Details

Time bar (total: 4.1s)

sample78.0ms

Algorithm
intervals
Results
14.0ms33×body1280valid
13.0ms182×body80valid
12.0ms32×body2560valid
5.0ms81×body80nan
3.0ms14×body640valid
1.0ms6×body320valid
1.0ms8×body160valid
0.0ms1×body5120valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.9b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b
(* (* 3.0 a) c)
1.6b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*r* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*l* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 76
Calls
4 calls:
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
5.0ms
(* (* 3.0 a) c)
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms
(* (* 3.0 a) c)
17.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0423738
11903648
25001637

prune153.0ms

Filtered
64 candidates to 88 candidates (-37.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80888
Fresh000
Picked101
Done000
Total81889

Merged error: 4.2b

Counts
89 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.6b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.2b
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

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
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
14.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06442693
131432447
250012434

prune300.0ms

Filtered
111 candidates to 166 candidates (-49.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1624166
Fresh167
Picked011
Done000
Total16311174

Merged error: 4.1b

Counts
174 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.6b
(/ (/ 1 (/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))) (* 3.0 a))
7.4b
(/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))
18.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
260×add-sqr-sqrt
259×*-un-lft-identity
159×add-cube-cbrt
154×add-exp-log
117×associate-/l*
94×div-exp
72×add-cbrt-cube
50×distribute-lft-out-- difference-of-squares
40×cbrt-undiv
30×prod-exp
28×sqrt-prod
25×distribute-rgt-neg-in
18×div-inv
12×cbrt-unprod
10×rec-exp 1-exp
8×add-log-exp
5×pow1
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num associate-/r* associate-/r/ flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 344
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
32.0ms
(/ (/ 1 (/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))) (* 3.0 a))
15.0ms
(/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series90.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
32.0ms
(/ (/ 1 (/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))) (* 3.0 a))
22.0ms
(/ (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (* a c))
20.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
356 → 356
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
017786142
150025529

prune572.0ms

Filtered
189 candidates to 356 candidates (-88.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3560356
Fresh099
Picked011
Done011
Total35611367

Merged error: 4.1b

Counts
367 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (* 3.0 a) c)
1.6b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

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:
3.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(* (* 3.0 a) c)
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series41.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(* (* 3.0 a) c)
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0302468
11299428
25001417

prune82.0ms

Filtered
52 candidates to 72 candidates (-38.5%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New71172
Fresh178
Picked011
Done022
Total721183

Merged error: 4.1b

Counts
83 → 11

regimes488.0ms

Accuracy

83.4% (4.4b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 32.8b

bsearch71.0ms

Steps
ItersRangePoint
9
1.318498360392027e-43
5.6448683288908945e-37
5.585633092657171e-43
11
-3.2417942991699406e+183
-6.054191780274212e+145
-1.921995618228008e+148

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
13416

end0.0ms

sample1.5s

Algorithm
intervals
Results
326.0ms1101×body2560valid
302.0ms5823×body80valid
202.0ms845×body1280valid
127.0ms2639×body80nan
86.0ms445×body640valid
41.0ms116×body5120valid
32.0ms232×body320valid
10.0ms104×body160valid

Profiling

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