Details

Time bar (total: 5.4s)

sample39.0ms

Algorithm
intervals
Results
7.0ms32×body2560valid
6.0ms179×body80valid
6.0ms36×body1280valid
4.0ms110×body80nan
1.0ms13×body320valid
1.0ms9×body640valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
25.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (* 3.0 a) c)
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms
(- (* b b) (* (* 3.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0307470
11303428
25001417

prune204.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 3.0 a) c))
4.1b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.5b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

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) (* (* 3.0 a) c))
21.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series633.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 3.0 a) c))
146.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
372.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06352579
131252333
250012320

prune444.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 3.0 a) c))
3.8b
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
13.4b
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
26×times-frac
19×cbrt-undiv div-exp
18×add-sqr-sqrt prod-exp cbrt-unprod
17×add-cube-cbrt *-un-lft-identity
10×associate-*r/ associate-/r/
8×associate-/l*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×associate-/r*
3×sqrt-prod
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 110
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
16.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 3.0 a) c))
151.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
180.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify128.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
06821937
144161476
250021435

prune327.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 3.0 a) c))
3.8b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
13.5b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
175×add-sqr-sqrt
174×*-un-lft-identity
118×add-cube-cbrt
45×associate-/l*
41×add-exp-log
28×distribute-lft-out-- difference-of-squares
24×div-exp
23×add-cbrt-cube
18×div-inv
17×sqrt-prod
14×distribute-rgt-neg-in
11×cbrt-undiv
6×add-log-exp
5×pow1
4×prod-exp associate-/r* associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l/
2×frac-2neg sqrt-div clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 239
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
24.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
12.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 3.0 a) c))
137.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
101.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify64.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011284220
150013871

prune556.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

regimes297.0ms

Accuracy

87.6% (2.9b remaining)

Error of 8.6b against oracle of 5.7b and baseline of 29.3b

bsearch184.0ms

Steps
ItersRangePoint
6
389373804.8346531
2491217878.346211
2445759453.473797
11
-2.9129801656201065e-276
-1.2526982634953812e-296
-2.874102223994037e-279
9
-3.2701742958179892e+66
-3.862137329617324e+60
-3.2376935939558906e+66

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04939
15139
25139

end0.0ms

sample1.1s

Algorithm
intervals
Results
244.0ms1095×body2560valid
212.0ms5837×body80valid
163.0ms935×body1280valid
97.0ms2925×body80nan
63.0ms448×body640valid
26.0ms101×body5120valid
24.0ms235×body320valid
9.0ms102×body160valid