Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
8.0ms	29×	body	2560	valid
7.0ms	29×	body	1280	valid
4.0ms	88×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	7×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

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))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune235.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 6.1b

Counts

90 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
0.5b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
96.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	992
1	2048	866
2	5002	857

prune209.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	98	7	105

Merged error: 6.1b

Counts

105 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

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

series371.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	361	863
1	1479	768
2	5002	759

prune384.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Merged error: 6.0b

Counts

95 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.5b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
160.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	502	969
1	3028	812
2	5001	794

prune194.0ms

Filtered

83 candidates to 63 candidates (75.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Merged error: 6.0b

Counts

91 → 9

regimes207.0ms

Accuracy

88.5% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 33.1b

bsearch204.0ms

Steps

Iters	Range	Point
9	1.0750476286016474e+90	7.888871963785644e+94	2.875793803750894e+92
8	-6.384489542018262e-201	-9.024224085054453e-204	-6.268104183272254e-203
9	-2.0560691900424517e+121	-1.9544616975333591e+114	-6.4084520243200054e+119

Iters

Range

Point

1.0750476286016474e+90

7.888871963785644e+94

2.875793803750894e+92

-6.384489542018262e-201

-9.024224085054453e-204

-6.268104183272254e-203

-2.0560691900424517e+121

-1.9544616975333591e+114

-6.4084520243200054e+119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample1.4s

Algorithm

intervals

Results

305.0ms	1057×	body	2560	valid
303.0ms	5970×	body	80	valid
213.0ms	907×	body	1280	valid
146.0ms	2969×	body	80	nan
87.0ms	439×	body	640	valid
38.0ms	103×	body	5120	valid
27.0ms	193×	body	320	valid
12.0ms	123×	body	160	valid

Details

sample48.0ms

simplify14.0ms

prune3.0ms

localize15.0ms

rewrite30.0ms

series301.0ms

simplify47.0ms

prune235.0ms

localize13.0ms

rewrite33.0ms

series295.0ms

simplify57.0ms

prune209.0ms

localize13.0ms

rewrite32.0ms

series371.0ms

simplify46.0ms

prune384.0ms

localize15.0ms

rewrite35.0ms

series352.0ms

simplify101.0ms

prune194.0ms

regimes207.0ms

bsearch204.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling