Details

analyze7.0ms (0.3%)

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)

sample87.0ms (3.1%)

Algorithm

1×

intervals

Results

55.0ms	67×	body	512	valid
5.0ms	146×	body	128	valid
2.0ms	37×	body	256	valid
1.0ms	6×	body	1024	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify11.0ms (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

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)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite65.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

363×	`times-frac_binary64`
359×	`*-un-lft-identity_binary64`
274×	`add-sqr-sqrt_binary64`
250×	`add-cube-cbrt_binary64`
234×	`prod-diff_binary64`

Counts

1 → 298

Calls

1 calls:

19.0ms

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

simplify335.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-neg_binary64`
827×	`difference-of-squares_binary64`
554×	`fma-def_binary64`
331×	`times-frac_binary64`
287×	`sub-neg_binary64`

Counts

310 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	11244
1	328	6283
2	864	4815
3	2970	4806
4	4001	4806
5	4733	4806
6	4847	4806
7	4992	4806
8	4786	4806

prune384.0ms (13.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	2	270

Error

0.3b

Counts

270 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 -1 (fma.f64 x x x))
	33.0b	(fma.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) -1) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 10475 to 7946 computations (24.1% 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))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(/.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 (3%)

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

prune39.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Error

0.0b

Counts

54 → 7

Alt Table

Status	Error	Program
	17.3b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	33.0b	(fma.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) -1) (/.f64 -1 (pow.f64 x 4)))
	33.6b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
▶	1.2b	(.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))))
	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))))
	17.4b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x x))) (/.f64 -1 (sqrt.f64 (fma.f64 x x x))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))

Compiler

Compiled 866 to 462 computations (46.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓	0.4b	(*.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))))
✓	14.5b	(cbrt.f64 (fma.f64 x x x))

series31.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
8.0ms	(cbrt.f64 (fma.f64 x x x))
7.0ms	(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
7.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.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)))
3.0ms	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
1.0ms	(cbrt.f64 (fma.f64 x x x))

simplify116.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-neg_binary64`
425×	`times-frac_binary64`
417×	`fma-def_binary64`
319×	`associate-l_binary64`
275×	`associate-r_binary64`

Counts

181 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	3541
1	538	3241
2	1337	2998
3	4033	2987
4	4905	2987

prune222.0ms (7.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	299	4	303
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	301	9	310

Error

Counts

310 → 9

Alt Table

Status	Error	Program
	17.3b	(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
	33.0b	(fma.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 x) -1) (/.f64 -1 (pow.f64 x 4)))
	33.6b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓	1.2b	(.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))))
	1.5b	(.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 (/.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))))
▶	1.2b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -2) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	40.0b	(*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
✓	0.3b	(/.f64 -1 (fma.f64 x x x))
	24.3b	(.f64 (/.f64 1 (cbrt.f64 (.f64 (fma.f64 x x x) (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))

Compiler

Compiled 8788 to 3482 computations (60.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -2) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	0.3b	(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x x x)) -2)
	14.5b	(cbrt.f64 (fma.f64 x x x))

series20.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x x)) -2)
6.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -2) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
22×	`associate-r_binary64`
22×	`cbrt-prod_binary64`
21×	`*-un-lft-identity_binary64`

Counts

2 → 86

Calls

2 calls:

10.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -2) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
2.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x x)) -2)

simplify95.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-*l/_binary64`
385×	`associate-/l*_binary64`
375×	`associate-*r/_binary64`
359×	`fma-def_binary64`
286×	`times-frac_binary64`

Counts

110 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	2763
1	463	2482
2	1397	2262
3	4197	2230
4	4917	2230

prune226.0ms (8.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	295	7	302

Error

Counts

302 → 7

Alt Table

Status	Error	Program
	33.6b	(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓	1.2b	(.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))))
	1.5b	(.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 (/.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))))
	40.0b	(*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
	1.1b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x x)) -2) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
✓	0.3b	(/.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 7034 to 3240 computations (53.9% saved)

regimes253.0ms (9%)

Accuracy

Total 0.2b remaining (51.7%)

Threshold costs 0.2b (51.7%)

Counts

90 → 1

Compiler

Compiled 3468 to 2444 computations (29.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

sample741.0ms (26.4%)

Algorithm

1×

intervals

Results

193.0ms	2078×	body	512	valid
158.0ms	4471×	body	128	valid
73.0ms	1043×	body	256	valid
48.0ms	408×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 160 to 79 computations (50.6% 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

analyze7.0ms (0.3%)

sample87.0ms (3.1%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite65.0ms (2.3%)

simplify335.0ms (11.9%)

prune384.0ms (13.7%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify83.0ms (3%)

prune39.0ms (1.4%)

localize8.0ms (0.3%)

series31.0ms (1.1%)

rewrite30.0ms (1.1%)

simplify116.0ms (4.2%)

prune222.0ms (7.9%)

localize7.0ms (0.2%)

series20.0ms (0.7%)

rewrite20.0ms (0.7%)

simplify95.0ms (3.4%)

prune226.0ms (8.1%)

regimes253.0ms (9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample741.0ms (26.4%)

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