Details

analyze5.0ms (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 (36.3%)

Results

432.0ms	2090×	body	512	valid
390.0ms	4676×	body	128	valid
143.0ms	1017×	body	256	valid
129.0ms	473×	body	1024	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify13.0ms (0.4%)

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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	3.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite66.0ms (2.1%)

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))

simplify283.0ms (9.1%)

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

prune347.0ms (11.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	2	325

Error

0.4b

Counts

325 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 -1 (fma.f64 x x x))
	31.3b	(-.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))

Compiler

Compiled 11298 to 8603 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.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))

rewrite40.0ms (1.3%)

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 (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

prune33.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	48	6	54

Error

0.2b

Counts

54 → 6

Alt Table

Status	Error	Program
▶	1.5b	(/.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)))
	30.7b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
	15.7b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
✓	0.4b	(/.f64 -1 (fma.f64 x x x))
	15.6b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	33.2b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 x x x)) 3))

Compiler

Compiled 800 to 420 computations (47.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
✓	0.7b	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
✓	15.0b	(cbrt.f64 (fma.f64 x x x))

series26.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
8.0ms	(cbrt.f64 (fma.f64 x x x))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
3.0ms	(/.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)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

6.0ms	(/.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)))
5.0ms	(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
1.0ms	(cbrt.f64 (fma.f64 x x x))

simplify147.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
574×	`times-frac_binary64`
403×	`associate-l_binary64`
354×	`associate-/l/_binary64`
292×	`associate-/r/_binary64`

Counts

200 → 298

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5328
1	613	4956
2	1628	4414
3	4604	4414
4	5054	4414

prune221.0ms (7.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	360	2	362
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	361	7	368

Error

0.2b

Counts

368 → 7

Alt Table

Status	Error	Program
✓	1.5b	(/.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)))
	16.1b	(/.f64 (/.f64 -1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))))
✓	0.4b	(/.f64 -1 (fma.f64 x x x))
	16.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 -1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))) (cbrt.f64 (/.f64 -1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))) (/.f64 (cbrt.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))))
	30.7b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
▶	15.7b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
	33.2b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 x x x)) 3))

Compiler

Compiled 9969 to 3402 computations (65.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (sqrt.f64 (fma.f64 x x x)))
✓	0.1b	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
✓	14.2b	(sqrt.f64 (fma.f64 x x x))

series20.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

7.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
5.0ms	(/.f64 1 (sqrt.f64 (fma.f64 x x x)))
5.0ms	(sqrt.f64 (fma.f64 x x x))
3.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
94×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`
56×	`sqrt-prod_binary64`

Counts

4 → 188

Calls

4 calls:

13.0ms	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
3.0ms	(/.f64 1 (sqrt.f64 (fma.f64 x x x)))
3.0ms	(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
1.0ms	(sqrt.f64 (fma.f64 x x x))

simplify143.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

621×	`div-sub_binary64`
451×	`fma-def_binary64`
317×	`associate-/l*_binary64`
216×	`sub-neg_binary64`
215×	`associate-l_binary64`

Counts

224 → 304

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	189	4732
1	454	3990
2	1145	3747
3	2923	3507
4	4341	3447
5	5110	3447

prune218.0ms (7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	342	7	349

Error

0.2b

Counts

349 → 7

Alt Table

Status	Error	Program
✓	1.5b	(/.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)))
	16.1b	(/.f64 (/.f64 -1 (.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))))
	30.7b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓	15.7b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
✓	0.4b	(/.f64 -1 (fma.f64 x x x))
	33.2b	(cbrt.f64 (pow.f64 (/.f64 -1 (fma.f64 x x x)) 3))
	15.8b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x)))))

Compiler

Compiled 7571 to 3137 computations (58.6% saved)

regimes157.0ms (5.1%)

Accuracy

Total 0.2b remaining (58.5%)

Threshold costs 0.2b (58.5%)

Counts

86 → 1

Compiler

Compiled 3144 to 1778 computations (43.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end77.0ms (2.5%)

Compiler: Compiled 135 to 64 computations (52.6% 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

analyze5.0ms (0.2%)

sample1.1s (36.3%)

simplify13.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite66.0ms (2.1%)

simplify283.0ms (9.1%)

prune347.0ms (11.2%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite40.0ms (1.3%)

simplify79.0ms (2.6%)

prune33.0ms (1.1%)

localize7.0ms (0.2%)

series26.0ms (0.8%)

rewrite29.0ms (0.9%)

simplify147.0ms (4.7%)

prune221.0ms (7.1%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite35.0ms (1.1%)

simplify143.0ms (4.6%)

prune218.0ms (7%)

regimes157.0ms (5.1%)

simplify2.0ms (0.1%)

end77.0ms (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