Details

Time bar (total: 5.3s)

sample48.0ms

Algorithm
intervals
Results
10.0ms39×body2560valid
9.0ms180×body80valid
7.0ms30×body1280valid
4.0ms100×body80nan
2.0ms12×body640valid
1.0ms4×body5120valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

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: 33.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.9b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
50.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674

prune216.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74882
Fresh000
Picked011
Done000
Total74983

Merged error: 6.0b

Counts
83 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.0b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

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) (* 4.0 (* a c)))))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
154.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify104.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06402692
129112439
250012426

prune389.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1633166
Fresh077
Picked011
Done101
Total16411175

Merged error: 5.9b

Counts
175 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

13.1b
(cbrt (+ 0 (* 4.0 (* a c))))
13.1b
(cbrt (+ 0 (* 4.0 (* a c))))
13.1b
(cbrt (+ 0 (* 4.0 (* a c))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 sqrt-prod flip-+
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 54
Calls
4 calls:
2.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
102.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
103.0ms
(cbrt (+ 0 (* 4.0 (* a c))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0239531
1877490
25001456

prune264.0ms

Filtered
66 candidates to 61 candidates (92.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh099
Picked011
Done011
Total661177

Merged error: 5.9b

Counts
77 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

9.0b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
62×*-un-lft-identity
42×times-frac
30×add-cube-cbrt
16×distribute-lft-out-- difference-of-squares
14×associate-/r* sqrt-prod
8×add-exp-log distribute-rgt-neg-in add-cbrt-cube
6×pow1 associate-/l*
4×flip3-- sqrt-div associate-/r/ flip-- associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ div-inv
Counts
4 → 124
Calls
4 calls:
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (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))))

series527.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
03351978
115211834
250011818

prune428.0ms

Filtered
136 candidates to 98 candidates (72.1%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1360136
Fresh088
Picked011
Done022
Total13611147

Merged error: 5.9b

Counts
147 → 11

regimes218.0ms

Accuracy

87.7% (3.4b remaining)

Error of 8.8b against oracle of 5.4b and baseline of 33.0b

bsearch211.0ms

Steps
ItersRangePoint
8
4.1433580792185867e+68
2.296567048635946e+73
2.425005151022521e+69
9
8.879718769428669e-232
8.562504904991818e-226
9.159933660727599e-231
10
-1.218044689452388e+116
-9.206374310818687e+98
-3.4298668229790213e+115

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04629
14829
24829

end0.0ms

sample1.3s

Algorithm
intervals
Results
284.0ms1019×body2560valid
279.0ms5854×body80valid
204.0ms919×body1280valid
137.0ms2973×body80nan
80.0ms458×body640valid
34.0ms105×body5120valid
31.0ms237×body320valid
9.0ms98×body160valid

Profiling

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