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 (30.8%)

Results

416.0ms	2070×	body	512	valid
387.0ms	4672×	body	128	valid
157.0ms	1095×	body	256	valid
108.0ms	419×	body	1024	valid

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

13.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.1b	(-.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))

rewrite69.0ms (1.9%)

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))

simplify337.0ms (9.4%)

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

prune331.0ms (9.3%)

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

0.2b

Counts

325 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 11262 to 8573 computations (23.9% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.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))

simplify80.0ms (2.2%)

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 (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Error

0.2b

Counts

53 → 3

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)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))
	17.3b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))

Compiler

Compiled 728 to 386 computations (47% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.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))))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	15.0b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))

series77.0ms (2.2%)

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))))

26.0ms

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

12.0ms

(*.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))))

rewrite40.0ms (1.1%)

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:

12.0ms

(*.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)))

simplify200.0ms (5.6%)

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

prune371.0ms (10.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	524	3	527
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	525	5	530

Error

0.1b

Counts

530 → 5

Alt Table

Status	Error	Program
▶	1.0b	(.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))))
	40.9b	(.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))))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 -1)) (cbrt.f64 -1)) (.f64 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))
	17.3b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))

Compiler

Compiled 16631 to 9219 computations (44.6% saved)

localize67.0ms (1.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
	0.4b	(*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
	15.0b	(cbrt.f64 (/.f64 -1 (fma.f64 x x x)))
✓	15.2b	(cbrt.f64 (fma.f64 x x x))

series16.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(.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))))
6.0ms	(cbrt.f64 (fma.f64 x x x))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod_binary64`
40×	`associate-r_binary64`
40×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`

Counts

2 → 87

Calls

2 calls:

15.0ms	(.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))))
1.0ms	(cbrt.f64 (fma.f64 x x x))

simplify186.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
518×	`associate-/l*_binary64`
332×	`associate-*r/_binary64`
320×	`associate-*l/_binary64`
289×	`times-frac_binary64`

Counts

111 → 162

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	185	4125
1	500	3707
2	1506	3578
3	3890	2733
4	4179	2360
5	4667	2360
6	4999	2360
7	5000	2360
8	4885	2360

prune292.0ms (8.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	395	0	395
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	395	5	400

Error

0.1b

Counts

400 → 5

Alt Table

Status	Error	Program
✓	1.0b	(.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))))
	40.9b	(.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))))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 -1) (cbrt.f64 -1)) (cbrt.f64 -1)) (.f64 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))))
✓	0.2b	(/.f64 -1 (fma.f64 x x x))
	17.3b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))

Compiler

Compiled 13277 to 7051 computations (46.9% saved)

regimes222.0ms (6.2%)

Accuracy

Total 0.1b remaining (15.3%)

Threshold costs 0.1b (15.3%)

Counts

99 → 1

Compiler

Compiled 4956 to 3726 computations (24.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end72.0ms (2%)

Compiler: Compiled 107 to 62 computations (42.1% 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 (30.8%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite69.0ms (1.9%)

simplify337.0ms (9.4%)

prune331.0ms (9.3%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify80.0ms (2.2%)

prune33.0ms (0.9%)

localize7.0ms (0.2%)

series77.0ms (2.2%)

rewrite40.0ms (1.1%)

simplify200.0ms (5.6%)

prune371.0ms (10.4%)

localize67.0ms (1.9%)

series16.0ms (0.5%)

rewrite26.0ms (0.7%)

simplify186.0ms (5.2%)

prune292.0ms (8.2%)

regimes222.0ms (6.2%)

simplify2.0ms (0%)

end72.0ms (2%)

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