Details

Time bar (total: 4.8s)

sample45.0ms

Algorithm
intervals
Results
10.0ms34×body2560valid
7.0ms172×body80valid
6.0ms32×body1280valid
3.0ms79×body80nan
2.0ms9×body5120valid
2.0ms16×body640valid
1.0ms9×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: 35.6b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b
(sqrt (- (* b b) (* 4.0 (* 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) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (- 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:
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674

prune238.0ms

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: 6.1b

Counts
83 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.8b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

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) (* 4.0 (* a c)))))
20.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify104.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
06402692
129442439
250012426

prune425.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1633166
Fresh459
Picked011
Done000
Total1679176

Merged error: 6.0b

Counts
176 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0413627
12231543
25001535

prune222.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New81182
Fresh167
Picked101
Done011
Total83891

Merged error: 6.0b

Counts
91 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
108×div-exp
56×prod-exp
49×add-cbrt-cube
37×1-exp
31×times-frac
24×add-sqr-sqrt
23×cbrt-undiv *-un-lft-identity
19×add-cube-cbrt
13×associate-/l*
12×rec-exp cbrt-unprod
10×add-log-exp
5×pow1 flip3-- associate-/r/ flip--
4×sqrt-prod
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 140
Calls
4 calls:
24.0ms
(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series379.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (/ 1 1) (* (/ 2.0 (* (/ 4.0 1) c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
09031941
141981560
250011525

prune268.0ms

Filtered
152 candidates to 71 candidates (46.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1511152
Fresh246
Picked011
Done011
Total1537160

Merged error: 6.0b

Counts
160 → 7

regimes155.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.1b

bsearch186.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
3.8636444360254825e+121
7
-6.311599190677229e-174
-9.330924568125125e-176
-8.277677308210192e-175
9
-1.8864815038392082e+94
-1.5243980513895428e+89
-6.875360452843506e+92

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05128
15328
25328

end0.0ms

sample1.3s

Algorithm
intervals
Results
438.0ms1052×body2560valid
235.0ms5820×body80valid
168.0ms891×body1280valid
107.0ms2865×body80nan
67.0ms469×body640valid
31.0ms111×body5120valid
26.0ms235×body320valid
9.0ms122×body160valid