Details

analyze266.0ms

Algorithm

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample37.0ms

Algorithm

intervals

Results

13.0ms	144×	body	160	valid
8.0ms	277×	pre	80	true
5.0ms	112×	body	80	valid
1.0ms	21×	body	80	nan

simplify247.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (245.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
27.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

series81.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
35.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune99.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.3b

Counts

83 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.2b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.3b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 155

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

series152.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
52.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
71.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune260.0ms

Filtered

124 candidates to 167 candidates (-34.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	156	11	167
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	161	11	172

Merged error: 0.0b

Counts

172 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

series103.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
57.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify70.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune125.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 0b

Counts

94 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))
0.6b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64` `times-frac_binary64` `sqrt-prod_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64` `cube-div_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `pow-pow_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
8.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))
7.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3)

series99.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
17.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3))
13.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) 3)

simplify44.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4937	1858
1	4937	1858

prune98.0ms

Filtered

72 candidates to 119 candidates (-65.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	119	11	130

Merged error: 0b

Counts

130 → 11

regimes217.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	22
1	87	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

423.0ms	4424×	body	160	valid
254.0ms	8829×	pre	80	true
179.0ms	3576×	body	80	valid
39.0ms	829×	body	80	nan

Details

analyze266.0ms

sample37.0ms

simplify247.0ms

prune10.0ms

localize10.0ms

rewrite30.0ms

series81.0ms

simplify50.0ms

prune99.0ms

localize12.0ms

rewrite43.0ms

series152.0ms

simplify61.0ms

prune260.0ms

localize12.0ms

rewrite25.0ms

series103.0ms

simplify70.0ms

prune125.0ms

localize16.0ms

rewrite35.0ms

series99.0ms

simplify44.0ms

prune98.0ms

regimes217.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling