Details

analyze246.0ms

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
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample71.0ms

Algorithm

intervals

Results

29.0ms	52×	body	1280	valid
16.0ms	47×	body	640	valid
10.0ms	126×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	8×	body	80	invalid
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	overflowed

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5443	27

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
1.9b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub_binary64`
78×	`exp-neg_binary64`
76×	`frac-times_binary64`
59×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-r/_binary64` `associate-l/_binary64`
31×	`flip3--_binary64` `flip--_binary64`
27×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`un-div-inv_binary64`
17×	`*-un-lft-identity_binary64`
14×	`associate-l_binary64`
12×	`exp-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `times-frac_binary64`
5×	`add-exp-log_binary64`
4×	`rem-exp-log_binary64`
3×	`associate-r_binary64` `difference-of-sqr-1_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

15.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
18.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
33.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5507	5772

prune209.0ms

Filtered

96 candidates to 176 candidates (-83.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	2	177

Merged error: 0.2b

Counts

177 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
8.0b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-l_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

7.0ms	(*.f64 2/3 (pow.f64 x 3))
8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(*.f64 2/3 (pow.f64 x 3))
5.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5491	454

prune34.0ms

Filtered

31 candidates to 51 candidates (-64.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.2b

Counts

53 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
0.8b	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 x 3))))
8.0b	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow1_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`log-prod_binary64` `log-pow_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64` `exp-to-pow_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `exp-prod_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

3 → 59

Calls

3 calls:

7.0ms	(*.f64 2/3 (pow.f64 x 3))
2.0ms	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 x 3))))
8.0ms	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(*.f64 2/3 (pow.f64 x 3))
4.0ms	(log.f64 (exp.f64 (*.f64 2/3 (pow.f64 x 3))))
5.0ms	(-.f64 (+.f64 (log.f64 (exp.f64 (.f64 2/3 (pow.f64 x 3)))) 2) (.f64 x x))

simplify33.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5545	565

prune41.0ms

Filtered

42 candidates to 68 candidates (-61.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	68	3	71

Merged error: 0.2b

Counts

71 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

8.0b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
12.1b	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
12.1b	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
12.1b	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64`
3×	`pow1/3_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
10.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
9.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
10.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4868	1237
1	4868	1237

prune107.0ms

Filtered

60 candidates to 68 candidates (-13.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	68	3	71

Merged error: 0.2b

Counts

71 → 3

regimes70.0ms

Accuracy

96.8% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 17.2b

bsearch81.0ms

Steps

Iters	Range		Point
10	0.4843321903513168	12659538206410.568	10.091899336379667

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	179	48
1	179	48

end0.0ms

sample2.1s

Algorithm

intervals

Results

968.0ms	1748×	body	1280	valid
431.0ms	1250×	body	640	valid
330.0ms	4119×	body	80	valid
140.0ms	599×	body	320	valid
43.0ms	284×	body	160	valid
17.0ms	202×	body	80	invalid
16.0ms	210×	body	80	overflowed
7.0ms	12×	body	1280	invalid
5.0ms	14×	body	640	invalid
1.0ms	5×	body	320	invalid
0.0ms	1×	body	160	invalid

Details

analyze246.0ms

sample71.0ms

simplify64.0ms

prune8.0ms

localize17.0ms

rewrite54.0ms

series54.0ms

simplify63.0ms

prune209.0ms

localize8.0ms

rewrite16.0ms

series9.0ms

simplify32.0ms

prune34.0ms

localize10.0ms

rewrite18.0ms

series13.0ms

simplify33.0ms

prune41.0ms

localize12.0ms

rewrite36.0ms

series31.0ms

simplify51.0ms

prune107.0ms

regimes70.0ms

bsearch81.0ms

simplify4.0ms

end0.0ms

sample2.1s

Profiling