Details

Time bar (total: 5.6s)

sample55.0ms

Algorithm
intervals
Results
12.0ms164×body160valid
10.0ms516×pre80true
9.0ms260×body80nan
5.0ms44×body320valid
2.0ms48×body80valid

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: 45.0b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
39.2b
(+ (- b) (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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
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))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune211.0ms

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: 0.2b

Counts
83 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 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)))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
145.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
06422664
131752400
250032388

prune445.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1549163
Fresh516
Picked101
Done000
Total16010170

Merged error: 0.0b

Counts
170 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.3b
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
130×pow1
49×add-sqr-sqrt
36×pow-prod-up
33×add-exp-log add-cbrt-cube
32×pow-prod-down
30×times-frac
29×*-un-lft-identity
24×difference-of-squares
22×pow-sqr
21×add-cube-cbrt sqr-pow
18×pow-plus
17×prod-exp cbrt-unprod
13×pow2
10×associate-/l*
9×unpow-prod-down
4×associate-*r* distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow pow-exp associate-/r* rem-cube-cbrt
2×flip3-+ associate-*r/ associate-*l* associate-/r/ *-commutative flip-+ associate-/l/
1×cbrt-undiv distribute-rgt-in cube-mult pow-to-exp flip3-- frac-2neg distribute-lft-in unpow3 div-sub cube-prod swap-sqr div-exp clear-num flip-- div-inv unswap-sqr
Counts
4 → 173
Calls
4 calls:
25.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
13.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
10.0ms
(* (* b b) (* b b))
6.0ms
(pow (* (* 4.0 a) c) 3)

series291.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
74.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
30.0ms
(* (* b b) (* b b))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify144.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
07022174
138412029
250012015

prune622.0ms

Filtered
185 candidates to 96 candidates (51.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1850185
Fresh099
Picked011
Done000
Total18510195

Merged error: 0.0b

Counts
195 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
61×*-un-lft-identity
51×add-exp-log
46×times-frac
29×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×add-log-exp
8×cbrt-undiv distribute-rgt-neg-in sqrt-prod cbrt-unprod
7×associate-*r* associate-/r*
6×pow1
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×diff-log div-inv associate-/l*
2×sub-neg associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times frac-2neg flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 146
Calls
4 calls:
9.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify140.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
07352387
139472043
250022036

prune386.0ms

Filtered
158 candidates to 100 candidates (63.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1571158
Fresh358
Picked011
Done011
Total1608168

Merged error: 0.0b

Counts
168 → 8

regimes134.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02712
12912
22912

end0.0ms

sample1.5s

Algorithm
intervals
Results
351.0ms4911×body160valid
320.0ms16410×pre80true
289.0ms8410×body80nan
144.0ms1345×body320valid
66.0ms1744×body80valid