Details

analyze387.0ms (10.7%)

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
25%	74.9%	0.2%	4
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
37.4%	62.4%	0.2%	7
56.1%	43.7%	0.2%	8
56.1%	43.7%	0.2%	9
56.1%	43.7%	0.2%	10
65.5%	34.3%	0.2%	11
76.4%	23.4%	0.2%	12
76.4%	23.4%	0.2%	13
76.4%	23.4%	0.2%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample1.0s (28.5%)

Infinites

28.3% of outputs are infinite.

Results

933.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-rgt-in_binary64`
685×	`div-sub_binary64`
652×	`distribute-lft-in_binary64`
409×	`distribute-neg-frac_binary64`
395×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	22
2	58	22
3	109	22
4	223	20
5	437	16
6	876	14
7	2098	14
8	2320	14
9	2451	14
10	3042	14
11	3226	14
12	3327	14
13	4913	14

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.1b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)

Compiler

Compiled 95 to 62 computations (34.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
✓	0.2b	(.f64 (.f64 z 3) y)
✓	0.2b	(/.f64 y (*.f64 z 3))
✓	4.5b	(/.f64 t (.f64 (.f64 z 3) y))

series40.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

19.0ms	(/.f64 t (.f64 (.f64 z 3) y))
10.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
7.0ms	(/.f64 y (*.f64 z 3))
4.0ms	(.f64 (.f64 z 3) y)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

6.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
5.0ms	(/.f64 t (.f64 (.f64 z 3) y))
4.0ms	(.f64 (.f64 z 3) y)
3.0ms	(/.f64 y (*.f64 z 3))

simplify112.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
515×	`associate-*l/_binary64`
392×	`associate-*r/_binary64`
308×	`associate-/l/_binary64`
175×	`exp-prod_binary64`

Counts

234 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2758
1	498	2435
2	1639	2122
3	4282	2122
4	4997	2122
5	4827	2122

prune168.0ms (4.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	6	171

Error

Counts

171 → 6

Alt Table

Status	Error	Program
▶	2.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 t (/.f64 1/3 (*.f64 y z))))
	27.7b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (/.f64 y (.f64 z 3))) (sqrt.f64 (/.f64 y (.f64 z 3))))) (/.f64 t (.f64 (*.f64 z 3) y)))
	35.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (sqrt.f64 t) (/.f64 (.f64 (*.f64 z 3) y) (sqrt.f64 t))))
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))

Compiler

Compiled 4234 to 2508 computations (40.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 z) (/.f64 y 3)))
	0.2b	(.f64 (.f64 z 3) y)
✓	0.2b	(*.f64 (/.f64 1 z) (/.f64 y 3))
	4.5b	(/.f64 t (.f64 (.f64 z 3) y))

series17.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(-.f64 x (*.f64 (/.f64 1 z) (/.f64 y 3)))
7.0ms	(*.f64 (/.f64 1 z) (/.f64 y 3))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
24×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 78

Calls

2 calls:

8.0ms	(*.f64 (/.f64 1 z) (/.f64 y 3))
3.0ms	(-.f64 x (*.f64 (/.f64 1 z) (/.f64 y 3)))

simplify119.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
391×	`associate-*l/_binary64`
351×	`associate-r_binary64`
313×	`associate-*r/_binary64`
303×	`associate-/l*_binary64`

Counts

138 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1501
1	344	1407
2	988	1295
3	2907	1290
4	4512	1290
5	4920	1290

prune184.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	201	6	207

Error

Counts

207 → 6

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
▶	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 t (/.f64 1/3 (*.f64 y z))))
	27.7b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (/.f64 y (.f64 z 3))) (sqrt.f64 (/.f64 y (.f64 z 3))))) (/.f64 t (.f64 (*.f64 z 3) y)))
	35.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (sqrt.f64 t) (/.f64 (.f64 (*.f64 z 3) y) (sqrt.f64 t))))
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))

Compiler

Compiled 4816 to 3061 computations (36.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.7b	(/.f64 1/3 (*.f64 y z))
✓	4.3b	(.f64 t (/.f64 1/3 (.f64 y z)))

series27.0ms (0.8%)

Counts

2 → 36

Calls

2 calls:

18.0ms	(.f64 t (/.f64 1/3 (.f64 y z)))
9.0ms	(/.f64 1/3 (*.f64 y z))

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(.f64 t (/.f64 1/3 (.f64 y z)))
3.0ms	(/.f64 1/3 (*.f64 y z))

simplify97.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-l_binary64`
412×	`fma-def_binary64`
381×	`times-frac_binary64`
373×	`associate-*l/_binary64`
351×	`associate-*r/_binary64`

Counts

88 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1048
1	185	919
2	659	918
3	2936	918
4	3391	918
5	3979	918
6	4752	918
7	5065	918

prune175.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	171	6	177

Error

Counts

177 → 6

Alt Table

Status	Error	Program
✓	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 t (/.f64 1/3 (*.f64 y z))))
▶	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (*.f64 t (/.f64 1 y)) (/.f64 1/3 z)))
✓	2.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	27.7b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (/.f64 y (.f64 z 3))) (sqrt.f64 (/.f64 y (.f64 z 3))))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))

Compiler

Compiled 4253 to 2383 computations (44% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 t (/.f64 1 y))
	0.2b	(/.f64 y (*.f64 z 3))
✓	0.4b	(/.f64 1/3 z)
✓	4.0b	(.f64 (.f64 t (/.f64 1 y)) (/.f64 1/3 z))

series28.0ms (0.8%)

Counts

3 → 60

Calls

3 calls:

20.0ms	(.f64 (.f64 t (/.f64 1 y)) (/.f64 1/3 z))
7.0ms	(*.f64 t (/.f64 1 y))
2.0ms	(/.f64 1/3 z)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`add-cbrt-cube_binary64`
29×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`

Counts

3 → 114

Calls

3 calls:

8.0ms	(.f64 (.f64 t (/.f64 1 y)) (/.f64 1/3 z))
5.0ms	(*.f64 t (/.f64 1 y))
3.0ms	(/.f64 1/3 z)

simplify178.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

592×	`associate-*l/_binary64`
506×	`associate-*r/_binary64`
432×	`associate-/l*_binary64`
293×	`*-commutative_binary64`
277×	`sqr-pow_binary64`

Counts

174 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	1744
1	335	1531
2	1154	1531
3	3279	1530
4	3631	1530
5	4301	1530
6	4901	1530
7	5010	1530

prune197.0ms (5.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	193	6	199

Error

Counts

199 → 6

Alt Table

Status	Error	Program
✓	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 t (/.f64 1/3 (*.f64 y z))))
✓	2.5b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (.f64 (*.f64 t (/.f64 1 y)) (/.f64 1/3 z)))
✓	2.1b	(+.f64 (-.f64 x (.f64 (/.f64 1 z) (/.f64 y 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.5b	(fma.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)) x)
	27.7b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (/.f64 y (.f64 z 3))) (sqrt.f64 (/.f64 y (.f64 z 3))))) (/.f64 t (.f64 (*.f64 z 3) y)))
	2.8b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 (/.f64 t (.f64 z 3)) y))

Compiler

Compiled 4437 to 2787 computations (37.2% saved)

regimes523.0ms (14.5%)

Accuracy

Total 2.1b remaining (99%)

Threshold costs 0b (0%)

Counts

60 → 2

Compiler

Compiled 7936 to 5455 computations (31.3% saved)

bsearch12.0ms (0.3%)

Steps

Iters	Range		Point
5	1.4667636266504704e-133	5.496239229709031e-133	4.5577939887046744e-133

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	53
1	40	53
2	51	53
3	60	53
4	66	53
5	68	53
6	67	53

end96.0ms (2.7%)

Compiler: Compiled 201 to 138 computations (31.3% saved)

Details

analyze387.0ms (10.7%)

sample1.0s (28.5%)

simplify88.0ms (2.5%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

series40.0ms (1.1%)

rewrite23.0ms (0.6%)

simplify112.0ms (3.1%)

prune168.0ms (4.7%)

localize10.0ms (0.3%)

series17.0ms (0.5%)

rewrite15.0ms (0.4%)

simplify119.0ms (3.3%)

prune184.0ms (5.1%)

localize10.0ms (0.3%)

series27.0ms (0.8%)

rewrite11.0ms (0.3%)

simplify97.0ms (2.7%)

prune175.0ms (4.9%)

localize11.0ms (0.3%)

series28.0ms (0.8%)

rewrite23.0ms (0.6%)

simplify178.0ms (4.9%)

prune197.0ms (5.5%)

regimes523.0ms (14.5%)

bsearch12.0ms (0.3%)

simplify5.0ms (0.1%)

end96.0ms (2.7%)

Profiling