Details

analyze220.0ms

Algorithm

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

sample17.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify197.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (188.0ms)

Iter	Nodes	Cost
0	4701	18
1	4701	18

prune1.0ms

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

Merged error: 5.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
1.2b	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
8.3b	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
10.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
5.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
7.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 5081767996463981/4503599627370496 (exp.f64 z))
44.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))))
50.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y))
89.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 x y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5290	1530

prune76.0ms

Filtered

66 candidates to 82 candidates (-24.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.0b

Counts

83 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x)))
0.1b	(/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x))
0.1b	(/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981))
0.2b	(*.f64 y 4503599627370496/5081767996463981)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64`
4×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `1-exp_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

14.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x)))
10.0ms	(/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x))
6.0ms	(/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981))
4.0ms	(*.f64 y 4503599627370496/5081767996463981)

series148.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x)))
75.0ms	(/.f64 1 (-.f64 (/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981)) x))
24.0ms	(/.f64 (exp.f64 z) (*.f64 y 4503599627370496/5081767996463981))
12.0ms	(*.f64 y 4503599627370496/5081767996463981)

simplify87.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5036	1734

prune76.0ms

Filtered

67 candidates to 105 candidates (-56.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Merged error: 0.0b

Counts

108 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 z (log.f64 5081767996463981/4503599627370496))
0.0b	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))))
1.2b	(-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))
8.3b	(/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64` `times-frac_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `distribute-lft-out_binary64` `log-prod_binary64` `associate-/l_binary64` `associate-+r+_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 68

Calls

4 calls:

4.0ms	(+.f64 z (log.f64 5081767996463981/4503599627370496))
12.0ms	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))))
7.0ms	(-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))
12.0ms	(/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+.f64 z (log.f64 5081767996463981/4503599627370496))
56.0ms	(+.f64 x (/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))))
56.0ms	(-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y))
115.0ms	(/.f64 y (-.f64 (exp.f64 (+.f64 z (log.f64 5081767996463981/4503599627370496))) (*.f64 x y)))

simplify88.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5255	1531

prune63.0ms

Filtered

63 candidates to 80 candidates (-27.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	80	3	83

Merged error: 0.0b

Counts

83 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))
3.9b	(/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
8.3b	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
24.4b	(/.f64 (-.f64 (.f64 x x) (/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))) (-.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (*.f64 y x)))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
41×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
17×	`difference-of-squares_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
10×	`associate-/r_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-out--_binary64`
4×	`pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `associate-r/_binary64` `associate-l/_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `prod-exp_binary64`

Counts

4 → 120

Calls

4 calls:

5.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))
16.0ms	(/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
7.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
42.0ms	(/.f64 (-.f64 (.f64 x x) (/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))) (-.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (*.f64 y x)))))

series424.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))
146.0ms	(/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))
86.0ms	(/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x)))
142.0ms	(/.f64 (-.f64 (.f64 x x) (/.f64 y (.f64 (-.f64 (/.f64 (exp.f64 z) (.f64 y 4503599627370496/5081767996463981)) x) (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (.f64 y x))))) (-.f64 x (/.f64 y (-.f64 (.f64 5081767996463981/4503599627370496 (exp.f64 z)) (*.f64 y x)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5094	6472

prune228.0ms

Filtered

110 candidates to 132 candidates (-20.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Merged error: 0.0b

Counts

135 → 4

regimes49.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	18
1	25	18

end0.0ms

sample470.0ms

Algorithm

intervals

Results

309.0ms	8000×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze220.0ms

sample17.0ms

simplify197.0ms

prune1.0ms

localize11.0ms

rewrite29.0ms

series195.0ms

simplify86.0ms

prune76.0ms

localize9.0ms

rewrite36.0ms

series148.0ms

simplify87.0ms

prune76.0ms

localize21.0ms

rewrite38.0ms

series275.0ms

simplify88.0ms

prune63.0ms

localize26.0ms

rewrite74.0ms

series424.0ms

simplify91.0ms

prune228.0ms

regimes49.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample470.0ms

Profiling