Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample37.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
8.0ms	47×	body	640	valid
4.0ms	125×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5238	10

prune7.0ms

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	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
0.0b	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
3.0b	(-.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 1.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`
5×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
6.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
11.0ms	(-.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 1.0)

series30.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
7.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
21.0ms	(-.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5352	834

prune95.0ms

Filtered

49 candidates to 68 candidates (-38.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 1.0 x) (.f64 (pow.f64 x 3) (+.f64 (*.f64 x 4.440892098500626e-16) 0.3333333333333335)))
0.1b	(.f64 (pow.f64 x 3) (+.f64 (.f64 x 4.440892098500626e-16) 0.3333333333333335))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `associate--r+_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(-.f64 (.f64 1.0 x) (.f64 (pow.f64 x 3) (+.f64 (*.f64 x 4.440892098500626e-16) 0.3333333333333335)))
9.0ms	(.f64 (pow.f64 x 3) (+.f64 (.f64 x 4.440892098500626e-16) 0.3333333333333335))

series25.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(-.f64 (.f64 1.0 x) (.f64 (pow.f64 x 3) (+.f64 (*.f64 x 4.440892098500626e-16) 0.3333333333333335)))
18.0ms	(.f64 (pow.f64 x 3) (+.f64 (.f64 x 4.440892098500626e-16) 0.3333333333333335))

simplify64.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5070	688

prune59.0ms

Filtered

37 candidates to 54 candidates (-45.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Merged error: 0.0b

Counts

58 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
0.0b	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
0.0b	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)
3.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
20×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`distribute-lft-out_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`difference-of-squares_binary64`
6×	`associate-/r/_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `cube-div_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 120

Calls

4 calls:

6.0ms	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
6.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
8.0ms	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)
20.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)) 1.0)

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))
7.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
13.0ms	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)
20.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 3)) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5216	1829

prune114.0ms

Filtered

76 candidates to 132 candidates (-73.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 2)
0.0b	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
0.0b	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
3.0b	(-.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (.f64 -2.0 x)))) 2) (.f64 1.0 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
20×	`unpow-prod-down_binary64`
11×	`distribute-lft-out_binary64` `add-exp-log_binary64`
8×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`unpow2_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `flip--_binary64`

Counts

4 → 116

Calls

4 calls:

7.0ms	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 2)
6.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
6.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
13.0ms	(-.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (.f64 -2.0 x)))) 2) (.f64 1.0 1.0))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x)))) 2)
7.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
10.0ms	(/.f64 2.0 (+.f64 1.0 (exp.f64 (*.f64 -2.0 x))))
28.0ms	(-.f64 (pow.f64 (/.f64 2.0 (+.f64 1.0 (exp.f64 (.f64 -2.0 x)))) 2) (.f64 1.0 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5529	1708

prune166.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Merged error: 0.0b

Counts

132 → 4

regimes445.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	115	63
1	115	63

end0.0ms

sample1.0s

Algorithm

intervals

Results

445.0ms	1757×	body	1280	valid
214.0ms	1263×	body	640	valid
135.0ms	4032×	body	80	valid
73.0ms	623×	body	320	valid
25.0ms	325×	body	160	valid

Details

analyze2.0ms

sample37.0ms

simplify87.0ms

prune7.0ms

localize7.0ms

rewrite23.0ms

series30.0ms

simplify59.0ms

prune95.0ms

localize9.0ms

rewrite15.0ms

series25.0ms

simplify64.0ms

prune59.0ms

localize9.0ms

rewrite44.0ms

series42.0ms

simplify54.0ms

prune114.0ms

localize13.0ms

rewrite36.0ms

series55.0ms

simplify45.0ms

prune166.0ms

regimes445.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling