Details

analyze290.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample61.0ms (1.4%)

Algorithm

1×

intervals

Results

26.0ms	71×	body	1024	valid
13.0ms	43×	body	2048	valid
8.0ms	44×	body	512	valid
4.0ms	81×	body	128	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

54.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	54.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))

Compiler

Compiled 20 to 14 computations (30% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.0b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.4b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
17.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite81.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

53.8b

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 704 to 424 computations (39.8% saved)

series70.0ms (1.6%)

Error

0.0b

Counts

3 → 26

Calls

3 calls:

15.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 781 to 646 computations (17.3% saved)

simplify104.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

409×	`sub-neg_binary64`
239×	`times-frac_binary64`
236×	`distribute-rgt-in_binary64`
226×	`cancel-sign-sub-inv_binary64`
179×	`distribute-lft-in_binary64`

Counts

68 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1119
1	322	1046
2	719	1016
3	1987	1010
4	4216	1010
5	4794	1010
6	4908	1010

prune60.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	44	8	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	8	53

Error

26.3b

Counts

53 → 8

Alt Table

Status	Error	Program
	54.2b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))))
	56.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) 3))) (log.f64 (+.f64 1 (.f64 x (+.f64 x (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 1/4 (*.f64 x x)))
	45.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	46.2b	(+.f64 (log.f64 2) (log.f64 x))
	54.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))
▶	45.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	52.9b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))))

Compiler

Compiled 944 to 641 computations (32.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 1/8 (pow.f64 x 3))
9.0b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))

rewrite97.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

26.3b

Rules

38×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64`

Counts

2 → 82

Calls

2 calls:

29.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 1235 to 996 computations (19.4% saved)

series22.0ms (0.5%)

Error

26.3b

Counts

2 → 7

Calls

2 calls:

11.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
7.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 207 to 176 computations (15% saved)

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-l_binary64`
518×	`log-prod_binary64`
515×	`times-frac_binary64`
418×	`associate-r_binary64`
279×	`associate-/l*_binary64`

Counts

89 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1349
1	265	1293
2	859	1278
3	4357	1222
4	4923	1222
5	5014	1222

prune35.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	59	8	67

Error

26.3b

Counts

67 → 8

Alt Table

Status	Error	Program
	54.2b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))))
	56.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) 3))) (log.f64 (+.f64 1 (.f64 x (+.f64 x (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))))
▶	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 1/4 (*.f64 x x)))
	45.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	46.2b	(+.f64 (log.f64 2) (log.f64 x))
	54.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))
✓	45.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	52.9b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))))

Compiler

Compiled 657 to 505 computations (23.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
0.4b	(/.f64 1/4 (*.f64 x x))

rewrite63.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

26.3b

Rules

16×	`log-prod_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-+r+_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 53

Calls

2 calls:

6.0ms	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
4.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 958 to 706 computations (26.3% saved)

series26.0ms (0.6%)

Error

26.3b

Counts

2 → 6

Calls

2 calls:

14.0ms	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
9.0ms	(/.f64 1/4 (*.f64 x x))

Compiler

Compiled 233 to 190 computations (18.5% saved)

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

429×	`sub-neg_binary64`
384×	`times-frac_binary64`
350×	`unsub-neg_binary64`
323×	`associate-l_binary64`
288×	`associate-/l/_binary64`

Counts

59 → 41

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	770
1	262	693
2	649	673
3	1802	673
4	3837	647
5	4935	647
6	4903	647

prune42.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	38	11	49

Error

26.3b

Counts

49 → 11

Alt Table

Status	Error	Program
	54.2b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))))
	56.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) 3))) (log.f64 (+.f64 1 (.f64 x (+.f64 x (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))))
✓	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 1/4 (*.f64 x x)))
	45.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 1 (/.f64 x (/.f64 1/4 x))))
	46.2b	(+.f64 (log.f64 2) (log.f64 x))
▶	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (*.f64 (/.f64 1/2 x) (/.f64 1/2 x)))
	54.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))
✓	45.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	46.0b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (cbrt.f64 (/.f64 1/64 (pow.f64 x 6))))
	52.9b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))))

Compiler

Compiled 787 to 566 computations (28.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
0.3b	(*.f64 (/.f64 1/2 x) (/.f64 1/2 x))

rewrite127.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

26.3b

Rules

50×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

2 → 99

Calls

2 calls:

10.0ms	(*.f64 (/.f64 1/2 x) (/.f64 1/2 x))
9.0ms	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))

Compiler

Compiled 2135 to 1666 computations (22% saved)

series25.0ms (0.6%)

Error

26.3b

Counts

2 → 6

Calls

2 calls:

14.0ms	(+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x)))
8.0ms	(*.f64 (/.f64 1/2 x) (/.f64 1/2 x))

Compiler

Compiled 251 to 210 computations (16.3% saved)

simplify108.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l*_binary64`
463×	`associate-*l/_binary64`
366×	`associate-*r/_binary64`
344×	`times-frac_binary64`
306×	`log-div_binary64`

Counts

105 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	177	1617
1	465	1385
2	1460	1238
3	4120	1162
4	4653	1158
5	4949	1158

prune69.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	90	12	102

Error

26.3b

Counts

102 → 12

Alt Table

Status	Error	Program
	54.2b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (.f64 (/.f64 (/.f64 1/2 x) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 1/2 (cbrt.f64 x))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 x)) 4) (.f64 (cbrt.f64 (/.f64 1/2 x)) (cbrt.f64 (/.f64 1/2 x)))))
	56.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 (+.f64 1 (.f64 x x))) 3))) (log.f64 (+.f64 1 (.f64 x (+.f64 x (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x)))))))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (/.f64 1/4 (*.f64 x x)))
	45.9b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (.f64 (.f64 (pow.f64 (/.f64 (cbrt.f64 1/2) (cbrt.f64 x)) 4) (/.f64 (cbrt.f64 1/2) (cbrt.f64 x))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 x))))
	46.2b	(+.f64 (log.f64 2) (log.f64 x))
	45.8b	(-.f64 (+.f64 (log.f64 1/2) (log.f64 (/.f64 -1 x))) (*.f64 (pow.f64 (cbrt.f64 (/.f64 1/2 x)) 5) (cbrt.f64 (/.f64 1/2 x))))
	54.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))) 3))
	45.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 -1/2 x)))
	52.9b	(log.f64 (/.f64 -1 (-.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))))

Compiler

Compiled 1426 to 1119 computations (21.5% saved)

regimes625.0ms (14%)

Accuracy

Total -28.7b remaining (-5932.4%)

Threshold costs -28.7b (-5932.4%)

Compiler

Compiled 4512 to 3292 computations (27% saved)

bsearch34.0ms (0.8%)

Steps

Iters	Range		Point
10	2.5887401331905805e-08	45227333.711761914	1.2649867250390596
10	-13.073684663564622	-7.487947192160513e-17	-0.9010685812254454

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	39
1	26	39
2	34	39
3	38	39
4	40	39
5	39	39

end3.0ms (0.1%)

Compiler: Compiled 27 to 20 computations (25.9% saved)

sample2.3s (50.7%)

Algorithm

1×

intervals

Results

911.0ms	2532×	body	1024	valid
369.0ms	1160×	body	2048	valid
260.0ms	1273×	body	512	valid
114.0ms	2349×	body	128	valid
81.0ms	655×	body	256	valid
14.0ms	31×	body	4096	valid

Compiler

Compiled 252 to 191 computations (24.2% saved)

Details

analyze290.0ms (6.5%)

sample61.0ms (1.4%)

simplify8.0ms (0.2%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite81.0ms (1.8%)

series70.0ms (1.6%)

simplify104.0ms (2.3%)

prune60.0ms (1.3%)

localize7.0ms (0.2%)

rewrite97.0ms (2.2%)

series22.0ms (0.5%)

simplify109.0ms (2.4%)

prune35.0ms (0.8%)

localize9.0ms (0.2%)

rewrite63.0ms (1.4%)

series26.0ms (0.6%)

simplify96.0ms (2.2%)

prune42.0ms (0.9%)

localize10.0ms (0.2%)

rewrite127.0ms (2.9%)

series25.0ms (0.6%)

simplify108.0ms (2.4%)

prune69.0ms (1.5%)

regimes625.0ms (14%)

bsearch34.0ms (0.8%)

simplify7.0ms (0.2%)

end3.0ms (0.1%)

sample2.3s (50.7%)

Profiling