Details

sample63.0ms

Algorithm

intervals

Results

14.0ms	176×	body	80	valid
11.0ms	33×	body	2560	valid
7.0ms	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	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 35.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify29.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5009	1230

prune171.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 5.7b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
14.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
47.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
65.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5568	2538

prune193.0ms

Filtered

79 candidates to 126 candidates (-59.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Merged error: 5.5b

Counts

135 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.5b	(- (neg 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))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 90

Calls

4 calls:

11.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(- (neg 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))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify36.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5165	1786

prune169.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Merged error: 5.5b

Counts

111 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `distribute-rgt-neg-in` `flip3-+` `neg-log` `flip-+`

Counts

4 → 60

Calls

4 calls:

9.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4955	956
1	4955	956

prune215.0ms

Filtered

62 candidates to 72 candidates (-16.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	71	10	81

Merged error: 5.5b

Counts

81 → 10

regimes438.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.5b

bsearch94.0ms

Steps

Iters	Range	Point
6	1.1487243557305423e+102	6.148420459531844e+102	3.3017963849877737e+102
8	-7.67443757966827e-305	8.126837495347253e-308	-6.542684670484036e-309
9	-1.5966504054646543e+104	-1.4637683111029664e+99	-4.7868277875676773e+101

Iters

Range

Point

1.1487243557305423e+102

6.148420459531844e+102

3.3017963849877737e+102

-7.67443757966827e-305

8.126837495347253e-308

-6.542684670484036e-309

-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	62
1	51	62

end0.0ms

sample1.8s

Algorithm

intervals

Results

352.0ms	1070×	body	2560	valid
333.0ms	5830×	body	80	valid
241.0ms	906×	body	1280	valid
167.0ms	2972×	body	80	nan
105.0ms	484×	body	640	valid
50.0ms	130×	body	5120	valid
31.0ms	198×	body	320	valid
11.0ms	102×	body	160	valid

Details

sample63.0ms

simplify3.0ms

prune8.0ms

localize12.0ms

rewrite30.0ms

series71.0ms

simplify29.0ms

prune171.0ms

localize13.0ms

rewrite47.0ms

series137.0ms

simplify35.0ms

prune193.0ms

localize16.0ms

rewrite31.0ms

series95.0ms

simplify36.0ms

prune169.0ms

localize24.0ms

rewrite23.0ms

series65.0ms

simplify50.0ms

prune215.0ms

regimes438.0ms

bsearch94.0ms

simplify1.0ms

end0.0ms

sample1.8s

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