Details

Time bar (total: 7.2s)

sample49.0ms

Algorithm
intervals
Results
18.0ms290×body80valid
7.0ms105×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune6.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.1b

Counts
2 → 1

localize147.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0248644
1898606
23863590
35001586

prune419.0ms

Filtered
75 candidates to 60 candidates (20.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New67875
Fresh000
Picked101
Done000
Total68876

Merged error: 8.0b

Counts
76 → 8

localize148.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.2b
(/ (* a c) b)
27.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series53.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0455639
12202559
25001553

prune565.0ms

Filtered
86 candidates to 65 candidates (24.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New82486
Fresh257
Picked101
Done000
Total85994

Merged error: 6.4b

Counts
94 → 9

localize150.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
3.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
27.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
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
3×associate-/r* sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 112
Calls
4 calls:
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
14.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
10.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07501327
137841149
250011098

prune1.3s

Filtered
124 candidates to 91 candidates (26.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1213124
Fresh088
Picked101
Done000
Total12211133

Merged error: 6.4b

Counts
133 → 11

localize159.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
1.9b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
27.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
30×add-sqr-sqrt
27×add-cbrt-cube
25×times-frac
17×*-un-lft-identity
16×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
13×add-cube-cbrt associate-*r*
10×cbrt-prod
8×sqrt-prod add-log-exp unswap-sqr
7×pow1 associate-*l*
3×associate-/r* div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 111
Calls
4 calls:
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
28.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series127.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b))))
58.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (cbrt (sqrt b)))) (/ (cbrt c) (cbrt (sqrt b))))) (* 2 b)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
010022015
147721723
250021720

prune1.7s

Filtered
123 candidates to 93 candidates (24.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1203123
Fresh2810
Picked101
Done000
Total12311134

Merged error: 6.4b

Counts
134 → 11

regimes402.0ms

Accuracy

92.5% (1.1b remaining)

Error of 7.9b against oracle of 6.8b and baseline of 21.2b

bsearch179.0ms

Steps
ItersRangePoint
4
3.1466272044128187e+123
6.05509838734878e+123
3.3833596292024335e+123
10
-8.56091843340189e+161
-1.1976703346365243e+147
-1.3658955203717612e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06994
16994

end0.0ms

sample1.2s

Algorithm
intervals
Results
572.0ms8732×body80valid
183.0ms2913×body80nan

Profiling

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