Details

sample55.0ms

Algorithm

intervals

Results

12.0ms	44×	body	2560	valid
8.0ms	169×	body	80	valid
8.0ms	33×	body	1280	valid
4.0ms	89×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify202.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

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	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b	(- (* b b) (* (* 4.0 a) c))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5863	1230

prune155.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.2b

Counts

83 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.5b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.7b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `sqrt-prod` `add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `distribute-rgt-neg-in` `flip--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

10.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
55.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4974	2702
1	4974	2702

prune174.0ms

Filtered

84 candidates to 132 candidates (-57.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	133	9	142

Merged error: 6.1b

Counts

142 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.8b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:

10.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4991	1785
1	4991	1785

prune144.0ms

Filtered

71 candidates to 102 candidates (-43.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	102	9	111

Merged error: 5.9b

Counts

111 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
5.6b	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
15.2b	(- (neg b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4932	1113
1	4932	1113

prune113.0ms

Filtered

58 candidates to 80 candidates (-37.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	78	11	89

Merged error: 5.9b

Counts

89 → 11

regimes309.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.9b

bsearch79.0ms

Steps

Iters	Range	Point
5	1.1994113433831075e+59	2.551497614016684e+59	1.722862686819048e+59
7	-1.5288248722247393e-196	-2.8030120978369076e-198	-2.8405866436241524e-198
9	-7.957515769842868e+111	-7.937815030826972e+105	-3.3421727427471946e+111

Iters

Range

Point

1.1994113433831075e+59

2.551497614016684e+59

1.722862686819048e+59

-1.5288248722247393e-196

-2.8030120978369076e-198

-2.8405866436241524e-198

-7.957515769842868e+111

-7.937815030826972e+105

-3.3421727427471946e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	158	75
1	158	75

end0.0ms

sample1.6s

Algorithm

intervals

Results

315.0ms	1082×	body	2560	valid
295.0ms	5801×	body	80	valid
211.0ms	888×	body	1280	valid
144.0ms	2933×	body	80	nan
87.0ms	455×	body	640	valid
38.0ms	256×	body	320	valid
35.0ms	99×	body	5120	valid
11.0ms	119×	body	160	valid

Details

sample55.0ms

simplify202.0ms

prune10.0ms

localize11.0ms

rewrite29.0ms

series63.0ms

simplify42.0ms

prune155.0ms

localize12.0ms

rewrite47.0ms

series127.0ms

simplify70.0ms

prune174.0ms

localize13.0ms

rewrite29.0ms

series82.0ms

simplify45.0ms

prune144.0ms

localize17.0ms

rewrite30.0ms

series50.0ms

simplify39.0ms

prune113.0ms

regimes309.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling