Details

Time bar (total: 4.4s)

sample36.0ms

Algorithm
intervals
Results
7.0ms206×body80valid
6.0ms32×body2560valid
4.0ms23×body1280valid
3.0ms103×body80nan
3.0ms19×body640valid
0.0ms3×body320valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

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: 33.7b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b
(- (* b b) (* (* 3.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
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)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms
(- (* b b) (* (* 3.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0433855
11670751
25001736

prune249.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New948102
Fresh000
Picked101
Done000
Total958103

Merged error: 6.1b

Counts
103 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b
(- (* b b) (* (* 3.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/r*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 89
Calls
4 calls:
11.0ms
(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 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)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0399830
11688721
25001704

prune227.0ms

Filtered
101 candidates to 80 candidates (79.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New983101
Fresh077
Picked011
Done000
Total9811109

Merged error: 6.1b

Counts
109 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b
(- (* b b) (* (* 3.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
24×add-cube-cbrt
19×associate-*r*
16×add-cbrt-cube
13×associate-*l*
10×fma-def add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1 distribute-rgt-neg-in
6×unswap-sqr
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log associate-*l/ *-commutative flip-+
Counts
4 → 124
Calls
4 calls:
18.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
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)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms
(- (* b b) (* (* 3.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06451311
131291145
250011130

prune287.0ms

Filtered
136 candidates to 99 candidates (72.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1342136
Fresh189
Picked011
Done011
Total13512147

Merged error: 6.1b

Counts
147 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
0.4b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.8b
(- (* b b) (* (* 3.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 106
Calls
4 calls:
11.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
7.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
74.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
48.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04801247
119041005
25002973

prune216.0ms

Filtered
118 candidates to 77 candidates (65.3%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1171118
Fresh099
Picked011
Done022
Total11713130

Merged error: 6.1b

Counts
130 → 13

regimes453.0ms

Accuracy

83% (4.8b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 33.9b

bsearch100.0ms

Steps
ItersRangePoint
10
2.319058093766752e-122
4.8666627780759835e-109
2.86122009180682e-109
8
-7.85932808106197e+156
-9.798525195327539e+152
-3.2144453057618232e+153

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13115

end0.0ms

sample1.2s

Algorithm
intervals
Results
247.0ms1056×body2560valid
226.0ms5771×body80valid
174.0ms954×body1280valid
109.0ms2946×body80nan
68.0ms482×body640valid
32.0ms114×body5120valid
25.0ms227×body320valid
11.0ms110×body160valid