Details

analyze199.0ms (2.9%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
43.7%	40.6%	15.7%	7
56.2%	23.4%	20.4%	8
57.8%	21.1%	21.2%	9
64%	12.5%	23.5%	10
64.8%	10.7%	24.5%	11
67.9%	6.4%	25.7%	12
68.3%	5.4%	26.3%	13
69.9%	3.3%	26.9%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.5s (22.2%)

Results

1.4s	8256×	body	128	valid
33.0ms	166×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

388×	`fma-def_binary64`
286×	`fma-neg_binary64`
71×	`distribute-rgt-in_binary64`
70×	`associate-l_binary64`
69×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

prune5.0ms (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	(.f64 2 (.f64 x (-.f64 x y)))
▶	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 58 to 37 computations (36.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
✓	0.0b	(-.f64 (.f64 x x) (.f64 x y))

series26.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
9.0ms	(-.f64 (.f64 x x) (.f64 x y))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 46

Calls

2 calls:

10.0ms	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))
5.0ms	(-.f64 (.f64 x x) (.f64 x y))

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-neg_binary64`
500×	`associate-l_binary64`
430×	`associate-r_binary64`
208×	`fma-def_binary64`
177×	`distribute-rgt-neg-out_binary64`

Counts

94 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1026
1	193	954
2	582	936
3	2421	936
4	4654	936
5	4890	936

prune79.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Error

0.0b

Counts

89 → 3

Alt Table

Status	Error	Program
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 2 (-.f64 x y)))) (cbrt.f64 (.f64 x (.f64 2 (-.f64 x y))))) (cbrt.f64 (.f64 x (.f64 2 (-.f64 x y)))))
▶	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 1326 to 499 computations (62.4% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

series13.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(*.f64 x (*.f64 2 (-.f64 x y)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
36×	`prod-diff_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

1 → 74

Calls

1 calls:

15.0ms

(*.f64 x (*.f64 2 (-.f64 x y)))

simplify174.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
381×	`*-commutative_binary64`
334×	`exp-prod_binary64`
295×	`distribute-lft-neg-out_binary64`
290×	`distribute-rgt-neg-out_binary64`

Counts

98 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1726
1	260	1429
2	790	1213
3	2192	1105
4	4566	1105
5	4891	1105

prune88.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	84	3	87

Error

0.0b

Counts

87 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))
▶	36.0b	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))
✓	0.0b	(.f64 2 (-.f64 (.f64 x x) (*.f64 x y)))

Compiler

Compiled 1866 to 751 computations (59.8% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y y) (.f64 x y))
✓	0.2b	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
✓	2.4b	(.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
✓	32.9b	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))

series106.0ms (1.6%)

Counts

4 → 78

Calls

4 calls:

52.0ms	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))
26.0ms	(.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
20.0ms	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
8.0ms	(+.f64 (.f64 y y) (.f64 x y))

rewrite465.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Rules

720×	`prod-diff_binary64`
628×	`distribute-lft-in_binary64`
628×	`distribute-rgt-in_binary64`
409×	`add-sqr-sqrt_binary64`
395×	`*-un-lft-identity_binary64`

Counts

4 → 897

Calls

4 calls:

74.0ms	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))
67.0ms	(.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))))
25.0ms	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
6.0ms	(+.f64 (.f64 y y) (.f64 x y))

simplify1.3s (18.7%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-r_binary64`
638×	`associate-l_binary64`
581×	`fma-neg_binary64`
444×	`*-commutative_binary64`
209×	`exp-prod_binary64`

Counts

975 → 615

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	795	27135
1	763	23100
2	3607	23036
3	4704	23036
4	4951	23036

prune1.1s (15.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	614	1	615
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	615	3	618

Error

Counts

618 → 3

Alt Table

Status	Error	Program
▶	31.4b	(.f64 (/.f64 x (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))))
✓	36.0b	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 29552 to 15198 computations (48.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 (pow.f64 x 3) (pow.f64 y 3))
✓	14.2b	(/.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x))))
✓	14.7b	(.f64 (/.f64 x (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))))
✓	14.8b	(sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))

series97.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

61.0ms

(*.f64 (/.f64 x (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) (/.f64 (*.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))))

23.0ms

(/.f64 (*.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))

13.0ms

(sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))

rewrite120.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
24×	`*-un-lft-identity_binary64`

Counts

3 → 107

Calls

3 calls:

50.0ms

(/.f64 (*.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x))))

39.0ms

(*.f64 (/.f64 x (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))) (/.f64 (*.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))))

2.0ms

(sqrt.f64 (fma.f64 y (+.f64 y x) (*.f64 x x)))

simplify223.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

668×	`times-frac_binary64`
455×	`fma-def_binary64`
334×	`distribute-rgt-in_binary64`
173×	`associate-*r/_binary64`
166×	`associate-/l*_binary64`

Counts

179 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	6034
1	651	4683
2	2272	4633
3	5068	4633

prune563.0ms (8.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	420	0	420
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	420	3	423

Error

Counts

423 → 3

Alt Table

Status	Error	Program
✓	31.4b	(.f64 (/.f64 x (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x)))))
✓	36.0b	(/.f64 (.f64 x (.f64 2 (-.f64 (pow.f64 x 3) (pow.f64 y 3)))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x y))))
✓	0.0b	(.f64 x (.f64 2 (-.f64 x y)))

Compiler

Compiled 18152 to 6836 computations (62.3% saved)

regimes374.0ms (5.5%)

Accuracy

Total 0.0b remaining (25.8%)

Threshold costs 0.0b (25.8%)

Counts

43 → 1

Compiler

Compiled 3938 to 2442 computations (38% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	26	16
3	36	16
4	43	16
5	48	16
6	50	16
7	49	16

end115.0ms (1.7%)

Compiler: Compiled 93 to 58 computations (37.6% saved)

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10

Details

analyze199.0ms (2.9%)

sample1.5s (22.2%)

simplify43.0ms (0.6%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series26.0ms (0.4%)

rewrite19.0ms (0.3%)

simplify119.0ms (1.8%)

prune79.0ms (1.2%)

localize11.0ms (0.2%)

series13.0ms (0.2%)

rewrite30.0ms (0.4%)

simplify174.0ms (2.6%)

prune88.0ms (1.3%)

localize29.0ms (0.4%)

series106.0ms (1.6%)

rewrite465.0ms (6.9%)

simplify1.3s (18.7%)

prune1.1s (15.7%)

localize27.0ms (0.4%)

series97.0ms (1.4%)

rewrite120.0ms (1.8%)

simplify223.0ms (3.3%)

prune563.0ms (8.3%)

regimes374.0ms (5.5%)

simplify5.0ms (0.1%)

end115.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	8	10
1	18	10
2	40	10
3	88	10
4	154	10
5	217	10
6	386	10
7	511	10
8	657	10
9	727	10
10	777	10
11	724	10