Details

sample59.0ms

Algorithm

intervals

Results

10.0ms	33×	body	2560	valid
10.0ms	176×	body	80	valid
8.0ms	29×	body	1280	valid
4.0ms	78×	body	80	nan
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	16
1	91	16

prune8.0ms

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: 35.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

12.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
10.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4959	1319
1	4959	1319

prune173.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 5.7b

Counts

85 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.8b	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
9.9b	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
50×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`div-inv`
3×	`flip3--` `flip3-+` `div-sub` `distribute-frac-neg` `sqrt-prod` `flip--` `flip-+` `associate-/l/`
2×	`frac-2neg` `sub0-neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 122

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
10.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
48.0ms	(/ (/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
67.0ms	(/ (- 0 (* 4.0 (* a c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5094	3114

prune269.0ms

Filtered

100 candidates to 134 candidates (-34.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	5	134
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	133	11	144

Merged error: 5.6b

Counts

144 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
15.0b	(/ (* a c) (* a 2.0))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

6.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(/ (* a c) (* a 2.0))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(/ (* a c) (* a 2.0))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4941	742
1	4941	742

prune128.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	73	10	83

Merged error: 5.6b

Counts

83 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
0.5b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

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 → 72

Calls

4 calls:

8.0ms	(/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
6.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 4.0 (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5531	1322

prune133.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	83	11	94

Merged error: 5.6b

Counts

94 → 11

regimes335.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.6b

bsearch88.0ms

Steps

Iters	Range	Point
6	1.1487243557305423e+102	6.148420459531844e+102	2.480507165822079e+102
7	-3.9639939611996993e-296	-1.2313747004456891e-297	-2.459714357747724e-297
9	-1.5966504054646543e+104	-1.4637683111029664e+99	-4.7868277875676773e+101

Iters

Range

Point

1.1487243557305423e+102

6.148420459531844e+102

2.480507165822079e+102

-3.9639939611996993e-296

-1.2313747004456891e-297

-2.459714357747724e-297

-1.5966504054646543e+104

-1.4637683111029664e+99

-4.7868277875676773e+101

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	61
1	51	61

end0.0ms

sample1.8s

Algorithm

intervals

Results

346.0ms	1070×	body	2560	valid
344.0ms	5830×	body	80	valid
236.0ms	906×	body	1280	valid
165.0ms	2972×	body	80	nan
102.0ms	484×	body	640	valid
53.0ms	130×	body	5120	valid
31.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample59.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite33.0ms

series71.0ms

simplify44.0ms

prune173.0ms

localize16.0ms

rewrite37.0ms

series140.0ms

simplify39.0ms

prune269.0ms

localize14.0ms

rewrite23.0ms

series47.0ms

simplify37.0ms

prune128.0ms

localize13.0ms

rewrite24.0ms

series73.0ms

simplify43.0ms

prune133.0ms

regimes335.0ms

bsearch88.0ms

simplify1.0ms

end0.0ms

sample1.8s

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