Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

sample21.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	499	10
1	499	10

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: 8.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.7b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
6×	`associate-/r*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 55

Calls

2 calls:

6.0ms	(/.f64 x0 (-.f64 1 x1))
12.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/.f64 x0 (-.f64 1 x1))
28.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

simplify71.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4961	931
1	4961	931

prune38.0ms

Filtered

45 candidates to 61 candidates (-35.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 6.9b

Counts

62 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.2b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r*_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`associate-r/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

11.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
27.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
6.0ms	(/.f64 x0 (-.f64 1 x1))
18.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
111.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
28.0ms	(/.f64 x0 (-.f64 1 x1))
68.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

simplify90.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5570	2563

prune120.0ms

Filtered

96 candidates to 140 candidates (-45.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Merged error: 5.4b

Counts

142 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (-.f64 x1 2))
0.5b	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.2b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`difference-of-squares_binary64`
10×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out--_binary64`
5×	`associate-r_binary64`
4×	`flip3--_binary64` `associate-r/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `flip--_binary64`
3×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(*.f64 x1 (-.f64 x1 2))
23.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
6.0ms	(/.f64 x0 (-.f64 1 x1))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

series300.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 x1 (-.f64 x1 2))
122.0ms	(/.f64 (.f64 x0 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
28.0ms	(/.f64 x0 (-.f64 1 x1))
127.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

simplify84.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5847	2315

prune107.0ms

Filtered

84 candidates to 118 candidates (-40.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	2	120

Merged error: 4.5b

Counts

120 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.2b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)))
6.2b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r*_binary64`
7×	`log-pow_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `prod-exp_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 100

Calls

4 calls:

26.0ms	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
6.0ms	(/.f64 x0 (-.f64 1 x1))
10.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)))
9.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

series289.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (.f64 x0 (log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (.f64 x1 (-.f64 x1 2)))) x0)))) (+.f64 x0 (/.f64 x0 (-.f64 1 x1))))
26.0ms	(/.f64 x0 (-.f64 1 x1))
75.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)))
71.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (-.f64 x1 2)))) x0)

simplify80.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5776	2461

prune108.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 3.5b

Counts

114 → 2

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 3.3b against oracle of 3.3b and baseline of 4.5b

bsearch14.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	108
1	65	108

end0.0ms

sample473.0ms

Algorithm

intervals

Results

209.0ms	8000×	pre	80	true
172.0ms	8000×	body	80	valid

Details

analyze3.0ms

sample21.0ms

simplify59.0ms

prune1.0ms

localize5.0ms

rewrite20.0ms

series56.0ms

simplify71.0ms

prune38.0ms

localize10.0ms

rewrite66.0ms

series215.0ms

simplify90.0ms

prune120.0ms

localize12.0ms

rewrite49.0ms

series300.0ms

simplify84.0ms

prune107.0ms

localize17.0ms

rewrite55.0ms

series289.0ms

simplify80.0ms

prune108.0ms

regimes19.0ms

bsearch14.0ms

simplify4.0ms

end0.0ms

sample473.0ms

Profiling