Details

analyze54.0ms (1.2%)

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 (1.9%)

Algorithm

1×

intervals

Symmetry

(sort a x)

Results

16.0ms	44×	body	2048	valid
8.0ms	50×	body	1024	valid
3.0ms	108×	body	128	valid
3.0ms	32×	body	512	valid
2.0ms	22×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify71.0ms (1.5%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (*.f64 a x))
	28.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize3.0ms (0.1%)

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))

simplify79.0ms (1.7%)

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

prune13.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	17	4	21

Error

0.0b

Counts

21 → 4

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	15.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
	28.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 299 to 147 computations (50.8% saved)

localize7.0ms (0.2%)

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))))
✓	9.4b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.1s (23.7%)

Counts

3 → 72

Calls

3 calls:

597.0ms

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

502.0ms

(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))))

rewrite26.0ms (0.6%)

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)))

simplify143.0ms (3.1%)

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

prune130.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
	15.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
	28.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 6873 to 1931 computations (71.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
	0.3b	(.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (*.f64 a x))))
	9.4b	(cbrt.f64 (expm1.f64 (*.f64 a x)))

series1.1s (23.6%)

Counts

2 → 48

Calls

2 calls:

1.1s	(log1p.f64 (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)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`

Counts

2 → 32

Calls

2 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
0.0ms	(log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

798×	`times-frac_binary64`
585×	`associate-/l*_binary64`
363×	`associate-/r*_binary64`
264×	`fma-def_binary64`
239×	`unswap-sqr_binary64`

Counts

80 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2539
1	409	1869
2	1208	1654
3	4968	1654

prune122.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	222	4	226

Error

Counts

226 → 4

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
▶	15.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
	28.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 7144 to 2275 computations (68.2% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.2b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	15.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series28.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
6.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
2.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

674×	`associate-l_binary64`
587×	`associate-r_binary64`
337×	`log-prod_binary64`
288×	`fma-def_binary64`
278×	`exp-prod_binary64`

Counts

96 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1262
1	202	1199
2	629	1177
3	3098	1171
4	4791	1171
5	4962	1171

prune48.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
✓	0.7b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (.f64 a x))) (cbrt.f64 (expm1.f64 (.f64 a x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))))))
✓	15.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))
	28.0b	(-.f64 (exp.f64 (*.f64 a x)) 1)

Compiler

Compiled 1321 to 700 computations (47% saved)

regimes47.0ms (1%)

Accuracy

Total 0.0b remaining (28.5%)

Threshold costs 0.0b (28.5%)

Counts

10 → 1

Compiler

Compiled 750 to 419 computations (44.1% 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)

sample1.4s (30.3%)

Algorithm

1×

intervals

Results

485.0ms	1435×	body	2048	valid
320.0ms	1807×	body	1024	valid
130.0ms	1060×	body	512	valid
123.0ms	3075×	body	128	valid
46.0ms	623×	body	256	valid
5.0ms	140×	body	128	invalid

Compiler

Compiled 61 to 39 computations (36.1% saved)

Details

analyze54.0ms (1.2%)

sample87.0ms (1.9%)

simplify71.0ms (1.5%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite1.0ms (0%)

simplify79.0ms (1.7%)

prune13.0ms (0.3%)

localize7.0ms (0.2%)

series1.1s (23.7%)

rewrite26.0ms (0.6%)

simplify143.0ms (3.1%)

prune130.0ms (2.8%)

localize8.0ms (0.2%)

series1.1s (23.6%)

rewrite8.0ms (0.2%)

simplify60.0ms (1.3%)

prune122.0ms (2.6%)

localize5.0ms (0.1%)

series28.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify85.0ms (1.8%)

prune48.0ms (1%)

regimes47.0ms (1%)

simplify2.0ms (0%)

end5.0ms (0.1%)

sample1.4s (30.3%)

Profiling