Details

analyze72.0ms

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

sample19.0ms

Algorithm

intervals

Results

6.0ms	186×	body	80	valid
3.0ms	24×	body	640	valid
2.0ms	15×	body	1280	valid
1.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify277.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (274.0ms)

Iter	Nodes	Cost
0	5206	11

prune5.0ms

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: 23.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 1.0 x) y)
3.5b	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
7.1b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

7.0ms	(*.f64 (-.f64 1.0 x) y)
7.0ms	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

series30.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(*.f64 (-.f64 1.0 x) y)
16.0ms	(-.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0)))
8.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 y 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5369	732

prune100.0ms

Filtered

52 candidates to 71 candidates (-36.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.3b

Counts

72 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 1.0 y))
0.0b	(*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y)))
3.5b	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`distribute-lft-out_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `associate-l_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`

Counts

3 → 87

Calls

3 calls:

5.0ms	(/.f64 y (+.f64 1.0 y))
12.0ms	(*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y)))
4.0ms	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/.f64 y (+.f64 1.0 y))
8.0ms	(*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y)))
14.0ms	(-.f64 1.0 (*.f64 (-.f64 1.0 x) (/.f64 y (+.f64 1.0 y))))

simplify47.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5083	1043

prune89.0ms

Filtered

69 candidates to 96 candidates (-39.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0.3b

Counts

100 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
0.1b	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
0.1b	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
4.7b	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity_binary64`
132×	`add-sqr-sqrt_binary64`
124×	`times-frac_binary64`
78×	`sqrt-prod_binary64`
72×	`add-cube-cbrt_binary64`
41×	`associate-l_binary64`
27×	`associate-r_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`distribute-lft-out_binary64`
15×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
14×	`associate-/r*_binary64`
9×	`unswap-sqr_binary64`
8×	`associate-/r/_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 217

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
32.0ms	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
6.0ms	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
6.0ms	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y)))
9.0ms	(*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y))))
11.0ms	(/.f64 y (sqrt.f64 (+.f64 1.0 y)))
18.0ms	(-.f64 1.0 (*.f64 (/.f64 (-.f64 1.0 x) (sqrt.f64 (+.f64 1.0 y))) (/.f64 y (sqrt.f64 (+.f64 1.0 y)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4963	3359
1	4963	3359

prune222.0ms

Filtered

139 candidates to 229 candidates (-64.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	229	4	233

Merged error: 0.3b

Counts

233 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

7.1b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.1b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.1b	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
8.1b	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`associate-/r*_binary64`
11×	`distribute-lft-out_binary64`
8×	`associate-/l/_binary64` `associate-/r/_binary64`
7×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
6×	`associate-*l/_binary64`
5×	`difference-of-squares_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
1×	`div-sub_binary64`

Counts

4 → 122

Calls

4 calls:

9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
9.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
15.0ms	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
7.0ms	(/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))
98.0ms	(/.f64 (-.f64 (.f64 1.0 1.0) (.f64 (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)) (/.f64 (.f64 (-.f64 1.0 x) y) (+.f64 1.0 y)))) (+.f64 1.0 (/.f64 (*.f64 (-.f64 1.0 x) y) (+.f64 1.0 y))))

simplify56.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4962	2310
1	4962	2310

prune201.0ms

Filtered

100 candidates to 134 candidates (-34.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	134	4	138

Merged error: 0.3b

Counts

138 → 4

regimes187.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.1b

bsearch28.0ms

Steps

Iters	Range		Point
9	8198245.812992215	662569279520.1381	168484587.68162763
8	-8260501411.424482	-11912045.116125666	-121916909.90807547

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	331	31
1	331	31

end0.0ms

sample523.0ms

Algorithm

intervals

Results

193.0ms	6130×	body	80	valid
87.0ms	727×	body	640	valid
55.0ms	361×	body	1280	valid
42.0ms	479×	body	320	valid
18.0ms	303×	body	160	valid

Details

analyze72.0ms

sample19.0ms

simplify277.0ms

prune5.0ms

localize7.0ms

rewrite25.0ms

series30.0ms

simplify45.0ms

prune100.0ms

localize7.0ms

rewrite25.0ms

series25.0ms

simplify47.0ms

prune89.0ms

localize9.0ms

rewrite63.0ms

series49.0ms

simplify76.0ms

prune222.0ms

localize12.0ms

rewrite46.0ms

series120.0ms

simplify56.0ms

prune201.0ms

regimes187.0ms

bsearch28.0ms

simplify8.0ms

end0.0ms

sample523.0ms

Profiling