Details

Time bar (total: 5.1s)

sample37.0ms

Algorithm
intervals
Results
8.0ms37×body2560valid
6.0ms180×body80valid
4.0ms23×body1280valid
3.0ms75×body80nan
2.0ms17×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.1b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.1b
(sqrt (- (* b b) (* (* 3.0 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
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
46.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0400780
11529686
25002675

prune236.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New721082
Fresh000
Picked101
Done000
Total731083

Merged error: 5.9b

Counts
83 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.5b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.7b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

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
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 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)))))
6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series478.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
174.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
79.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify123.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
06472692
131142439
250012426

prune368.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1633166
Fresh279
Picked101
Done000
Total16610176

Merged error: 5.8b

Counts
176 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.5b
(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
8.7b
(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
41×add-sqr-sqrt
34×*-un-lft-identity
30×add-cbrt-cube
27×associate-*r*
24×times-frac
17×add-cube-cbrt prod-exp
16×div-exp
9×cbrt-undiv cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×associate-/l/
4×frac-times distribute-rgt-neg-in flip3-+ associate-*l/ flip-+
3×rec-exp flip3-- 1-exp associate-*l* flip-- unswap-sqr
2×sqrt-div diff-log associate-*r/ associate-/r/ un-div-inv div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms
(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
18.0ms
(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series466.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
143.0ms
(/ (* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
175.0ms
(* (+ 0 (* 3.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify179.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (163.0ms)

IterNodesCost
07311779
146251453
250011437

prune289.0ms

Filtered
134 candidates to 87 candidates (64.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh099
Picked011
Done000
Total13410144

Merged error: 5.8b

Counts
144 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
0.6b
(- (* b b) (* (* 3.0 a) c))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
113×*-un-lft-identity
62×add-sqr-sqrt
61×add-cube-cbrt
26×distribute-lft-out
19×associate-/l*
13×distribute-rgt-neg-in
10×add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
3×cbrt-undiv div-exp associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- sqrt-div div-sub sum-log flip--
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log neg-log clear-num flip-+ associate-/l/
Counts
4 → 137
Calls
4 calls:
14.0ms
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
4.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
74.0ms
(- (* b b) (* (* 3.0 a) c))
100.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06101962
123531864
250021843

prune299.0ms

Filtered
149 candidates to 102 candidates (68.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1481149
Fresh088
Picked011
Done011
Total14811159

Merged error: 5.8b

Counts
159 → 11

regimes408.0ms

Accuracy

80.5% (5.3b remaining)

Error of 10.7b against oracle of 5.4b and baseline of 32.7b

bsearch98.0ms

Steps
ItersRangePoint
9
7.30455191105786e-90
1.8075577067303308e-84
1.4297233981116778e-84
7
-2.501148282372368e+59
-1.593441833549377e+57
-2.21751057489785e+59

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
13416

end0.0ms

sample1.1s

Algorithm
intervals
Results
234.0ms1050×body2560valid
221.0ms5823×body80valid
163.0ms883×body1280valid
101.0ms2908×body80nan
73.0ms488×body640valid
30.0ms243×body320valid
25.0ms91×body5120valid
9.0ms132×body160valid