Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample670.0ms (41.2%)

Symmetry

(sort a b)

Results

634.0ms

8256×

body

128

valid

Compiler

Compiled 57 to 34 computations (40.4% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	26	10
3	46	10
4	81	10
5	101	10
6	117	10
7	130	10
8	132	10
9	132	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 27 to 12 computations (55.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (+.f64 a b) (+.f64 a b))

rewrite56.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`
6×	`swap-sqr_binary64`

Counts

1 → 42

Calls

1 calls:

7.0ms

(*.f64 (+.f64 a b) (+.f64 a b))

simplify52.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-+l+_binary64`
594×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
327×	`fma-def_binary64`

Counts

66 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	994
1	200	853
2	739	757
3	2462	692
4	5240	692

prune42.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
	0.5b	(cbrt.f64 (pow.f64 (+.f64 b a) 6))
▶	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))
	0.1b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 945 to 300 computations (68.3% saved)

localize9.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

series8.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

8.0ms

(+.f64 (*.f64 2 (*.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
3×	`sum-log_binary64`
1×	`+-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`flip-+_binary64`

Counts

1 → 16

Calls

1 calls:

11.0ms

(+.f64 (*.f64 2 (*.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

559×	`fma-neg_binary64`
415×	`distribute-rgt-out_binary64`
388×	`associate-l_binary64`
320×	`associate-r_binary64`
288×	`fma-def_binary64`

Counts

28 → 34

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	494
1	138	416
2	540	363
3	2532	363
4	4928	363
5	4992	363

prune25.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Error

Counts

37 → 3

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
	0.5b	(cbrt.f64 (pow.f64 (+.f64 b a) 6))
✓	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

Compiler

Compiled 673 to 399 computations (40.7% saved)

localize10.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
✓	3.2b	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))

series19.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))
8.0ms	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

0.0ms	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))
0.0ms	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))

simplify60.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
580×	`associate-l_binary64`
478×	`associate-r_binary64`
410×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`

Counts

69 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1267
1	246	1103
2	831	1040
3	3857	1033
4	5055	1033

prune45.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	64	3	67

Error

Counts

67 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
▶	0.5b	(cbrt.f64 (pow.f64 (+.f64 b a) 6))
✓	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

Compiler

Compiled 1251 to 716 computations (42.8% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (+.f64 b a) 6)
✓	0.5b	(cbrt.f64 (pow.f64 (+.f64 b a) 6))

series21.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(pow.f64 (+.f64 b a) 6)
6.0ms	(cbrt.f64 (pow.f64 (+.f64 b a) 6))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

3.0ms	(pow.f64 (+.f64 b a) 6)
3.0ms	(cbrt.f64 (pow.f64 (+.f64 b a) 6))

simplify78.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

537×	`exp-prod_binary64`
455×	`associate-l_binary64`
423×	`log-prod_binary64`
404×	`associate-r_binary64`
317×	`fma-def_binary64`

Counts

86 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1331
1	203	1215
2	572	1116
3	2438	1064
4	4247	1064
5	4922	1064

prune52.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
✓	0.5b	(cbrt.f64 (pow.f64 (+.f64 b a) 6))
✓	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

Compiler

Compiled 986 to 618 computations (37.3% saved)

regimes153.0ms (9.4%)

Accuracy

Total 0.0b remaining (81%)

Threshold costs 0.0b (81%)

Counts

36 → 1

Compiler

Compiled 1691 to 1133 computations (33% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	9	16

end217.0ms (13.4%)

Compiler: Compiled 88 to 57 computations (35.2% saved)

Details

analyze2.0ms (0.1%)

sample670.0ms (41.2%)

simplify9.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.4%)

rewrite56.0ms (3.4%)

simplify52.0ms (3.2%)

prune42.0ms (2.6%)

localize9.0ms (0.5%)

series8.0ms (0.5%)

rewrite12.0ms (0.7%)

simplify61.0ms (3.7%)

prune25.0ms (1.6%)

localize10.0ms (0.6%)

series19.0ms (1.1%)

rewrite1.0ms (0.1%)

simplify60.0ms (3.7%)

prune45.0ms (2.7%)

localize4.0ms (0.3%)

series21.0ms (1.3%)

rewrite7.0ms (0.4%)

simplify78.0ms (4.8%)

prune52.0ms (3.2%)

regimes153.0ms (9.4%)

simplify2.0ms (0.1%)

end217.0ms (13.4%)

Profiling