Details

analyze598.0ms (20.4%)

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
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
21.1%	78%	0.9%	9
37.3%	60.3%	2.5%	10
39.7%	56.1%	4.2%	11
45.6%	48.7%	5.7%	12
55.9%	35.1%	8.9%	13
57.6%	32.1%	10.3%	14

Compiler

Compiled 13 to 8 computations (38.5% saved)

sample1.1s (38.3%)

Results

851.0ms	8256×	body	128	valid
114.0ms	1122×	body	128	invalid

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify108.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2064×	`fma-neg_binary64`
381×	`div-sub_binary64`
365×	`associate-/l*_binary64`
334×	`distribute-neg-frac_binary64`
322×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	11
2	25	11
3	47	11
4	82	11
5	143	11
6	228	11
7	442	11
8	1041	11
9	2472	11
10	2805	11
11	2944	11
12	3273	11
13	3441	11
14	3513	11
15	4986	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

10.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.1b	(/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

Compiler

Compiled 44 to 23 computations (47.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))
✓	9.4b	(/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

series27.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

13.0ms	(/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)
7.0ms	(*.f64 y (-.f64 z x))
7.0ms	(+.f64 x (*.f64 y (-.f64 z x)))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
42×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`distribute-lft-in_binary64`

Counts

3 → 123

Calls

3 calls:

6.0ms	(*.f64 y (-.f64 z x))
4.0ms	(+.f64 x (*.f64 y (-.f64 z x)))
4.0ms	(/.f64 (+.f64 x (*.f64 y (-.f64 z x))) z)

simplify124.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
694×	`fma-def_binary64`
546×	`fma-neg_binary64`
474×	`distribute-rgt-in_binary64`
195×	`exp-prod_binary64`

Counts

219 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	2678
1	400	2331
2	1328	2223
3	4381	2223
4	4999	2223
5	4929	2223

prune107.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	191	6	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	6	198

Error

0.0b

Counts

198 → 6

Alt Table

Status	Error	Program
	36.9b	(/.f64 (+.f64 x (.f64 (sqrt.f64 (.f64 y (-.f64 z x))) (sqrt.f64 (*.f64 y (-.f64 z x))))) z)
	40.2b	(.f64 (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (cbrt.f64 z)))
	10.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 y (-.f64 z x))) z)
	10.2b	(.f64 (+.f64 x (.f64 y (-.f64 z x))) (/.f64 1 z))
▶	2.9b	(fma.f64 (/.f64 (-.f64 1 y) z) x y)
	3.3b	(-.f64 (+.f64 y (/.f64 x z)) (/.f64 (*.f64 y x) z))

Compiler

Compiled 3885 to 960 computations (75.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 y) z)
✓	2.7b	(fma.f64 (/.f64 (-.f64 1 y) z) x y)

series18.0ms (0.6%)

Counts

2 → 52

Calls

2 calls:

12.0ms	(fma.f64 (/.f64 (-.f64 1 y) z) x y)
7.0ms	(/.f64 (-.f64 1 y) z)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

2 → 54

Calls

2 calls:

4.0ms	(/.f64 (-.f64 1 y) z)
0.0ms	(fma.f64 (/.f64 (-.f64 1 y) z) x y)

simplify72.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
429×	`neg-mul-1_binary64`
424×	`associate-/l/_binary64`
291×	`distribute-rgt-neg-out_binary64`
281×	`fma-neg_binary64`

Counts

106 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1312
1	225	1203
2	575	1199
3	1759	1199
4	4062	1199
5	5080	1199

prune56.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Error

Counts

87 → 5

Alt Table

Status	Error	Program
	3.3b	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
	40.2b	(.f64 (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (cbrt.f64 z)))
	10.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 y (-.f64 z x))) z)
▶	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)
	31.6b	(fma.f64 (/.f64 (/.f64 (-.f64 1 y) (sqrt.f64 z)) (sqrt.f64 z)) x y)

Compiler

Compiled 1275 to 694 computations (45.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)

series12.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 x z) (-.f64 1 y) y)

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

705×	`distribute-rgt-neg-out_binary64`
469×	`distribute-neg-out_binary64`
368×	`unsub-neg_binary64`
332×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	586
1	78	509
2	194	497
3	424	497
4	2300	497
5	4502	497
6	5263	497

prune16.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Error

Counts

28 → 5

Alt Table

Status	Error	Program
▶	3.3b	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
	40.2b	(.f64 (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (+.f64 x (.f64 y (-.f64 z x)))) (cbrt.f64 z)))
	10.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 y (-.f64 z x))) z)
✓	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)
	31.6b	(fma.f64 (/.f64 (/.f64 (-.f64 1 y) (sqrt.f64 z)) (sqrt.f64 z)) x y)

Compiler

Compiled 406 to 199 computations (51% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
✓	0.0b	(-.f64 x (*.f64 x y))
✓	3.1b	(/.f64 (-.f64 x (*.f64 x y)) z)

series31.0ms (1%)

Counts

3 → 96

Calls

3 calls:

14.0ms	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
13.0ms	(/.f64 (-.f64 x (*.f64 x y)) z)
4.0ms	(-.f64 x (*.f64 x y))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
13×	`fma-def_binary64`

Counts

3 → 80

Calls

3 calls:

6.0ms	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
3.0ms	(/.f64 (-.f64 x (*.f64 x y)) z)
2.0ms	(-.f64 x (*.f64 x y))

simplify89.0ms (3%)

Algorithm

1×	egg-herbie

Rules

476×	`associate-l_binary64`
413×	`associate-r_binary64`
373×	`fma-neg_binary64`
305×	`distribute-rgt-in_binary64`
283×	`distribute-lft-in_binary64`

Counts

176 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2021
1	354	1957
2	932	1848
3	4518	1848
4	5048	1848

prune92.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
✓	3.3b	(+.f64 (/.f64 (-.f64 x (*.f64 x y)) z) y)
	10.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x) (.f64 y (-.f64 z x))) z)
	34.2b	(+.f64 (.f64 (/.f64 (sqrt.f64 (-.f64 x (.f64 x y))) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 x y))) (cbrt.f64 z))) y)
✓	0.1b	(fma.f64 (/.f64 x z) (-.f64 1 y) y)
	31.6b	(fma.f64 (/.f64 (/.f64 (-.f64 1 y) (sqrt.f64 z)) (sqrt.f64 z)) x y)

Compiler

Compiled 2463 to 842 computations (65.8% saved)

regimes255.0ms (8.7%)

Accuracy

Total 0.0b remaining (63.2%)

Threshold costs 0.0b (63.2%)

Counts

72 → 1

Compiler

Compiled 4504 to 2430 computations (46% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	12	11
2	16	11
3	18	11
4	19	11
5	18	11

end63.0ms (2.2%)

Compiler: Compiled 105 to 58 computations (44.8% saved)

Details

analyze598.0ms (20.4%)

sample1.1s (38.3%)

simplify108.0ms (3.7%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (0.9%)

rewrite23.0ms (0.8%)

simplify124.0ms (4.2%)

prune107.0ms (3.7%)

localize8.0ms (0.3%)

series18.0ms (0.6%)

rewrite7.0ms (0.3%)

simplify72.0ms (2.5%)

prune56.0ms (1.9%)

localize5.0ms (0.2%)

series12.0ms (0.4%)

rewrite1.0ms (0%)

simplify64.0ms (2.2%)

prune16.0ms (0.5%)

localize5.0ms (0.2%)

series31.0ms (1%)

rewrite15.0ms (0.5%)

simplify89.0ms (3%)

prune92.0ms (3.1%)

regimes255.0ms (8.7%)

simplify2.0ms (0.1%)

end63.0ms (2.2%)

Profiling