Details

analyze1.0ms (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)

sample957.0ms (45%)

Symmetry

(sort a b)

Results

922.0ms

8256×

body

128

valid

Compiler

Compiled 57 to 34 computations (40.4% saved)

simplify10.0ms (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 (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite9.0ms (0.4%)

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:

6.0ms

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

simplify50.0ms (2.4%)

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

prune43.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))
▶	0.0b	(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))

Compiler

Compiled 959 to 298 computations (68.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series21.0ms (1%)

Counts

3 → 72

Calls

3 calls:

9.0ms	(*.f64 a (+.f64 a b))
7.0ms	(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))
5.0ms	(*.f64 b (+.f64 a b))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-*r/_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`flip-+_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms	(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))
4.0ms	(*.f64 a (+.f64 a b))
4.0ms	(*.f64 b (+.f64 a b))

simplify94.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
401×	`*-commutative_binary64`
387×	`associate-+l+_binary64`
371×	`cancel-sign-sub-inv_binary64`
370×	`associate-+r+_binary64`

Counts

145 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	1613
1	380	1512
2	1536	1408
3	3300	1408
4	4869	1408
5	4958	1408

prune94.0ms (4.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	2	133

Error

Counts

133 → 2

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))
✓	0.0b	(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))

Compiler

Compiled 2326 to 515 computations (77.9% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 b b) (.f64 a b))
✓	0.0b	(+.f64 (.f64 a a) (-.f64 (.f64 b b) (*.f64 a b)))
✓	0.3b	(*.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b))
✓	0.5b	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))

series45.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

21.0ms	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))
9.0ms	(*.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b))
9.0ms	(+.f64 (.f64 a a) (-.f64 (.f64 b b) (*.f64 a b)))
6.0ms	(-.f64 (.f64 b b) (.f64 a b))

rewrite48.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
14×	`flip-+_binary64`
14×	`flip3-+_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`

Counts

4 → 106

Calls

4 calls:

19.0ms	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))
12.0ms	(*.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b))
7.0ms	(+.f64 (.f64 a a) (-.f64 (.f64 b b) (*.f64 a b)))
3.0ms	(-.f64 (.f64 b b) (.f64 a b))

simplify162.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

509×	`times-frac_binary64`
366×	`fma-neg_binary64`
216×	`cancel-sign-sub-inv_binary64`
216×	`unswap-sqr_binary64`
204×	`distribute-rgt-in_binary64`

Counts

202 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3553
1	549	3247
2	2490	3236
3	4536	3236
4	4973	3236
5	5000	3236
6	4955	3236

prune143.0ms (6.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	206	2	208

Error

Counts

208 → 2

Alt Table

Status	Error	Program
✓	0.6b	(/.f64 (.f64 (+.f64 (pow.f64 a 3) (pow.f64 b 3)) (+.f64 a b)) (+.f64 (.f64 a a) (-.f64 (.f64 b b) (.f64 a b))))
✓	0.0b	(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))

Compiler

Compiled 6550 to 2461 computations (62.4% saved)

regimes340.0ms (16%)

Accuracy

Total 0.0b remaining (40.2%)

Threshold costs 0.0b (40.2%)

Counts

81 → 1

Compiler

Compiled 5666 to 3200 computations (43.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	11	16
2	11	16

end56.0ms (2.6%)

Remove: (sort a b)
Compiler: Compiled 90 to 45 computations (50% saved)

Details

analyze1.0ms (0.1%)

sample957.0ms (45%)

simplify10.0ms (0.5%)

prune1.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.3%)

rewrite9.0ms (0.4%)

simplify50.0ms (2.4%)

prune43.0ms (2%)

localize7.0ms (0.3%)

series21.0ms (1%)

rewrite19.0ms (0.9%)

simplify94.0ms (4.4%)

prune94.0ms (4.4%)

localize14.0ms (0.7%)

series45.0ms (2.1%)

rewrite48.0ms (2.2%)

simplify162.0ms (7.6%)

prune143.0ms (6.7%)

regimes340.0ms (16%)

simplify3.0ms (0.1%)

end56.0ms (2.6%)

Profiling