Details

analyze64.0ms

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

sample28.0ms

Algorithm

intervals

Results

15.0ms	237×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify131.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5682	9

prune3.0ms

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: 0.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

3.0ms	(+.f64 1 (exp.f64 x))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(+.f64 1 (exp.f64 x))
9.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4907	235
1	4907	235

prune37.0ms

Filtered

23 candidates to 33 candidates (-43.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	2	34

Merged error: 0.2b

Counts

34 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
0.7b	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64`
5×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`log-prod_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `sqr-pow_binary64` `log-div_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+.f64 1 (exp.f64 x))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
3.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+.f64 1 (exp.f64 x))
9.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
9.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
14.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4913	693
1	4913	693

prune61.0ms

Filtered

47 candidates to 87 candidates (-85.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	87	2	89

Merged error: 0.2b

Counts

89 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4))))
0.2b	(.f64 (.f64 x x) (+.f64 (*.f64 3/8 (log.f64 2)) 3/4))
0.8b	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
6.8b	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

32×	`associate-*r/_binary64`
15×	`pow1_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
9×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
8×	`frac-add_binary64`
6×	`cbrt-div_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`log-pow_binary64`
1×	`pow1/3_binary64` `cbrt-prod_binary64`

Counts

4 → 88

Calls

4 calls:

20.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4))))
17.0ms	(.f64 (.f64 x x) (+.f64 (*.f64 3/8 (log.f64 2)) 3/4))
10.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
10.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4)))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4))))
11.0ms	(.f64 (.f64 x x) (+.f64 (*.f64 3/8 (log.f64 2)) 3/4))
18.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
34.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 3/8 (log.f64 2)) 3/4)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5120	2273

prune166.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	100	2	102

Merged error: 0.2b

Counts

102 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
0.9b	(exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))))))
6.1b	(log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))
6.8b	(cbrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/_binary64`
18×	`log-div_binary64`
16×	`flip3-+_binary64` `flip-+_binary64`
13×	`pow1_binary64`
12×	`frac-add_binary64` `exp-diff_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `cbrt-prod_binary64`
3×	`pow-prod-down_binary64` `associate-r_binary64` `log-prod_binary64`
2×	`rem-log-exp_binary64` `exp-sum_binary64` `prod-exp_binary64`
1×	`cbrt-unprod_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

7.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
11.0ms	(exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))))))
11.0ms	(log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))
12.0ms	(cbrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
14.0ms	(exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4))))))
16.0ms	(log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))
24.0ms	(cbrt.f64 (exp.f64 (log.f64 (.f64 (log.f64 2) (+.f64 (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))) (.f64 (.f64 x x) (+.f64 (.f64 (log.f64 2) 3/8) 3/4)))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5018	2986

prune192.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	91	2	93

Merged error: 0.2b

Counts

93 → 2

regimes68.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	12
1	39	12

end0.0ms

sample684.0ms

Algorithm

intervals

Results

334.0ms	7311×	body	80	valid
78.0ms	259×	body	640	valid
65.0ms	118×	body	1280	valid
38.0ms	204×	body	320	valid
12.0ms	108×	body	160	valid
2.0ms	40×	body	80	invalid
0.0ms	8×	body	80	overflowed

Details

analyze64.0ms

sample28.0ms

simplify131.0ms

prune3.0ms

localize7.0ms

rewrite8.0ms

series11.0ms

simplify60.0ms

prune37.0ms

localize9.0ms

rewrite15.0ms

series34.0ms

simplify74.0ms

prune61.0ms

localize16.0ms

rewrite62.0ms

series74.0ms

simplify43.0ms

prune166.0ms

localize22.0ms

rewrite44.0ms

series72.0ms

simplify62.0ms

prune192.0ms

regimes68.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample684.0ms

Profiling