Details

analyze742.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample44.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	26×	body	80	nan
1.0ms	14×	body	80	invalid

simplify629.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	5048	37

prune14.0ms

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: 17.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 62

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4935	1063
1	4935	1063

prune211.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Merged error: 4.3b

Counts

75 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (* 2.0 c) (+ (* a (* c (/ 2.0 b))) (* b -2)))
5.2b	(* a (* c (/ 2.0 b)))
21.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(/ (* 2.0 c) (+ (* a (* c (/ 2.0 b))) (* b -2)))
6.0ms	(* a (* c (/ 2.0 b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (* 2.0 c) (+ (* a (* c (/ 2.0 b))) (* b -2)))
6.0ms	(* a (* c (/ 2.0 b)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4921	1103
1	4921	1103

prune186.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Merged error: 4.3b

Counts

90 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b	(* c (* (/ 2.0 b) (cbrt a)))
3.0b	(* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a))))
3.6b	(/ (* 2.0 c) (+ (* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a)))) (* b -2)))
21.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
36×	`add-cbrt-cube`
31×	`pow1`
28×	`prod-exp` `cbrt-unprod`
18×	`pow-prod-down`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`cbrt-undiv` `div-exp`
4×	`associate-l` `add-log-exp`
3×	`times-frac` `associate-r/` `associate-/r` `sqrt-prod`
2×	`sqrt-div` `associate-r` `associate-l/` `associate-/r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

9.0ms	(* c (* (/ 2.0 b) (cbrt a)))
15.0ms	(* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a))))
16.0ms	(/ (* 2.0 c) (+ (* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a)))) (* b -2)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* c (* (/ 2.0 b) (cbrt a)))
10.0ms	(* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a))))
22.0ms	(/ (* 2.0 c) (+ (* (* (cbrt a) (cbrt a)) (* c (* (/ 2.0 b) (cbrt a)))) (* b -2)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4981	1160
1	4981	1160

prune184.0ms

Filtered

65 candidates to 104 candidates (-60.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	103	7	110

Merged error: 4.3b

Counts

110 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b	(* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a)))
3.6b	(/ (* 2.0 c) (+ (* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a))) (* b -2)))
21.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
30×	`prod-exp`
26×	`add-cbrt-cube`
14×	`cbrt-unprod`
11×	`*-un-lft-identity`
10×	`pow1`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`div-exp`
4×	`cbrt-undiv`
3×	`pow-to-exp` `times-frac` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `associate-r` `associate-l` `neg-log` `associate-l/` `clear-num` `-commutative` `flip--` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a)))
14.0ms	(/ (* 2.0 c) (+ (* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a))) (* b -2)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a)))
21.0ms	(/ (* 2.0 c) (+ (* (* c (pow (cbrt a) 2)) (* (/ 2.0 b) (cbrt a))) (* b -2)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4962	1197
1	4962	1197

prune163.0ms

Filtered

64 candidates to 96 candidates (-50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 4.3b

Counts

103 → 7

regimes289.0ms

Accuracy

93.3% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 21.1b

bsearch102.0ms

Steps

Iters	Range	Point
9	5.0977943293546214e+129	5.100855502619046e+136	7.95014129048444e+132
8	-4.3110756026756833e-299	-1.0135985580458824e-302	-8.39637267994406e-301
7	-2.2125953678132807e+54	-2.6582108611640813e+52	-2.174680080071626e+54

Iters

Range

Point

5.0977943293546214e+129

5.100855502619046e+136

7.95014129048444e+132

-4.3110756026756833e-299

-1.0135985580458824e-302

-8.39637267994406e-301

-2.2125953678132807e+54

-2.6582108611640813e+52

-2.174680080071626e+54

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	320	176
1	320	176

end0.0ms

sample1.0s

Algorithm

intervals

Results

745.0ms	8000×	body	80	valid
53.0ms	628×	body	80	nan
33.0ms	356×	body	80	invalid

Details

analyze742.0ms

sample44.0ms

simplify629.0ms

prune14.0ms

localize24.0ms

rewrite43.0ms

series70.0ms

simplify54.0ms

prune211.0ms

localize25.0ms

rewrite30.0ms

series55.0ms

simplify57.0ms

prune186.0ms

localize29.0ms

rewrite48.0ms

series73.0ms

simplify68.0ms

prune184.0ms

localize34.0ms

rewrite40.0ms

series62.0ms

simplify49.0ms

prune163.0ms

regimes289.0ms

bsearch102.0ms

simplify5.0ms

end0.0ms

sample1.0s

Profiling