Details

analyze589.0ms (14%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample124.0ms (3%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

9.0ms	256×	body	128	valid
5.0ms	87×	body	128	invalid

Compiler

Compiled 31 to 23 computations (25.8% saved)

simplify162.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1491×	`fma-neg_binary64`
579×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
419×	`div-sub_binary64`
329×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	70	13
4	138	13
5	257	13
6	498	13
7	922	13
8	1615	13
9	2472	13
10	2435	13
11	2431	13
12	2427	13
13	2428	13
14	2428	13
15	3596	13
16	3260	13
17	3260	13
18	3260	13
19	3140	13

prune2.0ms (0%)

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 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

series22.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

22.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-/l*_binary64`
6×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 32

Calls

1 calls:

7.0ms

(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

429×	`div-sub_binary64`
352×	`distribute-rgt-in_binary64`
333×	`distribute-lft-in_binary64`
268×	`neg-mul-1_binary64`
200×	`associate-/l*_binary64`

Counts

80 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1540
1	274	1260
2	889	1216
3	3171	1099
4	4711	1099
5	5041	1099

prune40.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

0.0b

Counts

62 → 4

Alt Table

Status	Error	Program
	33.4b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
▶	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 1065 to 454 computations (57.4% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (/.f64 z t))
✓	0.0b	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))

series75.0ms (1.8%)

Counts

3 → 66

Calls

3 calls:

35.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
33.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
6.0ms	(*.f64 1/2 (/.f64 z t))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`

Counts

3 → 78

Calls

3 calls:

7.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
5.0ms	(+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t)))
5.0ms	(*.f64 1/2 (/.f64 z t))

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
435×	`associate-*l/_binary64`
336×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`
191×	`cancel-sign-sub-inv_binary64`

Counts

144 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	2459
1	451	2255
2	1548	2185
3	4963	2185

prune144.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Error

0.0b

Counts

136 → 4

Alt Table

Status	Error	Program
	33.4b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
▶	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 3353 to 1594 computations (52.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

series22.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

22.0ms

(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

11.0ms

(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64`
427×	`associate-r_binary64`
356×	`div-sub_binary64`
350×	`associate-*r/_binary64`
340×	`associate-*l/_binary64`

Counts

89 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1760
1	327	1464
2	1329	1288
3	3680	1288
4	4980	1288
5	5099	1288

prune47.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Error

Counts

85 → 5

Alt Table

Status	Error	Program
	33.4b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
▶	0.8b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))

Compiler

Compiled 1475 to 649 computations (56% saved)

localize59.0ms (1.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
✓	0.4b	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))
✓	0.5b	(/.f64 (sqrt.f64 1/2) t)

series97.0ms (2.3%)

Counts

3 → 84

Calls

3 calls:

82.0ms	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
11.0ms	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))
3.0ms	(/.f64 (sqrt.f64 1/2) t)

rewrite63.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
28×	`associate-r_binary64`

Counts

3 → 117

Calls

3 calls:

17.0ms	(*.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2))
12.0ms	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))
3.0ms	(/.f64 (sqrt.f64 1/2) t)

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-/l*_binary64`
466×	`associate-*l/_binary64`
450×	`associate-*r/_binary64`
406×	`div-sub_binary64`
283×	`fma-def_binary64`

Counts

201 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3676
1	471	3073
2	1669	2821
3	4426	2797
4	5827	2797

prune105.0ms (2.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	183	5	188

Error

Counts

188 → 5

Alt Table

Status	Error	Program
	33.4b	(/.f64 (-.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 z z)) (.f64 (.f64 t 2) (+.f64 (+.f64 x y) z)))
✓	0.3b	(*.f64 (-.f64 (+.f64 x y) z) (/.f64 1/2 t))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 x t)) (.f64 1/2 (/.f64 y t))) (*.f64 1/2 (/.f64 z t)))
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
✓	0.8b	(.f64 (.f64 (+.f64 y (-.f64 x z)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) t))

Compiler

Compiled 3648 to 2091 computations (42.7% saved)

regimes1.3s (31.8%)

Accuracy

Total 0.0b remaining (94.7%)

Threshold costs 0.0b (94.7%)

Counts

71 → 1

Compiler

Compiled 9144 to 6644 computations (27.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	19	13
3	21	13
4	22	13
5	22	13

end6.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 39 to 27 computations (30.8% saved)

sample885.0ms (21.1%)

Algorithm

1×

intervals

Results

325.0ms	8000×	body	128	valid
115.0ms	2807×	body	128	invalid

Compiler

Compiled 120 to 82 computations (31.7% saved)

Details

analyze589.0ms (14%)

sample124.0ms (3%)

simplify162.0ms (3.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series22.0ms (0.5%)

rewrite9.0ms (0.2%)

simplify72.0ms (1.7%)

prune40.0ms (0.9%)

localize11.0ms (0.3%)

series75.0ms (1.8%)

rewrite21.0ms (0.5%)

simplify71.0ms (1.7%)

prune144.0ms (3.4%)

localize6.0ms (0.1%)

series22.0ms (0.5%)

rewrite13.0ms (0.3%)

simplify84.0ms (2%)

prune47.0ms (1.1%)

localize59.0ms (1.4%)

series97.0ms (2.3%)

rewrite63.0ms (1.5%)

simplify119.0ms (2.8%)

prune105.0ms (2.5%)

regimes1.3s (31.8%)

simplify4.0ms (0.1%)

end6.0ms (0.1%)

sample885.0ms (21.1%)

Profiling