Details

analyze611.0ms (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample53.0ms (0.9%)

Algorithm

1×

intervals

Symmetry

(sort V l)

Results

14.0ms	256×	body	128	valid
5.0ms	100×	body	128	nan
1.0ms	19×	body	128	invalid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	15	12
3	15	12

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.5b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.7b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	4.2b	(/.f64 A (*.f64 V l))
✓	15.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series123.0ms (2.1%)

Counts

3 → 12

Calls

3 calls:

66.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
39.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
3.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
3.0ms	(/.f64 A (*.f64 V l))

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
679×	`associate-/r/_binary64`
449×	`div-sub_binary64`
262×	`times-frac_binary64`
261×	`sub-neg_binary64`

Counts

84 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1084
1	194	1009
2	561	1009
3	1631	1009
4	2187	1009
5	2446	1009
6	3196	1009
7	4340	1009
8	4698	1009

prune91.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	71	15	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	15	87

Error

8.3b

Counts

87 → 15

Alt Table

Status	Error	Program
	51.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
▶	17.7b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	18.2b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	17.9b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (*.f64 V l) (cbrt.f64 A)))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	17.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
	17.9b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	18.2b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.4b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	51.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	51.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))

Compiler

Compiled 1722 to 627 computations (63.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
✓	2.3b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	4.2b	(/.f64 A (*.f64 V l))
	15.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series598.0ms (10.4%)

Counts

2 → 36

Calls

2 calls:

533.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
64.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`sqrt-prod_binary64`
13×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`sqrt-div_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 59

Calls

2 calls:

13.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
3.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
461×	`unswap-sqr_binary64`
396×	`fma-def_binary64`
254×	`sqr-pow_binary64`
246×	`div-sub_binary64`

Counts

95 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1643
1	254	1503
2	586	1503
3	911	1359
4	1414	1359
5	2651	1359
6	4575	1359
7	4992	1359

prune160.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	211	14	225

Error

8.3b

Counts

225 → 14

Alt Table

Status	Error	Program
▶	17.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (pow.f64 (/.f64 A (.f64 V l)) 1/4))
	17.9b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (*.f64 V l) (cbrt.f64 A)))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	17.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
	17.9b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	51.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
	18.2b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.4b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	51.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	51.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))

Compiler

Compiled 5234 to 1146 computations (78.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.3b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	4.2b	(/.f64 A (*.f64 V l))
	15.6b	(sqrt.f64 (/.f64 A (*.f64 V l)))
✓	18.1b	(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

series759.0ms (13.2%)

Counts

1 → 36

Calls

1 calls:

759.0ms

(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64`
7×	`unpow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

539×	`fma-neg_binary64`
492×	`log-prod_binary64`
258×	`exp-prod_binary64`
251×	`*-commutative_binary64`
234×	`unswap-sqr_binary64`

Counts

61 → 43

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	115	972
1	228	864
2	446	840
3	1368	786
4	3670	770
5	4961	770
6	4931	770

prune137.0ms (2.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	149	14	163

Error

8.3b

Counts

163 → 14

Alt Table

Status	Error	Program
✓	17.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (pow.f64 (/.f64 A (.f64 V l)) 1/4))
	17.9b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (*.f64 V l) (cbrt.f64 A)))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
▶	17.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
	17.9b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	51.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
	18.2b	(.f64 (.f64 c0 (.f64 (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))) (cbrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.4b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (/.f64 A (*.f64 V l)))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	51.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	51.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))

Compiler

Compiled 3792 to 1324 computations (65.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (*.f64 V l))
✓	1.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
✓	4.4b	(.f64 A (/.f64 1 (.f64 V l)))
✓	15.6b	(sqrt.f64 (.f64 A (/.f64 1 (.f64 V l))))

series126.0ms (2.2%)

Counts

4 → 48

Calls

4 calls:

65.0ms	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
37.0ms	(sqrt.f64 (.f64 A (/.f64 1 (.f64 V l))))
16.0ms	(.f64 A (/.f64 1 (.f64 V l)))
8.0ms	(/.f64 1 (*.f64 V l))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`prod-exp_binary64`
14×	`pow1_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(.f64 A (/.f64 1 (.f64 V l)))
7.0ms	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
4.0ms	(sqrt.f64 (.f64 A (/.f64 1 (.f64 V l))))
3.0ms	(/.f64 1 (*.f64 V l))

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
570×	`fma-def_binary64`
398×	`times-frac_binary64`
318×	`sqr-pow_binary64`
313×	`associate-*l/_binary64`

Counts

150 → 136

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	117	1514
1	226	1373
2	676	1373
3	2144	1373
4	2354	1373
5	2690	1373
6	3216	1373
7	4110	1373
8	4861	1373
9	5108	1373

prune120.0ms (2.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	136	14	150

Error

8.3b

Counts

150 → 14

Alt Table

Status	Error	Program
✓	17.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (pow.f64 (/.f64 A (.f64 V l)) 1/4))
	17.9b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 (*.f64 V l) (cbrt.f64 A)))))
	38.2b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
✓	17.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 1 (*.f64 V l)))))
	17.9b	(.f64 (.f64 c0 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))
	51.0b	(.f64 c0 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 A) V)) (sqrt.f64 (/.f64 (sqrt.f64 A) l))))
	17.7b	(.f64 c0 (sqrt.f64 (.f64 A (/.f64 (/.f64 1 V) l))))
	39.6b	(.f64 (sqrt.f64 c0) (.f64 (sqrt.f64 c0) (sqrt.f64 (.f64 A (/.f64 1 (.f64 V l))))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
	38.2b	(.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (/.f64 1 (*.f64 V l))))
	19.3b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V) (/.f64 (cbrt.f64 A) l))))
	51.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	51.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	50.3b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) V))) (sqrt.f64 (/.f64 (cbrt.f64 A) l)))

Compiler

Compiled 2271 to 1130 computations (50.2% saved)

regimes1.1s (18.6%)

Accuracy

Total 4.6b remaining (33.6%)

Threshold costs 0b (0%)

Counts

69 → 3

Compiler

Compiled 12198 to 7374 computations (39.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	62
1	34	62
2	33	62

end7.0ms (0.1%)

Compiler: Compiled 135 to 78 computations (42.2% saved)

sample1.4s (24.4%)

Algorithm

1×

intervals

Results

414.0ms	8000×	body	128	valid
139.0ms	2915×	body	128	nan
40.0ms	843×	body	128	invalid

Compiler

Compiled 299 to 191 computations (36.1% saved)

Details

analyze611.0ms (10.6%)

sample53.0ms (0.9%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series123.0ms (2.1%)

rewrite15.0ms (0.3%)

simplify92.0ms (1.6%)

prune91.0ms (1.6%)

localize8.0ms (0.1%)

series598.0ms (10.4%)

rewrite20.0ms (0.3%)

simplify94.0ms (1.6%)

prune160.0ms (2.8%)

localize12.0ms (0.2%)

series759.0ms (13.2%)

rewrite5.0ms (0.1%)

simplify72.0ms (1.2%)

prune137.0ms (2.4%)

localize8.0ms (0.1%)

series126.0ms (2.2%)

rewrite25.0ms (0.4%)

simplify123.0ms (2.1%)

prune120.0ms (2.1%)

regimes1.1s (18.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end7.0ms (0.1%)

sample1.4s (24.4%)

Profiling