Details

sample63.0ms

Algorithm

intervals

Results

13.0ms	188×	body	80	valid
12.0ms	44×	body	2560	valid
7.0ms	33×	body	1280	valid
5.0ms	105×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 36.8b

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))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune375.0ms

Filtered

82 candidates to 63 candidates (23.2%)

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: 5.9b

Counts

83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
27.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series138.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	635	2693
1	2974	2447
2	5001	2434

prune961.0ms

Filtered

166 candidates to 111 candidates (33.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	165	11	176

Merged error: 5.8b

Counts

176 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

14.0ms	(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* 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))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	470	914
1	2126	788
2	5001	776

prune368.0ms

Filtered

92 candidates to 65 candidates (29.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	92	11	103

Merged error: 5.8b

Counts

103 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
27.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	380	774
1	1335	699
2	5001	697

prune274.0ms

Filtered

84 candidates to 60 candidates (28.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	84	11	95

Merged error: 5.8b

Counts

95 → 11

regimes379.0ms

Accuracy

83.3% (4.5b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 32.8b

bsearch152.0ms

Steps

Iters	Range		Point
9	1.4958858181332487e-84	1.457638978688563e-75	7.723146983287944e-82
10	-8.56091843340189e+161	-1.1976703346365243e+147	-1.0090011346354097e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	14
1	31	14

end0.0ms

sample1.5s

Algorithm

intervals

Results

295.0ms	1089×	body	2560	valid
279.0ms	5799×	body	80	valid
200.0ms	910×	body	1280	valid
134.0ms	2913×	body	80	nan
88.0ms	496×	body	640	valid
38.0ms	116×	body	5120	valid
32.0ms	229×	body	320	valid
8.0ms	93×	body	160	valid

Details

sample63.0ms

simplify9.0ms

prune5.0ms

localize11.0ms

rewrite27.0ms

series68.0ms

simplify43.0ms

prune375.0ms

localize16.0ms

rewrite47.0ms

series138.0ms

simplify98.0ms

prune961.0ms

localize13.0ms

rewrite34.0ms

series65.0ms

simplify56.0ms

prune368.0ms

localize10.0ms

rewrite27.0ms

series63.0ms

simplify42.0ms

prune274.0ms

regimes379.0ms

bsearch152.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling