Details

analyze980.0ms (15.7%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
6.2%	93.7%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.9%	0.1%	8
16.4%	83.5%	0.1%	9
19.1%	80.8%	0.1%	10
20.5%	79.4%	0.1%	11
22%	78%	0.1%	12
22.7%	77.2%	0.1%	13
23.4%	76.5%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample3.8s (60.7%)

Symmetry

(sort a x)

Results

1.4s	2661×	body	8192	exit
945.0ms	1516×	body	2048	valid
642.0ms	1767×	body	1024	valid
333.0ms	3176×	body	128	valid
288.0ms	1142×	body	512	valid
115.0ms	655×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify72.0ms (1.2%)

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)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(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))

simplify70.0ms (1.1%)

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

prune14.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

0.0b

Counts

20 → 4

Alt Table

Status	Error	Program
	27.3b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))
	41.4b	(.f64 (sqrt.f64 (expm1.f64 (.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))
▶	16.1b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

Compiler

Compiled 295 to 147 computations (50.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 (*.f64 a x))
✓	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	16.2b	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

series29.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))

rewrite6.0ms (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)

simplify84.0ms (1.4%)

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

prune49.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	89	4	93

Error

0.0b

Counts

93 → 4

Alt Table

Status	Error	Program
	27.3b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
▶	16.1b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))
	26.8b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 (*.f64 a x)) 1) 3))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1351 to 728 computations (46.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))
	0.0b	(expm1.f64 (*.f64 a x))
	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	16.2b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))

series30.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))
7.0ms	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`cbrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 24

Calls

2 calls:

1.0ms	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))
0.0ms	(expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

443×	`distribute-rgt-in_binary64`
438×	`distribute-lft-in_binary64`
418×	`associate-l_binary64`
394×	`associate-r_binary64`
286×	`fma-def_binary64`

Counts

72 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	995
1	162	911
2	478	897
3	2083	887
4	4633	848
5	4989	848
6	4995	848

prune86.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	111	4	115

Error

0.0b

Counts

115 → 4

Alt Table

Status	Error	Program
	23.6b	(cbrt.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3) (pow.f64 (expm1.f64 (.f64 a x)) 3)) (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))
▶	16.2b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))
	27.3b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 1894 to 1140 computations (39.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(pow.f64 (expm1.f64 (*.f64 a x)) 3)
✓	0.1b	(.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))))
	16.2b	(cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))
✓	16.2b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))

series23.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

15.0ms

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))))

8.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 54

Calls

2 calls:

6.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))

5.0ms

(*.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3)))))

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

616×	`unswap-sqr_binary64`
543×	`distribute-rgt-in_binary64`
415×	`associate-l_binary64`
348×	`associate-r_binary64`
277×	`fma-def_binary64`

Counts

102 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	1846
1	198	1382
2	543	1322
3	2046	1300
4	4751	1279
5	5014	1279

prune322.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	293	2	295
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	295	4	299

Error

0.0b

Counts

299 → 4

Alt Table

Status	Error	Program
	27.3b	(.f64 x (fma.f64 x (.f64 1/2 (*.f64 a a)) a))
	16.2b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3)))) (cbrt.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))
	20.8b	(cbrt.f64 (.f64 (cbrt.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))) (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (.f64 a x)) 3))))) (cbrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 10447 to 6256 computations (40.1% saved)

regimes361.0ms (5.8%)

Accuracy

Total 0.0b remaining (29.2%)

Threshold costs 0.0b (29.2%)

Counts

71 → 1

Compiler

Compiled 6962 to 4896 computations (29.7% 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

end85.0ms (1.4%)

Remove: (sort a x)
Compiler: Compiled 103 to 68 computations (34% saved)

Details

analyze980.0ms (15.7%)

sample3.8s (60.7%)

simplify72.0ms (1.2%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify70.0ms (1.1%)

prune14.0ms (0.2%)

localize6.0ms (0.1%)

series29.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify84.0ms (1.4%)

prune49.0ms (0.8%)

localize8.0ms (0.1%)

series30.0ms (0.5%)

rewrite2.0ms (0%)

simplify85.0ms (1.4%)

prune86.0ms (1.4%)

localize13.0ms (0.2%)

series23.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify90.0ms (1.4%)

prune322.0ms (5.2%)

regimes361.0ms (5.8%)

simplify2.0ms (0%)

end85.0ms (1.4%)

Profiling