Details

analyze1.3s (26.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.3s (26.3%)

Results

482.0ms	2108×	body	512	valid
434.0ms	4610×	body	128	valid
226.0ms	1077×	body	256	valid
138.0ms	461×	body	1024	valid

Compiler

Compiled 21 to 17 computations (19% saved)

simplify11.0ms (0.2%)

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

prune10.0ms (0.2%)

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

16.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.0b	(-.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))
✓	4.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite80.0ms (1.6%)

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:

24.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify301.0ms (6%)

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

prune281.0ms (5.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	323	1	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	324	1	325

Error

0.1b

Counts

325 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11262 to 8573 computations (23.9% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.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))

rewrite4.0ms (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))

simplify79.0ms (1.6%)

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

prune33.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Error

0.0b

Counts

53 → 6

Alt Table

Status	Error	Program
▶	1.1b	(.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))))
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
	11.8b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.1b	(/.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)))
	29.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
	31.9b	(cbrt.f64 (/.f64 (.f64 (.f64 -1 -1) -1) (.f64 (.f64 (fma.f64 x x x) (fma.f64 x x x)) (fma.f64 x x x))))

Compiler

Compiled 840 to 438 computations (47.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.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))))
✓	14.3b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

series78.0ms (1.6%)

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))))

28.0ms

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

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))))

rewrite45.0ms (0.9%)

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)))

simplify151.0ms (3%)

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

prune439.0ms (8.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	525	2	527
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	527	6	533

Error

0.0b

Counts

533 → 6

Alt Table

Status	Error	Program
	11.8b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
▶	1.0b	(/.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
	1.1b	(/.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)))
	29.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))

Compiler

Compiled 16625 to 9203 computations (44.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
	14.3b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))
✓	14.5b	(cbrt.f64 (fma.f64 x x x))

series45.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

22.0ms

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

11.0ms

(cbrt.f64 (fma.f64 x x x))

11.0ms

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
16×	`associate-r_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 84

Calls

3 calls:

10.0ms

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

9.0ms

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

1.0ms

(cbrt.f64 (fma.f64 x x x))

simplify124.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
423×	`associate-*l/_binary64`
409×	`associate-/l/_binary64`
299×	`*-commutative_binary64`
269×	`associate-/r*_binary64`

Counts

120 → 166

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	205	3474
1	510	3117
2	1681	3039
3	4110	2963
4	4812	2955
5	5042	2955

prune214.0ms (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	262	6	268

Error

0.0b

Counts

268 → 6

Alt Table

Status	Error	Program
	11.8b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	1.0b	(pow.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) 3)
	29.3b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
	0.9b	(/.f64 (*.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (/.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))))
✓	0.1b	(/.f64 -1 (fma.f64 x x x))
	1.0b	(/.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))))

Compiler

Compiled 8403 to 4537 computations (46% saved)

regimes345.0ms (6.9%)

Accuracy

Total 0.3b remaining (59.3%)

Threshold costs 0.3b (59.3%)

Counts

150 → 1

Compiler

Compiled 7958 to 5008 computations (37.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end87.0ms (1.7%)

Compiler: Compiled 122 to 64 computations (47.5% 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

analyze1.3s (26.2%)

sample1.3s (26.3%)

simplify11.0ms (0.2%)

prune10.0ms (0.2%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite80.0ms (1.6%)

simplify301.0ms (6%)

prune281.0ms (5.6%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify79.0ms (1.6%)

prune33.0ms (0.7%)

localize7.0ms (0.1%)

series78.0ms (1.6%)

rewrite45.0ms (0.9%)

simplify151.0ms (3%)

prune439.0ms (8.7%)

localize10.0ms (0.2%)

series45.0ms (0.9%)

rewrite28.0ms (0.5%)

simplify124.0ms (2.5%)

prune214.0ms (4.2%)

regimes345.0ms (6.9%)

simplify2.0ms (0%)

end87.0ms (1.7%)

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