Details

sample50.0ms

Algorithm

intervals

Results

12.0ms	195×	body	80	valid
9.0ms	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

simplify12.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune229.0ms

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

localize16.0ms

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)))

rewrite42.0ms

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:

3.0ms	(- (* 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)))

series637.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
228.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
289.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	637	2582
1	3178	2341
2	5002	2328

prune388.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	160	9	169

Merged error: 4.5b

Counts

169 → 9

localize17.0ms

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))
19.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
17.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* 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))
284.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify202.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (186.0ms)

Iter	Nodes	Cost
0	706	1667
1	4685	1355
2	5001	1339

prune306.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Merged error: 4.5b

Counts

137 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
364×	`add-sqr-sqrt`
363×	`*-un-lft-identity`
167×	`add-cube-cbrt`
155×	`distribute-rgt-neg-in`
106×	`distribute-lft-neg-in` `neg-mul-1`
98×	`distribute-lft-out--` `difference-of-squares`
54×	`associate-/l*`
52×	`sqrt-prod`
16×	`associate-/r/`
13×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg`
2×	`neg-sub0` `frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 457

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(/ (/ (neg (* (* 4.0 a) c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (neg (* 2.0 a)))
12.0ms	(/ (neg (* (* 4.0 a) c)) (- (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:

44.0ms	(- (* b b) (* (* 4.0 a) c))
239.0ms	(/ (/ (neg (* (* 4.0 a) c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (neg (* 2.0 a)))
289.0ms	(/ (neg (* (* 4.0 a) c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

469 → 469

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1501	10226
1	5001	9991

prune1.0s

Filtered

469 candidates to 293 candidates (62.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	468	1	469
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	468	10	478

Merged error: 4.5b

Counts

478 → 10

regimes231.0ms

Accuracy

88.9% (3.0b remaining)

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

bsearch187.0ms

Steps

Iters	Range	Point
7	3.263606559388633e+51	2.0290859359939484e+53	4.17085281078165e+51
7	-2.999445374281946e-225	-1.6701016132161723e-226	-1.6837285519813682e-226
10	-1.563367407659085e+162	-1.2401372487940452e+151	-2.4193401252269544e+151

Iters

Range

Point

3.263606559388633e+51

2.0290859359939484e+53

4.17085281078165e+51

-2.999445374281946e-225

-1.6701016132161723e-226

-1.6837285519813682e-226

-1.563367407659085e+162

-1.2401372487940452e+151

-2.4193401252269544e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	30
1	66	30
2	66	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

301.0ms	1063×	body	2560	valid
301.0ms	5912×	body	80	valid
206.0ms	863×	body	1280	valid
142.0ms	2882×	body	80	nan
86.0ms	450×	body	640	valid
40.0ms	110×	body	5120	valid
32.0ms	230×	body	320	valid
13.0ms	116×	body	160	valid

Details

sample50.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite28.0ms

series342.0ms

simplify49.0ms

prune229.0ms

localize16.0ms

rewrite42.0ms

series637.0ms

simplify118.0ms

prune388.0ms

localize17.0ms

rewrite49.0ms

series640.0ms

simplify202.0ms

prune306.0ms

localize14.0ms

rewrite72.0ms

series652.0ms

simplify120.0ms

prune1.0s

regimes231.0ms

bsearch187.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling