Details

Time bar (total: 4.9s)

sample52.0ms

Algorithm
intervals
Results
10.0ms33×body2560valid
9.0ms181×body80valid
7.0ms27×body1280valid
5.0ms101×body80nan
4.0ms21×body640valid
2.0ms5×body5120valid
1.0ms6×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))
0.4b
(- (* b b) (* (* 4.0 a) c))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25001674

prune218.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New75782
Fresh000
Picked101
Done000
Total76783

Merged error: 6.3b

Counts
83 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 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) (* (* 4.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06512694
131392439
250022426

prune407.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1633166
Fresh156
Picked011
Done000
Total1649173

Merged error: 6.2b

Counts
173 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.5b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

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×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ 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 → 72
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0485952
12854745
25001737

prune212.0ms

Filtered
84 candidates to 58 candidates (69.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New82284
Fresh347
Picked011
Done101
Total86793

Merged error: 6.2b

Counts
93 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
0.6b
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
26×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
16×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×div-exp associate-/r*
5×pow1 cbrt-undiv div-inv
4×sqrt-prod
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div prod-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 1-exp neg-log clear-num associate-/r/ cbrt-unprod
Counts
4 → 94
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05421186
122311070
250011068

prune258.0ms

Filtered
106 candidates to 80 candidates (75.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1051106
Fresh055
Picked011
Done011
Total1058113

Merged error: 6.2b

Counts
113 → 8

regimes179.0ms

Accuracy

94.9% (1.2b remaining)

Error of 7.2b against oracle of 6.0b and baseline of 30.4b

bsearch178.0ms

Steps
ItersRangePoint
6
6.333441064762502e+69
2.6854631551896503e+70
2.6627070202833933e+70
8
-1.820258497722058e-231
-5.550307098040058e-234
-5.631981429033553e-234
8
-1.666412824726956e+124
-3.415589734864014e+119
-5.377788818048344e+121

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
15128
25128

end0.0ms

sample1.5s

Algorithm
intervals
Results
321.0ms5875×body80valid
313.0ms1055×body2560valid
226.0ms902×body1280valid
149.0ms2921×body80nan
83.0ms426×body640valid
38.0ms100×body5120valid
35.0ms242×body320valid
10.0ms106×body160valid