Details

sample49.0ms

Algorithm

intervals

Results

12.0ms	195×	body	80	valid
8.0ms	37×	body	1280	valid
7.0ms	26×	body	2560	valid
3.0ms	73×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify11.0ms

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

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: 32.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(- (* b b) (* 4.0 (* a c)))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune220.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 4.6b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* 4.0 (* a c)))
2.9b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.6b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* 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))))

series656.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
236.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
299.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	626	2580
1	2991	2341
2	5003	2328

prune368.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	5	160
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 4.6b

Counts

169 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* 4.0 (* a c)))
2.9b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
8.6b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
37×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cbrt-cube`
27×	`associate-r`
24×	`times-frac`
17×	`add-cube-cbrt` `prod-exp`
16×	`div-exp`
9×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1`
6×	`sqrt-prod` `associate-/l/` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
3×	`rec-exp` `flip3--` `distribute-rgt-neg-in` `1-exp` `associate-l` `flip--` `unswap-sqr`
2×	`sqrt-div` `associate-*r/` `associate-/r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 116

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
18.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* 4.0 (* a c)))
232.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
299.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify166.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (151.0ms)

Iter	Nodes	Cost
0	686	1667
1	4349	1356
2	5002	1332

prune284.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Merged error: 4.6b

Counts

138 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.4b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b	(- (* b b) (* 4.0 (* a c)))
19.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

17.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms	(+ (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))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
84.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	525	1585
1	2550	1372
2	5001	1305

prune209.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 4.6b

Counts

136 → 10

regimes223.0ms

Accuracy

89% (3.0b remaining)

Error of 8.7b against oracle of 5.7b and baseline of 32.9b

bsearch197.0ms

Steps

Iters	Range	Point
7	3.263606559388633e+51	2.0290859359939484e+53	4.58958184988612e+51
8	1.4703555930409849e-245	1.7596017740419908e-242	1.0507151752689849e-244
10	-1.563367407659085e+162	-1.2401372487940452e+151	-2.4193401252269544e+151

Iters

Range

Point

3.263606559388633e+51

2.0290859359939484e+53

4.58958184988612e+51

1.4703555930409849e-245

1.7596017740419908e-242

1.0507151752689849e-244

-1.563367407659085e+162

-1.2401372487940452e+151

-2.4193401252269544e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	30
1	49	30
2	49	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

299.0ms	1063×	body	2560	valid
295.0ms	5912×	body	80	valid
207.0ms	863×	body	1280	valid
139.0ms	2882×	body	80	nan
83.0ms	450×	body	640	valid
40.0ms	110×	body	5120	valid
32.0ms	230×	body	320	valid
13.0ms	116×	body	160	valid

Details

sample49.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite28.0ms

series347.0ms

simplify46.0ms

prune220.0ms

localize13.0ms

rewrite45.0ms

series656.0ms

simplify101.0ms

prune368.0ms

localize14.0ms

rewrite49.0ms

series652.0ms

simplify166.0ms

prune284.0ms

localize12.0ms

rewrite35.0ms

series391.0ms

simplify67.0ms

prune209.0ms

regimes223.0ms

bsearch197.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling