Details

sample66.0ms

Algorithm

intervals

Results

17.0ms	47×	body	2560	valid
12.0ms	167×	body	80	valid
9.0ms	32×	body	1280	valid
7.0ms	107×	body	80	nan
4.0ms	16×	body	640	valid
2.0ms	4×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

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:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune234.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
4.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

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:

2.0ms	(- (* b b) (* (* 4.0 a) c))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 a) c))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320

prune433.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
16.5b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
153.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	486	961
1	2986	812
2	5001	807

prune246.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3--` `flip--` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`associate-*r/` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `flip3-+` `clear-num` `associate-/r*` `flip-+` `div-inv`

Counts

4 → 72

Calls

4 calls:

16.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4.0 a) c))))))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	433	1456
1	2849	1059
2	5001	970

prune323.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes202.0ms

Accuracy

86.3% (3.7b remaining)

Error of 9.3b against oracle of 5.6b and baseline of 32.2b

bsearch182.0ms

Steps

Iters	Range		Point
5	1.5768668050097488e+97	4.47556672091261e+97	3.3602536904640645e+97
8	5.985396523089189e-220	7.016417792036605e-216	4.53688576501435e-218
7	-2.3860448187824777e+68	-1.0929352752278947e+66	-2.3202538172935113e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	29
1	52	29
2	52	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

413.0ms	5747×	body	80	valid
394.0ms	1108×	body	2560	valid
278.0ms	926×	body	1280	valid
183.0ms	2804×	body	80	nan
111.0ms	481×	body	640	valid
47.0ms	106×	body	5120	valid
39.0ms	215×	body	320	valid
15.0ms	117×	body	160	valid