Details

analyze127.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample51.0ms (1.8%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true
0.0ms	8×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify83.0ms (3%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

15.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.3b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
▶	15.3b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

Compiler

Compiled 79 to 45 computations (43% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
✓	0.0b	(-.f64 (.f64 a a) (.f64 b b))
✓	14.9b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series61.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
26.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
9.0ms	(-.f64 (.f64 a a) (.f64 b b))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
11×	`times-frac_binary64`
10×	`fabs-mul_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 75

Calls

3 calls:

7.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
7.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
3.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify128.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
330×	`associate-l_binary64`
306×	`associate-/l*_binary64`
296×	`fma-neg_binary64`
282×	`associate-r_binary64`

Counts

147 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2391
1	285	2222
2	879	2113
3	3871	2101
4	4888	2101
5	4981	2101

prune75.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
	0.1b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 2456 to 686 computations (72.1% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

series10.0ms (0.4%)

Counts

1 → 0

Calls

1 calls:

10.0ms

(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary64`
7×	`add-sqr-sqrt_binary64`
4×	`fabs-mul_binary64`
3×	`rem-sqrt-square_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

simplify132.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

623×	`div-sub_binary64`
521×	`fma-def_binary64`
500×	`unsub-neg_binary64`
476×	`distribute-neg-in_binary64`
362×	`unswap-sqr_binary64`

Counts

21 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	397
1	44	370
2	56	370
3	72	370
4	105	370
5	160	370
6	263	370
7	535	370
8	1105	370
9	2806	370
10	3741	370
11	4491	370
12	4947	370
13	4784	370

prune20.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	23	2	25

Error

Counts

25 → 2

Alt Table

Status	Error	Program
▶	0.1b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 459 to 229 computations (50.1% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
✓	0.1b	(*.f64 b (/.f64 b a))
✓	0.2b	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))

series54.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
19.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
13.0ms	(*.f64 b (/.f64 b a))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
17×	`add-exp-log_binary64`

Counts

3 → 106

Calls

3 calls:

8.0ms	(.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))
5.0ms	(*.f64 b (/.f64 b a))
2.0ms	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))

simplify153.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
468×	`associate-/l*_binary64`
386×	`associate-/r*_binary64`
350×	`associate-*l/_binary64`
276×	`associate-*r/_binary64`

Counts

178 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	2827
1	445	2609
2	1260	2413
3	3713	2403
4	4991	2403

prune198.0ms (7.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	173	2	175

Error

Counts

175 → 2

Alt Table

Status	Error	Program
✓	0.1b	(sqrt.f64 (fabs.f64 (.f64 (/.f64 1 a) (-.f64 a (.f64 b (/.f64 b a))))))
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) -1)))

Compiler

Compiled 3617 to 1538 computations (57.5% saved)

regimes154.0ms (5.6%)

Accuracy

Total 0.0b remaining (35.4%)

Threshold costs 0.0b (35.4%)

Counts

8 → 1

Compiler

Compiled 1065 to 655 computations (38.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	8	15

end1.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample1.4s (51.7%)

Algorithm

1×

intervals

Results

643.0ms	8000×	body	128	valid
281.0ms	8000×	pre	128	true
13.0ms	368×	pre	128	false

Compiler

Compiled 67 to 41 computations (38.8% saved)

Details

analyze127.0ms (4.6%)

sample51.0ms (1.8%)

simplify83.0ms (3%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series61.0ms (2.2%)

rewrite22.0ms (0.8%)

simplify128.0ms (4.7%)

prune75.0ms (2.7%)

localize7.0ms (0.3%)

series10.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify132.0ms (4.8%)

prune20.0ms (0.7%)

localize10.0ms (0.4%)

series54.0ms (1.9%)

rewrite21.0ms (0.8%)

simplify153.0ms (5.6%)

prune198.0ms (7.2%)

regimes154.0ms (5.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.4s (51.7%)

Profiling