Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample1.1s (34.3%)

Results

417.0ms	2098×	body	512	valid
387.0ms	4696×	body	128	valid
145.0ms	1021×	body	256	valid
113.0ms	441×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify10.0ms (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 (0.1%)

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

14.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.3b	(-.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))
✓	2.8b	(-.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))

rewrite69.0ms (2.2%)

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:

19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify280.0ms (8.7%)

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

prune251.0ms (7.8%)

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

0.3b

Counts

325 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11262 to 8573 computations (23.9% 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))

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(/.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))

simplify83.0ms (2.6%)

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

prune85.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	5	53

Error

0.1b

Counts

53 → 5

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 -1 (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)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	15.5b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	29.8b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 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 800 to 420 computations (47.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))
	0.3b	(/.f64 -1 (fma.f64 x x x))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	13.7b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

series62.0ms (1.9%)

Counts

3 → 36

Calls

3 calls:

31.0ms

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

21.0ms

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

9.0ms

(*.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))))

rewrite43.0ms (1.3%)

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))))

10.0ms

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

3.0ms

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

simplify175.0ms (5.5%)

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

prune459.0ms (14.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	526	1	527
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	526	6	532

Error

0.1b

Counts

532 → 6

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (/.f64 (cbrt.f64 -1) (cbrt.f64 (fma.f64 x x x))))
✓	0.3b	(/.f64 -1 (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)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	15.5b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	29.8b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 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 16633 to 9206 computations (44.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 -1 (fma.f64 x x x))
	0.4b	(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
	13.7b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))
✓	14.0b	(cbrt.f64 (fma.f64 x x x))

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

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

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary64`
677×	`unswap-sqr_binary64`
590×	`cancel-sign-sub-inv_binary64`
485×	`fma-def_binary64`
305×	`*-commutative_binary64`

Counts

25 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	399
1	135	393
2	280	379
3	673	379
4	1723	379
5	2887	379
6	4943	379
7	4951	379

prune284.0ms (8.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	368	0	368
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	368	6	374

Error

0.1b

Counts

374 → 6

Alt Table

Status	Error	Program
✓	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (/.f64 (cbrt.f64 -1) (cbrt.f64 (fma.f64 x x x))))
✓	0.3b	(/.f64 -1 (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)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	15.5b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	29.8b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 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 12524 to 6798 computations (45.7% saved)

regimes102.0ms (3.2%)

Accuracy

Total 0.2b remaining (60.5%)

Threshold costs 0.2b (60.5%)

Counts

53 → 1

Compiler

Compiled 1820 to 1158 computations (36.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end79.0ms (2.5%)

Compiler: Compiled 120 to 62 computations (48.3% 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 (0.2%)

sample1.1s (34.3%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite69.0ms (2.2%)

simplify280.0ms (8.7%)

prune251.0ms (7.8%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify83.0ms (2.6%)

prune85.0ms (2.7%)

localize7.0ms (0.2%)

series62.0ms (1.9%)

rewrite43.0ms (1.3%)

simplify175.0ms (5.5%)

prune459.0ms (14.4%)

localize10.0ms (0.3%)

series5.0ms (0.1%)

rewrite1.0ms (0%)

simplify68.0ms (2.1%)

prune284.0ms (8.9%)

regimes102.0ms (3.2%)

simplify2.0ms (0.1%)

end79.0ms (2.5%)

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