Details

analyze641.0ms (9.7%)

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)

sample54.0ms (0.8%)

Algorithm

1×

intervals

Symmetry

(sort V l)

Results

12.0ms	256×	body	128	valid
5.0ms	111×	body	128	nan
1.0ms	31×	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

prune2.0ms (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

17.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.2b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
✓	5.3b	(/.f64 A (*.f64 V l))
✓	14.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series121.0ms (1.8%)

Counts

3 → 12

Calls

3 calls:

65.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
38.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
17.0ms	(/.f64 A (*.f64 V l))

rewrite14.0ms (0.2%)

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

simplify94.0ms (1.4%)

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

prune86.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	72	14	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	14	87

Error

8.5b

Counts

87 → 14

Alt Table

Status	Error	Program
	49.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	17.8b	(.f64 c0 (.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l))))))
	50.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	18.9b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
▶	17.6b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	39.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	18.1b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	17.7b	(.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 (.f64 V l) A))))
	29.1b	(.f64 c0 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) (sqrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (/.f64 A (.f64 V l))))))
	40.1b	(/.f64 (.f64 c0 (sqrt.f64 A)) (sqrt.f64 (.f64 V l)))
	35.4b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
	39.1b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 3))
	18.1b	(.f64 c0 (.f64 (.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))))))
	18.1b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))

Compiler

Compiled 1690 to 593 computations (64.9% saved)

localize10.0ms (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)))))
✓	1.5b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	5.3b	(/.f64 A (*.f64 V l))
	14.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))

series675.0ms (10.2%)

Counts

2 → 36

Calls

2 calls:

600.0ms	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
74.0ms	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))

rewrite22.0ms (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:

14.0ms	(.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))))

simplify99.0ms (1.5%)

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

prune196.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	205	5	210
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	211	13	224

Error

8.5b

Counts

224 → 13

Alt Table

Status	Error	Program
	39.1b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 3))
	17.7b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))))
	50.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	18.9b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
▶	17.5b	(.f64 (.f64 c0 (pow.f64 (/.f64 A (.f64 V l)) 1/4)) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	18.1b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	19.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))))
	35.4b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
	40.2b	(/.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (sqrt.f64 A))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 V l))) (sqrt.f64 (sqrt.f64 (*.f64 V l)))))
	34.2b	(.f64 (.f64 c0 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	49.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	39.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	18.1b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))

Compiler

Compiled 5246 to 1154 computations (78% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.5b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	5.3b	(/.f64 A (*.f64 V l))
	14.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))
✓	15.6b	(pow.f64 (/.f64 A (*.f64 V l)) 1/4)

series802.0ms (12.1%)

Counts

1 → 36

Calls

1 calls:

802.0ms

(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)

simplify81.0ms (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

prune151.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	149	13	162

Error

8.5b

Counts

162 → 13

Alt Table

Status	Error	Program
	39.1b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 3))
▶	17.7b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))))
	50.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	18.9b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
✓	17.5b	(.f64 (.f64 c0 (pow.f64 (/.f64 A (.f64 V l)) 1/4)) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	18.1b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	19.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))))
	35.4b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
	40.2b	(/.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (sqrt.f64 A))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 V l))) (sqrt.f64 (sqrt.f64 (*.f64 V l)))))
	34.2b	(.f64 (.f64 c0 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	49.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	39.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	18.1b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))

Compiler

Compiled 3804 to 1400 computations (63.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.5b	(sqrt.f64 (sqrt.f64 (/.f64 A (*.f64 V l))))
	5.3b	(/.f64 A (*.f64 V l))
	14.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))
✓	15.9b	(cbrt.f64 (/.f64 A (*.f64 V l)))

series762.0ms (11.5%)

Counts

1 → 36

Calls

1 calls:

762.0ms

(cbrt.f64 (/.f64 A (*.f64 V l)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(cbrt.f64 (/.f64 A (*.f64 V l)))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
526×	`fma-def_binary64`
338×	`exp-sum_binary64`
300×	`div-sub_binary64`
254×	`distribute-rgt-in_binary64`

Counts

54 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	996
1	163	946
2	284	909
3	738	695
4	1695	633
5	4242	633
6	4947	633

prune163.0ms (2.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	200	13	213

Error

8.5b

Counts

213 → 13

Alt Table

Status	Error	Program
	39.1b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 A (.f64 V l))) c0) 3))
✓	17.7b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 A (.f64 V l)))) (sqrt.f64 (cbrt.f64 (/.f64 A (.f64 V l)))))))
	50.2b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 (sqrt.f64 A) V))) (sqrt.f64 (/.f64 (sqrt.f64 A) l)))
	18.9b	(*.f64 c0 (sqrt.f64 (/.f64 (/.f64 A V) l)))
✓	17.5b	(.f64 (.f64 c0 (pow.f64 (/.f64 A (.f64 V l)) 1/4)) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	18.1b	(.f64 (.f64 (cbrt.f64 c0) (cbrt.f64 c0)) (.f64 (cbrt.f64 c0) (sqrt.f64 (/.f64 A (.f64 V l)))))
	19.1b	(.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))))
	35.4b	(.f64 (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))) (sqrt.f64 (.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))))
	40.2b	(/.f64 (.f64 (.f64 c0 (sqrt.f64 (sqrt.f64 A))) (sqrt.f64 (sqrt.f64 A))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 V l))) (sqrt.f64 (sqrt.f64 (*.f64 V l)))))
	34.2b	(.f64 (.f64 c0 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (/.f64 A V)) (log.f64 l))))) (sqrt.f64 (sqrt.f64 (/.f64 A (.f64 V l)))))
	49.9b	(.f64 (.f64 c0 (sqrt.f64 (/.f64 1 V))) (sqrt.f64 (/.f64 A l)))
	39.8b	(.f64 c0 (/.f64 (sqrt.f64 A) (sqrt.f64 (.f64 V l))))
	18.1b	(*.f64 c0 (sqrt.f64 (/.f64 1 (/.f64 V (/.f64 A l)))))

Compiler

Compiled 6525 to 1418 computations (78.3% saved)

regimes1.2s (18.7%)

Accuracy

Total 2.6b remaining (22.6%)

Threshold costs 0b (0%)

Counts

81 → 4

Compiler

Compiled 16823 to 9818 computations (41.6% saved)

bsearch3.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	83
1	42	83
2	41	83

end7.0ms (0.1%)

Compiler: Compiled 177 to 99 computations (44.1% saved)

sample1.3s (19.3%)

Algorithm

1×

intervals

Results

416.0ms	8000×	body	128	valid
141.0ms	2921×	body	128	nan
38.0ms	801×	body	128	invalid

Compiler

Compiled 332 to 201 computations (39.5% saved)

Details

analyze641.0ms (9.7%)

sample54.0ms (0.8%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series121.0ms (1.8%)

rewrite14.0ms (0.2%)

simplify94.0ms (1.4%)

prune86.0ms (1.3%)

localize10.0ms (0.1%)

series675.0ms (10.2%)

rewrite22.0ms (0.3%)

simplify99.0ms (1.5%)

prune196.0ms (3%)

localize13.0ms (0.2%)

series802.0ms (12.1%)

rewrite5.0ms (0.1%)

simplify81.0ms (1.2%)

prune151.0ms (2.3%)

localize13.0ms (0.2%)

series762.0ms (11.5%)

rewrite3.0ms (0%)

simplify75.0ms (1.1%)

prune163.0ms (2.5%)

regimes1.2s (18.7%)

bsearch3.0ms (0%)

simplify3.0ms (0.1%)

end7.0ms (0.1%)

sample1.3s (19.3%)

Profiling