Details

analyze266.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample61.0ms

Algorithm

intervals

Results

19.0ms	91×	body	2560	nan
15.0ms	100×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	43×	body	640	nan
2.0ms	24×	body	320	nan
0.0ms	6×	body	160	nan
0.0ms	6×	body	80	nan

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5257	9

prune2.0ms

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: 30.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
28.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64` `sqrt-prod_binary64`
3×	`add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `log-div_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 43

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

series22.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
6.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5188	615

prune56.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0b

Counts

53 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))
0.0b	(sqrt.f64 (+.f64 x (sqrt.f64 1.0)))
0.0b	(sqrt.f64 (-.f64 x (sqrt.f64 1.0)))
0.5b	(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`sqrt-div_binary64`
10×	`pow1_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))
4.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 1.0)))
5.0ms	(sqrt.f64 (-.f64 x (sqrt.f64 1.0)))
16.0ms	(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0)))))
6.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 1.0)))
6.0ms	(sqrt.f64 (-.f64 x (sqrt.f64 1.0)))
16.0ms	(*.f64 (sqrt.f64 (+.f64 x (sqrt.f64 1.0))) (sqrt.f64 (-.f64 x (sqrt.f64 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5065	1359

prune108.0ms

Filtered

75 candidates to 99 candidates (-32.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))))
0.0b	(log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
5.7b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
28.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
12×	`sqrt-prod_binary64`
11×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
7×	`log-pow_binary64` `exp-sum_binary64`
6×	`add-exp-log_binary64` `log-div_binary64` `sqrt-div_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`rem-log-exp_binary64` `exp-diff_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))))
6.0ms	(log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

series30.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))))
9.0ms	(log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0)))
5.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4997	956
1	4997	956

prune78.0ms

Filtered

67 candidates to 86 candidates (-28.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	86	2	88

Merged error: 0b

Counts

88 → 2

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

559.0ms	3062×	body	2560	nan
388.0ms	2540×	body	1280	nan
307.0ms	8000×	body	80	valid
147.0ms	1223×	body	640	nan
62.0ms	665×	body	320	nan
20.0ms	308×	body	160	nan
9.0ms	287×	body	80	nan

Details

analyze266.0ms

sample61.0ms

simplify77.0ms

prune2.0ms

localize7.0ms

rewrite20.0ms

series22.0ms

simplify48.0ms

prune56.0ms

localize10.0ms

rewrite31.0ms

series39.0ms

simplify46.0ms

prune108.0ms

localize11.0ms

rewrite30.0ms

series30.0ms

simplify42.0ms

prune78.0ms

regimes22.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling