Details

analyze595.0ms

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample41.0ms

Algorithm

intervals

Results

9.0ms	35×	body	2560	valid
8.0ms	157×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	22×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	9×	body	160	valid
1.0ms	17×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	9×	body	80	invalid

simplify479.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune12.0ms

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: 33.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5743	1403

prune130.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.2b

Counts

95 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
8.7b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
19.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`div-inv` `distribute-lft-out` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
50.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4932	2261
1	4932	2261

prune133.0ms

Filtered

96 candidates to 125 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 5.1b

Counts

134 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
0.7b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
19.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 71

Calls

4 calls:

7.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5326	1109

prune99.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 5.0b

Counts

91 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.0b	(* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
3.3b	(/ (* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
19.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
46×	`associate-r`
44×	`times-frac`
37×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`neg-mul-1` `prod-exp` `cbrt-unprod`
3×	`distribute-frac-neg` `associate-l` `associate-/r*` `sqrt-prod`
2×	`flip3--` `sqrt-div` `associate-*r/` `associate-/r/` `distribute-rgt-neg-out` `flip--` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `associate-/l/` `associate-/l`

Counts

4 → 117

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(/ (* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
42.0ms	(/ (* a (/ (neg c) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4926	1733
1	4926	1733

prune94.0ms

Filtered

88 candidates to 129 candidates (-46.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	129	9	138

Merged error: 5.0b

Counts

138 → 9

regimes279.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.5b against oracle of 5.7b and baseline of 29.1b

bsearch59.0ms

Steps

Iters	Range	Point
1	2.1109504708566102e+110	2.21554162003082e+110	2.1370982581501626e+110
11	-1.613943986483335e-289	1.506762825593828e-308	-4.178574910302904e-307
9	-1.2480166232968403e+157	-3.093195726440134e+150	-1.5492270254018601e+152

Iters

Range

Point

2.1109504708566102e+110

2.21554162003082e+110

2.1370982581501626e+110

-1.613943986483335e-289

1.506762825593828e-308

-4.178574910302904e-307

-1.2480166232968403e+157

-3.093195726440134e+150

-1.5492270254018601e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	66
1	101	66

end0.0ms

sample1.0s

Algorithm

intervals

Results

253.0ms	1059×	body	2560	valid
222.0ms	5091×	body	80	valid
184.0ms	911×	body	1280	valid
81.0ms	486×	body	640	valid
32.0ms	99×	body	5120	valid
29.0ms	726×	body	80	nan
26.0ms	224×	body	320	valid
10.0ms	130×	body	160	valid
10.0ms	241×	body	80	invalid

Details

analyze595.0ms

sample41.0ms

simplify479.0ms

prune12.0ms

localize10.0ms

rewrite30.0ms

series70.0ms

simplify54.0ms

prune130.0ms

localize11.0ms

rewrite35.0ms

series110.0ms

simplify65.0ms

prune133.0ms

localize9.0ms

rewrite22.0ms

series78.0ms

simplify47.0ms

prune99.0ms

localize11.0ms

rewrite41.0ms

series112.0ms

simplify59.0ms

prune94.0ms

regimes279.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling