Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
12.5%	0%	87.5%	1

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.6s (31%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify153.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune4.0ms (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
	0.1b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series148.0ms (2.9%)

Counts

4 → 80

Calls

4 calls:

102.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
23.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
18.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite85.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

20.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
19.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
14.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
13.0ms	(*.f64 m (-.f64 1 m))

simplify205.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
482×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3371
1	413	2852
2	1688	2595
3	4507	2594
4	4922	2594

prune482.0ms (9.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	241	6	247

Error

Counts

247 → 6

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	23.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.2b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	18.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)

Compiler

Compiled 5037 to 3074 computations (39% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 m) m)
✓	0.0b	(-.f64 (/.f64 (*.f64 (-.f64 1 m) m) v) 1)
✓	0.0b	(/.f64 (*.f64 (-.f64 1 m) m) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)

series62.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

24.0ms	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)
18.0ms	(/.f64 (*.f64 (-.f64 1 m) m) v)
17.0ms	(-.f64 (/.f64 (*.f64 (-.f64 1 m) m) v) 1)
3.0ms	(*.f64 (-.f64 1 m) m)

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 127

Calls

4 calls:

10.0ms	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)
9.0ms	(/.f64 (*.f64 (-.f64 1 m) m) v)
9.0ms	(-.f64 (/.f64 (*.f64 (-.f64 1 m) m) v) 1)
5.0ms	(*.f64 (-.f64 1 m) m)

simplify223.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

590×	`associate-/l*_binary64`
352×	`distribute-rgt-in_binary64`
348×	`associate-*l/_binary64`
338×	`distribute-lft-in_binary64`
251×	`fma-def_binary64`

Counts

211 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2902
1	376	2461
2	1189	2442
3	4560	2441
4	4980	2441
5	4965	2441

prune305.0ms (6.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	219	6	225

Error

Counts

225 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)
▶	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	23.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
	0.2b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	18.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 4281 to 2713 computations (36.6% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)
✓	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))

series105.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

91.0ms	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
13.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

5.0ms	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
1.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify148.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

467×	`fma-def_binary64`
364×	`fma-neg_binary64`
340×	`div-sub_binary64`
294×	`exp-prod_binary64`
286×	`associate-*l/_binary64`

Counts

80 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1280
1	137	1054
2	385	1024
3	1223	1024
4	3040	1024
5	4753	1024
6	4950	1024

prune129.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	75	6	81

Error

Counts

81 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)
✓	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	23.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
▶	0.2b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	18.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 1277 to 751 computations (41.2% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
✓	0.1b	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
✓	0.2b	(/.f64 m (sqrt.f64 v))
✓	0.2b	(/.f64 (-.f64 1 m) (sqrt.f64 v))

series229.0ms (4.6%)

Counts

4 → 50

Calls

4 calls:

79.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
58.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)
47.0ms	(/.f64 m (sqrt.f64 v))
44.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
33×	`sqrt-prod_binary64`

Counts

4 → 136

Calls

4 calls:

13.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))
5.0ms	(/.f64 m (sqrt.f64 v))
5.0ms	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
1.0ms	(fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1)

simplify241.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
277×	`fma-neg_binary64`
265×	`associate-/l*_binary64`
247×	`associate-l_binary64`
238×	`times-frac_binary64`

Counts

186 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	3169
1	352	2980
2	941	2765
3	2626	2649
4	4660	2649
5	4990	2649
6	4934	2649

prune279.0ms (5.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	184	6	190

Error

Counts

190 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 (-.f64 1 m) m) v) 1) m)
✓	0.1b	(*.f64 m (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	23.6b	(cbrt.f64 (pow.f64 (*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1)) 3))
	0.4b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (cbrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) (*.f64 m (cbrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1))))
✓	0.2b	(*.f64 (fma.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)) -1) m)
	18.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 3789 to 1876 computations (50.5% saved)

regimes383.0ms (7.6%)

Accuracy

Total 0.1b remaining (74.2%)

Threshold costs 0.1b (74.2%)

Counts

88 → 1

Compiler

Compiled 4550 to 3125 computations (31.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	18	16
2	22	16
3	24	16
4	25	16
5	23	16

end139.0ms (2.8%)

Compiler: Compiled 128 to 88 computations (31.3% saved)

Details

analyze3.0ms (0.1%)

sample1.6s (31%)

simplify153.0ms (3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series148.0ms (2.9%)

rewrite85.0ms (1.7%)

simplify205.0ms (4.1%)

prune482.0ms (9.6%)

localize14.0ms (0.3%)

series62.0ms (1.2%)

rewrite43.0ms (0.9%)

simplify223.0ms (4.4%)

prune305.0ms (6.1%)

localize13.0ms (0.2%)

series105.0ms (2.1%)

rewrite8.0ms (0.2%)

simplify148.0ms (2.9%)

prune129.0ms (2.6%)

localize18.0ms (0.4%)

series229.0ms (4.6%)

rewrite38.0ms (0.7%)

simplify241.0ms (4.8%)

prune279.0ms (5.6%)

regimes383.0ms (7.6%)

simplify4.0ms (0.1%)

end139.0ms (2.8%)

Profiling