Details

Time bar (total: 5.5s)

sample70.0ms

Algorithm
intervals
Results
14.0ms507×pre80true
13.0ms148×body160valid
12.0ms251×body80nan
7.0ms67×body80valid
6.0ms41×body320valid

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: 42.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.6b
(+ (- b) (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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune188.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New78482
Fresh000
Picked101
Done000
Total79483

Merged error: 0.2b

Counts
83 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))))

rewrite49.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* 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)))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (/ (+ 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)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250032388

prune419.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh213
Picked101
Done000
Total1589167

Merged error: 0b

Counts
167 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))

rewrite50.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
150.0ms
(* (/ (+ 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 (120.0ms)

IterNodesCost
07352387
139472043
250022036

prune382.0ms

Filtered
158 candidates to 100 candidates (63.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1562158
Fresh358
Picked011
Done000
Total1598167

Merged error: 0b

Counts
167 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(/ (* 4.0 (* a c)) (* 2.0 a))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
46×add-sqr-sqrt *-un-lft-identity
44×times-frac
19×cbrt-undiv div-exp
18×add-cube-cbrt prod-exp cbrt-unprod
14×distribute-lft-out-- difference-of-squares
10×div-inv add-log-exp
8×associate-/r*
7×distribute-rgt-neg-in sqrt-prod
6×associate-/l*
4×pow1
3×flip3-- diff-log flip--
2×sub-neg frac-2neg clear-num associate-/r/
1×associate--l- neg-sub0 neg-log associate-/l/
Counts
4 → 129
Calls
4 calls:
16.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))

series287.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))

simplify113.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06652019
141381714
250021714

prune256.0ms

Filtered
141 candidates to 79 candidates (56.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1392141
Fresh246
Picked101
Done101
Total1436149

Merged error: 0b

Counts
149 → 6

regimes100.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02514
12514

end0.0ms

sample1.9s

Algorithm
intervals
Results
448.0ms16385×pre80true
443.0ms4841×body160valid
384.0ms8385×body80nan
193.0ms1415×body320valid
83.0ms1744×body80valid