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(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:

0.0ms

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

simplify66.0ms (1%)

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

prune11.0ms (0.2%)

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
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	0.8b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	17.2b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 283 to 135 computations (52.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.3b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	8.3b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.1s (16%)

Counts

3 → 72

Calls

3 calls:

610.0ms

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

449.0ms

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

7.0ms

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

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

5.0ms

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

1.0ms

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

simplify129.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
437×	`*-commutative_binary64`
358×	`distribute-rgt-in_binary64`
343×	`distribute-lft-in_binary64`
260×	`unswap-sqr_binary64`

Counts

165 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2948
1	409	2621
2	1154	2203
3	2637	2016
4	4849	1965
5	4962	1965
6	4932	1965

prune126.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	266	3	269

Error

0.0b

Counts

269 → 3

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x))))) (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	22.7b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 6913 to 1923 computations (72.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.3b	(.f64 (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x))))) (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))))
✓	1.2b	(cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))))
	8.3b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.3s (20.3%)

Counts

2 → 48

Calls

2 calls:

681.0ms

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

669.0ms

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

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`cbrt-prod_binary64`
9×	`pow1_binary64`
7×	`pow1/3_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 47

Calls

2 calls:

5.0ms

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

3.0ms

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

simplify156.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`unswap-sqr_binary64`
487×	`fma-def_binary64`
411×	`*-commutative_binary64`
228×	`sqr-pow_binary64`
200×	`exp-prod_binary64`

Counts

95 → 96

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	154	2978
1	331	2820
2	871	2214
3	1912	2146
4	3555	1620
5	4680	1600
6	4959	1600
7	4907	1600

prune417.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	575	1	576
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	576	3	579

Error

0.0b

Counts

579 → 3

Alt Table

Status	Error	Program
	22.7b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
✓	0.0b	(expm1.f64 (*.f64 a x))
▶	1.0b	(.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) 2)) 2))) (cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))

Compiler

Compiled 31355 to 6253 computations (80.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)) 2)
✓	1.2b	(cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
	1.2b	(cbrt.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x)))))
	8.3b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.2s (18.6%)

Counts

2 → 48

Calls

2 calls:

636.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)) 2)
599.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
26×	`unpow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

4.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)) 2)
2.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

654×	`distribute-lft-out_binary64`
585×	`fma-def_binary64`
317×	`*-commutative_binary64`
274×	`sqr-pow_binary64`
228×	`distribute-rgt-out_binary64`

Counts

101 → 94

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	175	2520
1	378	2384
2	924	1988
3	2207	1904
4	3386	1794
5	4783	1764
6	4947	1764

prune238.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	242	3	245

Error

0.0b

Counts

245 → 3

Alt Table

Status	Error	Program
	1.8b	(.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) 2)) 2))) (exp.f64 (log.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) 2))))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	22.7b	(fma.f64 a x (.f64 (pow.f64 (.f64 a x) 2) 1/2))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 10605 to 4354 computations (58.9% saved)

regimes87.0ms (1.3%)

Accuracy

Total 0.0b remaining (35.4%)

Threshold costs 0.0b (35.4%)

Counts

16 → 1

Compiler

Compiled 2130 to 889 computations (58.3% saved)

simplify2.0ms (0%)

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

end5.0ms (0.1%)

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

sample1.3s (20.2%)

Algorithm

1×

intervals

Results

505.0ms	1454×	body	2048	valid
291.0ms	1757×	body	1024	valid
119.0ms	1099×	body	512	valid
100.0ms	3083×	body	128	valid
46.0ms	607×	body	256	valid
5.0ms	160×	body	128	invalid

Compiler

Compiled 66 to 44 computations (33.3% saved)

Details

analyze58.0ms (0.9%)

sample87.0ms (1.3%)

simplify73.0ms (1.1%)

prune3.0ms (0.1%)

localize3.0ms (0%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify66.0ms (1%)

prune11.0ms (0.2%)

localize8.0ms (0.1%)

series1.1s (16%)

rewrite17.0ms (0.3%)

simplify129.0ms (1.9%)

prune126.0ms (1.9%)

localize11.0ms (0.2%)

series1.3s (20.3%)

rewrite14.0ms (0.2%)

simplify156.0ms (2.3%)

prune417.0ms (6.3%)

localize16.0ms (0.2%)

series1.2s (18.6%)

rewrite9.0ms (0.1%)

simplify120.0ms (1.8%)

prune238.0ms (3.6%)

regimes87.0ms (1.3%)

simplify2.0ms (0%)

end5.0ms (0.1%)

sample1.3s (20.2%)

Profiling