Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample27.0ms

Algorithm

intervals

Results

7.0ms	47×	body	1280	valid
5.0ms	47×	body	640	valid
4.0ms	128×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune8.0ms

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: 30.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64_574`
60×	`times-frac_binary64_569`
57×	`add-sqr-sqrt_binary64_559`
25×	`add-cube-cbrt_binary64_545`
20×	`distribute-lft-out_binary64_618`
18×	`distribute-lft-out--_binary64_619`
14×	`difference-of-squares_binary64_603`
11×	`associate-/r*_binary64_637`
7×	`add-cbrt-cube_binary64_546` `associate-/l*_binary64_638` `add-exp-log_binary64_538`
5×	`difference-of-sqr-1_binary64_604` `add-log-exp_binary64_539`
4×	`associate-/r/_binary64_639`
3×	`pow1_binary64_520`
2×	`flip3--_binary64_573` `div-inv_binary64_575` `associate-/l/_binary64_640` `div-exp_binary64_527` `flip3-+_binary64_572` `frac-2neg_binary64_567` `flip-+_binary64_599` `clear-num_binary64_577` `flip--_binary64_600` `cbrt-undiv_binary64_544`
1×	`frac-sub_binary64_565` `diff-log_binary64_490` `sub-neg_binary64_578`

Counts

3 → 113

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 x 1))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
34.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series59.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 x (+.f64 x 1))
11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
37.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify68.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5189	2299

prune322.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(*.f64 x (/.f64 1 (+.f64 x 1)))
7.9b	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64_574`
62×	`add-sqr-sqrt_binary64_559`
54×	`times-frac_binary64_569`
35×	`add-cube-cbrt_binary64_545`
18×	`associate-r_binary64_633`
16×	`add-exp-log_binary64_538`
15×	`distribute-lft-out_binary64_618`
13×	`add-cbrt-cube_binary64_546`
11×	`associate-/r*_binary64_637`
10×	`difference-of-squares_binary64_603`
7×	`pow1_binary64_520` `associate-/l*_binary64_638`
6×	`associate-/r/_binary64_639` `add-log-exp_binary64_539`
5×	`distribute-lft-out--_binary64_619` `difference-of-sqr-1_binary64_604`
3×	`associate-l_binary64_634` `div-inv_binary64_575` `unswap-sqr_binary64_602` `div-exp_binary64_527` `flip3-+_binary64_572` `flip-+_binary64_599` `cbrt-undiv_binary64_544` `prod-exp_binary64_525`
2×	`flip3--_binary64_573` `frac-sub_binary64_565` `associate-/l/_binary64_640` `frac-2neg_binary64_567` `rec-exp_binary64_526` `cbrt-unprod_binary64_543` `clear-num_binary64_577` `flip--_binary64_600` `un-div-inv_binary64_576` `associate-*r/_binary64_635`
1×	`inv-pow_binary64_496` `pow-flip_binary64_504` `diff-log_binary64_490` `sub-neg_binary64_578` `*-commutative_binary64_642` `pow-prod-down_binary64_501`

Counts

4 → 144

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
10.0ms	(*.f64 x (/.f64 1 (+.f64 x 1)))
17.0ms	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 1 (+.f64 x 1))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(*.f64 x (/.f64 1 (+.f64 x 1)))
39.0ms	(-.f64 (*.f64 x (/.f64 1 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify97.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5065	2394

prune352.0ms

Filtered

95 candidates to 156 candidates (-64.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	156	4	160

Merged error: 0.0b

Counts

160 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.1b	(*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))
7.9b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_559`
69×	`*-un-lft-identity_binary64_574`
56×	`times-frac_binary64_569`
37×	`add-cube-cbrt_binary64_545`
27×	`associate-l_binary64_634`
16×	`add-exp-log_binary64_538`
14×	`difference-of-squares_binary64_603`
13×	`add-cbrt-cube_binary64_546`
11×	`associate-/r*_binary64_637`
7×	`pow1_binary64_520` `distribute-lft-out--_binary64_619` `difference-of-sqr-1_binary64_604`
6×	`associate-/r/_binary64_639` `associate-/l*_binary64_638` `add-log-exp_binary64_539`
5×	`frac-sub_binary64_565` `flip3-+_binary64_572` `flip-+_binary64_599` `distribute-lft-out_binary64_618`
4×	`frac-times_binary64_566` `associate-r_binary64_633` `associate-*r/_binary64_635`
3×	`flip3--_binary64_573` `div-inv_binary64_575` `unswap-sqr_binary64_602` `div-exp_binary64_527` `flip--_binary64_600` `cbrt-undiv_binary64_544` `prod-exp_binary64_525`
2×	`frac-2neg_binary64_567` `rec-exp_binary64_526` `cbrt-unprod_binary64_543` `clear-num_binary64_577` `distribute-lft-in_binary64_616` `associate--r+_binary64_629` `distribute-rgt-in_binary64_617` `associate-*l/_binary64_636`
1×	`inv-pow_binary64_496` `pow-flip_binary64_504` `diff-log_binary64_490` `sub-neg_binary64_578` `*-commutative_binary64_642` `pow-prod-down_binary64_501`

Counts

4 → 154

Calls

4 calls:

5.0ms	(/.f64 x (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))
14.0ms	(*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 x (+.f64 x 1))
8.0ms	(/.f64 1 (-.f64 x 1))
11.0ms	(*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))
34.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))

simplify85.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5094	2554

prune393.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Merged error: 0.0b

Counts

170 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 x 1))
0.2b	(cbrt.f64 (+.f64 x 1))
0.3b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
22.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_559`
34×	`*-un-lft-identity_binary64_574` `cbrt-prod_binary64_541`
16×	`cbrt-div_binary64_542`
14×	`add-cube-cbrt_binary64_545` `times-frac_binary64_569`
11×	`pow1_binary64_520`
9×	`swap-sqr_binary64_601`
8×	`pow1/3_binary64_512` `flip3-+_binary64_572` `flip-+_binary64_599` `distribute-lft-out_binary64_618` `difference-of-squares_binary64_603`
7×	`associate-l_binary64_634` `associate-r_binary64_633`
6×	`add-exp-log_binary64_538` `add-log-exp_binary64_539`
4×	`frac-times_binary64_566` `add-cbrt-cube_binary64_546` `unswap-sqr_binary64_602`
2×	`pow-prod-up_binary64_500` `associate-l/_binary64_636` `pow-sqr_binary64_607` `pow-prod-down_binary64_501` `associate-r/_binary64_635`
1×	`pow-plus_binary64_515` `flip3--_binary64_573` `frac-sub_binary64_565` `pow2_binary64_511` `distribute-lft-out--_binary64_619` `cbrt-unprod_binary64_543` `diff-log_binary64_490` `sub-neg_binary64_578` `flip--_binary64_600` `*-commutative_binary64_642` `prod-exp_binary64_525`

Counts

4 → 102

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
10.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
57.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt.f64 (+.f64 x 1))
24.0ms	(cbrt.f64 (+.f64 x 1))
26.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5112	2375

prune354.0ms

Filtered

86 candidates to 114 candidates (-32.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Merged error: 0.0b

Counts

118 → 4

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.1b

bsearch48.0ms

Steps

Iters	Range		Point
8	2899990995046755/562949953421312	5308712669051327/137438953472	13458.95778492134
11	-145714594316689216	-3930488085716857/2305843009213693952	-13944.835699645984

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	90	58
1	90	58

end0.0ms

sample742.0ms

Algorithm

intervals

Results

265.0ms	1841×	body	1280	valid
142.0ms	1232×	body	640	valid
136.0ms	4003×	body	80	valid
54.0ms	623×	body	320	valid
18.0ms	301×	body	160	valid

Details

analyze4.0ms

sample27.0ms

simplify86.0ms

prune8.0ms

localize10.0ms

rewrite52.0ms

series59.0ms

simplify68.0ms

prune322.0ms

localize11.0ms

rewrite46.0ms

series74.0ms

simplify97.0ms

prune352.0ms

localize12.0ms

rewrite46.0ms

series64.0ms

simplify85.0ms

prune393.0ms

localize24.0ms

rewrite77.0ms

series115.0ms

simplify104.0ms

prune354.0ms

regimes67.0ms

bsearch48.0ms

simplify4.0ms

end0.0ms

sample742.0ms

Profiling