Details

Time bar (total: 5.9s)

sample34.0ms

Algorithm
intervals
Results
15.0ms286×body80valid
3.0ms79×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize125.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
0227581
1878551
23814541
35002538

prune292.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize123.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.6b
(/ (* a c) b)
4.9b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt
8×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 81
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(/ (* a c) b)
47.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* a c) b)
183.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0440738
12043649
25001646

prune361.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize129.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.9b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity
33×times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 119
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
252.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
218.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07361436
136021249
250021207

prune577.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize130.0ms

Local error

Found 4 expressions with local error:

4.9b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
13.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
11×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt add-log-exp
6×pow1 sqrt-prod
5×times-frac associate-/r*
4×sqrt-div distribute-lft-out
3×flip3-- flip--
2×cbrt-undiv rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log div-exp associate-/r/
1×associate--l- neg-sub0 sub-neg frac-2neg flip3-+ neg-log prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l* difference-of-squares
Counts
4 → 72
Calls
4 calls:
253.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
6.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
80.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03851078
11601902
25001881

prune411.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

regimes254.0ms

Accuracy

92.6% (1.1b remaining)

Error of 7.9b against oracle of 6.9b and baseline of 21.5b

bsearch188.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
9
-3.226264717511912e+140
-2.187052964502477e+134
-3.505198499083171e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06272
16272

end0.0ms

sample823.0ms

Algorithm
intervals
Results
433.0ms8739×body80valid
126.0ms2862×body80nan