Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
75%	25%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.4s (33.1%)

Results

528.0ms	2054×	body	512	valid
526.0ms	4726×	body	128	valid
180.0ms	1055×	body	256	valid
127.0ms	421×	body	1024	valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

prune2.0ms (0%)

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

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	1.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite77.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

377×	`*-un-lft-identity_binary64`
375×	`times-frac_binary64`
284×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
234×	`prod-diff_binary64`

Counts

2 → 337

Calls

2 calls:

20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify310.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
395×	`sub-neg_binary64`
340×	`times-frac_binary64`
306×	`div-sub_binary64`
297×	`associate-l_binary64`

Counts

361 → 324

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	183	11806
1	380	6831
2	1040	5351
3	3726	5350
4	4176	5350
5	4425	5342
6	4803	5342

prune362.0ms (8.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	322	3	325

Error

0.2b

Counts

325 → 3

Alt Table

Status	Error	Program
✓	14.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	33.9b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
▶	0.3b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11320 to 8621 computations (23.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -1 (fma.f64 x x x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify117.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
327×	`distribute-rgt-out_binary64`
306×	`unswap-sqr_binary64`
201×	`sub-neg_binary64`
188×	`cancel-sign-sub-inv_binary64`

Counts

41 → 52

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	78	654
1	148	618
2	308	611
3	680	611
4	2297	611
5	4211	603
6	4978	603
7	4914	603

prune55.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	6	55

Error

0.2b

Counts

55 → 6

Alt Table

Status	Error	Program
✓	14.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	33.9b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
	18.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.3b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

Compiler

Compiled 826 to 448 computations (45.8% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 -1 (fma.f64 x x x))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	13.6b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

series79.0ms (1.9%)

Counts

3 → 36

Calls

3 calls:

38.0ms

(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

27.0ms

(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

14.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

11.0ms

(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

2.0ms

(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

simplify164.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-neg_binary64`
406×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`
226×	`associate-/l*_binary64`
221×	`associate-l_binary64`

Counts

196 → 275

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5284
1	587	5046
2	1739	4578
3	4554	4570
4	5027	4570

prune524.0ms (12.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	524	3	527
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	525	8	533

Error

0.2b

Counts

533 → 8

Alt Table

Status	Error	Program
✓	14.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	33.9b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
	40.2b	(.f64 (.f64 (pow.f64 (cbrt.f64 -1) 2) (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
	18.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.3b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
▶	1.3b	(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)
	1.5b	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) 6))) (cbrt.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

Compiler

Compiled 16719 to 9283 computations (44.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(/.f64 -1 (fma.f64 x x x))
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)
	13.6b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

series57.0ms (1.4%)

Counts

1 → 12

Calls

1 calls:

57.0ms

(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 calls:

4.0ms

(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-/l/_binary64`
383×	`associate-l_binary64`
299×	`associate-r_binary64`
242×	`log-prod_binary64`
206×	`exp-prod_binary64`

Counts

65 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1141
1	311	1046
2	737	1034
3	2622	1034
4	4883	1034

prune213.0ms (5.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	171	8	179

Error

0.2b

Counts

179 → 8

Alt Table

Status	Error	Program
✓	14.7b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	33.9b	(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
	40.2b	(.f64 (.f64 (pow.f64 (cbrt.f64 -1) 2) (cbrt.f64 (/.f64 1 (pow.f64 x 4)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
	18.4b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.3b	(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
✓	1.3b	(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)
	1.5b	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) 6))) (cbrt.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))

Compiler

Compiled 3010 to 1919 computations (36.2% saved)

regimes421.0ms (10%)

Accuracy

Total 0.1b remaining (16%)

Threshold costs 0.1b (16%)

Counts

88 → 1

Compiler

Compiled 6073 to 4145 computations (31.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end216.0ms (5.1%)

Compiler: Compiled 156 to 98 computations (37.2% saved)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13

Details

analyze6.0ms (0.1%)

sample1.4s (33.1%)

simplify13.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite77.0ms (1.8%)

simplify310.0ms (7.4%)

prune362.0ms (8.6%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify117.0ms (2.8%)

prune55.0ms (1.3%)

localize7.0ms (0.2%)

series79.0ms (1.9%)

rewrite41.0ms (1%)

simplify164.0ms (3.9%)

prune524.0ms (12.5%)

localize6.0ms (0.1%)

series57.0ms (1.4%)

rewrite7.0ms (0.2%)

simplify110.0ms (2.6%)

prune213.0ms (5.1%)

regimes421.0ms (10%)

simplify4.0ms (0.1%)

end216.0ms (5.1%)

Profiling

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	26	13
4	34	13
5	52	13
6	77	13
7	94	13
8	111	13
9	121	13
10	125	13
11	127	13
12	113	13