Details

analyze1.2s (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample188.0ms (0.8%)

Algorithm

1×

intervals

Results

41.0ms	67×	body	2048	valid
35.0ms	71×	body	1024	valid
34.0ms	42×	body	1024	nan
16.0ms	42×	body	512	valid
13.0ms	75×	body	128	overflowed
10.0ms	23×	body	512	nan
5.0ms	24×	body	256	valid
5.0ms	52×	body	128	valid
3.0ms	6×	body	512	invalid
3.0ms	12×	body	256	nan
2.0ms	2×	body	1024	invalid
1.0ms	12×	body	128	invalid
1.0ms	27×	body	128	nan
0.0ms	1×	body	256	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify142.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

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

31.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
2.9b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite90.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

31.4b

Rules

24×	`add-sqr-sqrt_binary64_441`
19×	`*-un-lft-identity_binary64_419`
16×	`unpow-prod-down_binary64_498`
13×	`pow-unpow_binary64_496`
12×	`add-cube-cbrt_binary64_454`
9×	`difference-of-squares_binary64_388` `times-frac_binary64_425`
8×	`sqr-pow_binary64_391`
7×	`cancel-sign-sub-inv_binary64_385`
4×	`add-log-exp_binary64_458`
3×	`pow1_binary64_480` `add-exp-log_binary64_457` `distribute-lft-out--_binary64_371`
2×	`add-cbrt-cube_binary64_455`
1×	`diff-log_binary64_511` `flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `distribute-lft-out_binary64_370` `div-inv_binary64_416` `pow-pow_binary64_491` `pow-to-exp_binary64_488` `pow-exp_binary64_487`

Counts

2 → 57

Calls

2 calls:

10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
3.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 1342 to 963 computations (28.2% saved)

series422.0ms (1.9%)

Error

0.7b

Counts

2 → 24

Calls

2 calls:

253.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
123.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 1935 to 1499 computations (22.5% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4992	1891
1	4992	1891

prune100.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Error

0.6b

Counts

82 → 4

Compiler

Compiled 1957 to 1334 computations (31.8% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(log.f64 (+.f64 1 x))
3.1b	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
5.0b	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
6.9b	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))

rewrite338.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

16×	`*-un-lft-identity_binary64_419`
15×	`add-log-exp_binary64_458`
11×	`log-prod_binary64_505`
10×	`pow1_binary64_480` `add-sqr-sqrt_binary64_441`
9×	`associate-*r/_binary64_361`
8×	`add-cube-cbrt_binary64_454`
7×	`cube-div_binary64_448`
6×	`log-pow_binary64_508`
5×	`add-exp-log_binary64_457` `frac-add_binary64_427` `frac-sub_binary64_428` `flip3-+_binary64_422` `flip-+_binary64_393` `cancel-sign-sub-inv_binary64_385` `associate--l+_binary64_356`
4×	`sum-log_binary64_510` `diff-log_binary64_511` `add-cbrt-cube_binary64_455` `distribute-lft-out--_binary64_371` `log-div_binary64_506`
3×	`associate--l-_binary64_357` `associate--r+_binary64_355`
2×	`flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `distribute-lft-out_binary64_370`
1×	`div-sub_binary64_424` `associate-+r-_binary64_353` `+-commutative_binary64_349` `difference-of-squares_binary64_388` `rem-log-exp_binary64_460`

Counts

4 → 77

Calls

4 calls:

26.0ms	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
10.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
7.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
3.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 5809 to 3886 computations (33.1% saved)

series1.7s (7.7%)

Error

0.6b

Counts

4 → 44

Calls

4 calls:

1.0s	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (-.f64 (log.f64 (+.f64 1 x)) (log.f64 x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
496.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
67.0ms	(-.f64 (log.f64 (+.f64 1 x)) (log.f64 x))
33.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 6190 to 4622 computations (25.3% saved)

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4983	5256
1	4983	5256

prune479.0ms (2.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Error

0.5b

Counts

125 → 14

Compiler

Compiled 8876 to 5828 computations (34.3% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(log.f64 (+.f64 1 x))
3.2b	(log.f64 (/.f64 (+.f64 x 1) x))
5.0b	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
6.9b	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (log.f64 (/.f64 (+.f64 x 1) x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))

rewrite350.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

21×	`*-un-lft-identity_binary64_419`
20×	`log-prod_binary64_505`
15×	`add-log-exp_binary64_458`
13×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
12×	`times-frac_binary64_425`
9×	`associate-*r/_binary64_361`
8×	`add-exp-log_binary64_457`
7×	`cube-div_binary64_448`
6×	`pow1_binary64_480`
5×	`frac-add_binary64_427` `frac-sub_binary64_428`
4×	`sum-log_binary64_510` `add-cbrt-cube_binary64_455` `flip3-+_binary64_422` `flip-+_binary64_393` `log-div_binary64_506` `distribute-lft-out_binary64_370`
3×	`diff-log_binary64_511` `rem-log-exp_binary64_460`
2×	`log-pow_binary64_508`
1×	`flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `div-sub_binary64_424` `associate-+r-_binary64_353` `associate--l-_binary64_357` `associate--l+_binary64_356` `+-commutative_binary64_349` `div-inv_binary64_416` `div-exp_binary64_470`

Counts

4 → 75

Calls

4 calls:

21.0ms	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (log.f64 (/.f64 (+.f64 x 1) x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
10.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
5.0ms	(log.f64 (/.f64 (+.f64 x 1) x))
3.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 5614 to 3821 computations (31.9% saved)

series1.6s (7.1%)

Error

0.5b

Counts

4 → 41

Calls

4 calls:

925.0ms	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (log.f64 (/.f64 (+.f64 x 1) x)) n)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
499.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
56.0ms	(log.f64 (/.f64 (+.f64 x 1) x))
24.0ms	(log.f64 (+.f64 1 x))

Compiler

Compiled 5771 to 4374 computations (24.2% saved)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4950	5173
1	4950	5173

prune471.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	8	116
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	118	12	130

Error

0.5b

Counts

130 → 12

Compiler

Compiled 8381 to 5575 computations (33.5% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(log.f64 (/.f64 (+.f64 x 1) x))
3.2b	(log.f64 (/.f64 (+.f64 x 1) x))
5.0b	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
6.9b	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x))) (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x)))) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))

rewrite428.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

32×	`*-un-lft-identity_binary64_419` `log-prod_binary64_505`
24×	`times-frac_binary64_425`
20×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
15×	`add-log-exp_binary64_458`
10×	`add-exp-log_binary64_457`
9×	`associate-*r/_binary64_361`
7×	`cube-div_binary64_448`
6×	`pow1_binary64_480` `distribute-lft-out_binary64_370`
5×	`frac-add_binary64_427` `frac-sub_binary64_428`
4×	`sum-log_binary64_510` `add-cbrt-cube_binary64_455` `rem-log-exp_binary64_460`
3×	`diff-log_binary64_511` `flip3-+_binary64_422` `flip-+_binary64_393`
2×	`log-pow_binary64_508` `log-div_binary64_506` `div-inv_binary64_416` `div-exp_binary64_470`
1×	`flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `associate--l+_binary64_356` `+-commutative_binary64_349`

Counts

4 → 86

Calls

4 calls:

18.0ms	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x))) (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x)))) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
11.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
5.0ms	(log.f64 (/.f64 (+.f64 x 1) x))
5.0ms	(log.f64 (/.f64 (+.f64 x 1) x))

Compiler

Compiled 7247 to 5000 computations (31% saved)

series1.7s (7.5%)

Error

0.5b

Counts

4 → 48

Calls

4 calls:

918.0ms	(-.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))) (/.f64 (.f64 (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x))) (sqrt.f64 (log.f64 (/.f64 (+.f64 x 1) x)))) n)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))
513.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3)))
61.0ms	(log.f64 (/.f64 (+.f64 x 1) x))
58.0ms	(log.f64 (/.f64 (+.f64 x 1) x))

Compiler

Compiled 7165 to 5423 computations (24.3% saved)

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5044	5595

prune510.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	133	13	146

Error

0.5b

Counts

146 → 13

Compiler

Compiled 9424 to 6267 computations (33.5% saved)

regimes1.7s (7.4%)

Accuracy

Total 6.4b remaining (92.6%)

Threshold costs 0b (0%)

Compiler

Compiled 25686 to 18960 computations (26.2% saved)

bsearch48.0ms (0.2%)

Steps

Iters	Range		Point
6	6263.552115601929	27373.17290926193	9954.50088089535

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	99
1	75	99

end0.0ms (0%)

sample10.6s (47.2%)

Algorithm

1×

intervals

Results

1.5s	2663×	body	1024	valid
1.1s	1493×	body	1024	nan
968.0ms	1732×	body	2048	valid
490.0ms	2741×	body	128	overflowed
445.0ms	1231×	body	512	valid
322.0ms	730×	body	512	nan
166.0ms	1784×	body	128	valid
152.0ms	169×	body	1024	invalid
134.0ms	590×	body	256	valid
119.0ms	249×	body	512	invalid
97.0ms	397×	body	256	nan
50.0ms	832×	body	128	nan
45.0ms	154×	body	256	invalid
29.0ms	235×	body	128	invalid
3.0ms	3×	body	2048	nan
1.0ms	1×	body	2048	invalid

Compiler

Compiled 6417 to 4730 computations (26.3% saved)

Details

analyze1.2s (5.2%)

sample188.0ms (0.8%)

simplify142.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite90.0ms (0.4%)

series422.0ms (1.9%)

simplify80.0ms (0.4%)

prune100.0ms (0.4%)

localize32.0ms (0.1%)

rewrite338.0ms (1.5%)

series1.7s (7.7%)

simplify81.0ms (0.4%)

prune479.0ms (2.1%)

localize34.0ms (0.2%)

rewrite350.0ms (1.6%)

series1.6s (7.1%)

simplify79.0ms (0.4%)

prune471.0ms (2.1%)

localize36.0ms (0.2%)

rewrite428.0ms (1.9%)

series1.7s (7.5%)

simplify88.0ms (0.4%)

prune510.0ms (2.3%)

regimes1.7s (7.4%)

bsearch48.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample10.6s (47.2%)

Profiling