Details

Time bar (total: 4.2s)

sample39.0ms

Algorithm
intervals
Results
8.0ms203×body80valid
6.0ms31×body1280valid
5.0ms23×body2560valid
3.0ms79×body80nan
3.0ms17×body640valid
1.0ms4×body5120valid
0.0ms4×body320valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

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: 32.9b

Counts
2 → 1

localize15.0ms

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)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
12.0ms
(/ (- (- 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))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune245.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New81889
Fresh000
Picked101
Done000
Total82890

Merged error: 6.2b

Counts
90 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
14.0ms
(/ 1 (/ (* 2.0 a) (- (- 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))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05331804
125441605
250021531

prune270.0ms

Filtered
137 candidates to 73 candidates (53.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1334137
Fresh437
Picked011
Done000
Total1378145

Merged error: 6.2b

Counts
145 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×sub-neg div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv distribute-rgt-in frac-times rec-exp distribute-rgt-neg-in distribute-lft-in sqrt-div 1-exp associate-*r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 88
Calls
4 calls:
16.0ms
(* (/ 1 (* 2.0 a)) (- (- 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))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
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))))

simplify59.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04751026
12257896
25001893

prune231.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh156
Picked011
Done011
Total1008108

Merged error: 6.2b

Counts
108 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.8b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
17.0b
(- (pow b 2) (pow b 2))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
19×add-exp-log
16×difference-of-squares
15×add-cube-cbrt
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- add-log-exp
8×distribute-lft-out--
7×div-exp
5×pow1 associate-/l/
4×cbrt-undiv prod-exp
3×flip3-+ times-frac associate-/r* sqrt-prod flip-+
2×frac-times flip3-- sqrt-div associate-*r/ sum-log flip-- cbrt-unprod distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
7.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
8.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series167.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms
(- (pow b 2) (pow b 2))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify198.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (188.0ms)

IterNodesCost
0595778
13991571
25002555

prune305.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1181119
Fresh145
Picked101
Done022
Total1207127

Merged error: 6.1b

Counts
127 → 7

regimes166.0ms

Accuracy

92.5% (1.8b remaining)

Error of 7.2b against oracle of 5.4b and baseline of 29.4b

bsearch147.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
5.78921681038671e+118
4
2.7062129888597453e-95
4.861630376334293e-95
2.7444235711350233e-95
8
-1.1853128331038075e+151
-1.0790742320216938e+148
-6.382198803132883e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04323
14323

end0.0ms

sample1.1s

Algorithm
intervals
Results
241.0ms1063×body2560valid
227.0ms5846×body80valid
165.0ms849×body1280valid
106.0ms2863×body80nan
68.0ms463×body640valid
31.0ms105×body5120valid
27.0ms231×body320valid
9.0ms126×body160valid