Details

analyze2.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample874.0ms (22.3%)

Results

756.0ms

8256×

body

128

valid

Compiler

Compiled 67 to 49 computations (26.9% saved)

simplify121.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	17

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize7.0ms (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 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)

series35.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify139.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune280.0ms (7.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	5	296

Error

Counts

296 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.0b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	13.4b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
	0.1b	(.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.5b	(.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 (-.f64 1 m) (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))

Compiler

Compiled 7279 to 4662 computations (36% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series33.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

rewrite139.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

666×	`times-frac_binary64`
573×	`add-sqr-sqrt_binary64`
539×	`*-un-lft-identity_binary64`
382×	`add-cube-cbrt_binary64`
249×	`prod-diff_binary64`

Counts

3 → 520

Calls

3 calls:

29.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
27.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
7.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify360.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

507×	`fma-neg_binary64`
232×	`associate-/l*_binary64`
222×	`*-commutative_binary64`
203×	`associate-*l/_binary64`
195×	`associate-l_binary64`

Counts

592 → 706

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	389	13572
1	864	12765
2	3553	12236
3	4666	12236
4	4951	12236

prune843.0ms (21.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	706	0	706
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	706	5	711

Error

Counts

711 → 5

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
✓	0.0b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	13.4b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
▶	0.1b	(.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.5b	(.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 (-.f64 1 m) (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))

Compiler

Compiled 21856 to 14663 computations (32.9% saved)

localize6.0ms (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 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)

series13.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

13.0ms

(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`prod-diff_binary64`
40×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
25×	`distribute-lft-in_binary64`

Counts

1 → 85

Calls

1 calls:

16.0ms

(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

simplify94.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-in_binary64`
536×	`distribute-lft-in_binary64`
444×	`fma-def_binary64`
296×	`associate-*l/_binary64`
240×	`associate-*r/_binary64`

Counts

109 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2887
1	314	2419
2	1067	2369
3	4421	2369
4	5106	2369

prune327.0ms (8.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	320	5	325

Error

Counts

325 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	13.4b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
✓	0.1b	(.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.0b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	0.5b	(.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 (-.f64 1 m) (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))

Compiler

Compiled 8126 to 5603 computations (31% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series21.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
10.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

5.0ms	(*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
0.0ms	(fma.f64 (/.f64 m v) (-.f64 1 m) -1)

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Rules

401×	`div-sub_binary64`
334×	`associate-*l/_binary64`
285×	`associate-*r/_binary64`
255×	`distribute-rgt-in_binary64`
246×	`distribute-lft-in_binary64`

Counts

85 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1617
1	182	1453
2	564	1407
3	1890	1343
4	4391	1343
5	5399	1343

prune76.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	79	5	84

Error

Counts

84 → 5

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 1 m) (fma.f64 (/.f64 m v) (-.f64 1 m) -1))
	13.4b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
✓	0.1b	(.f64 (-.f64 1 m) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.0b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	0.5b	(.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 (-.f64 1 m) (cbrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))

Compiler

Compiled 1466 to 906 computations (38.2% saved)

regimes279.0ms (7.1%)

Accuracy

Total 0.0b remaining (67.7%)

Threshold costs 0.0b (67.7%)

Counts

94 → 1

Compiler

Compiled 5614 to 4010 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	21	19
3	23	19
4	24	19
5	22	19

end87.0ms (2.2%)

Compiler: Compiled 142 to 104 computations (26.8% saved)

Details

analyze2.0ms (0%)

sample874.0ms (22.3%)

simplify121.0ms (3.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series35.0ms (0.9%)

rewrite47.0ms (1.2%)

simplify139.0ms (3.6%)

prune280.0ms (7.2%)

localize6.0ms (0.2%)

series33.0ms (0.8%)

rewrite139.0ms (3.6%)

simplify360.0ms (9.2%)

prune843.0ms (21.6%)

localize6.0ms (0.2%)

series13.0ms (0.3%)

rewrite24.0ms (0.6%)

simplify94.0ms (2.4%)

prune327.0ms (8.4%)

localize6.0ms (0.2%)

series21.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify78.0ms (2%)

prune76.0ms (1.9%)

regimes279.0ms (7.1%)

simplify3.0ms (0.1%)

end87.0ms (2.2%)

Profiling