Details

Time bar (total: 5.1s)

sample40.0ms

Algorithm
intervals
Results
19.0ms275×body80valid
5.0ms73×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

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: 20.4b

Counts
2 → 1

localize113.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(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:
4.0ms
(- (* 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)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
0227581
1878551
23814541
35002538

prune256.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New66672
Fresh000
Picked101
Done000
Total67673

Merged error: 8.4b

Counts
73 → 6

localize114.0ms

Local error

Found 4 expressions with local error:

11.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

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

series289.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0225725
1835631
23414609
35001589

prune271.0ms

Filtered
72 candidates to 60 candidates (83.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh055
Picked011
Done000
Total72678

Merged error: 8.4b

Counts
78 → 6

localize117.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.5b
(/ (* a c) b)
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

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:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
174.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
24.0ms
(/ (* a c) b)
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0440738
12043649
25001646

prune319.0ms

Filtered
93 candidates to 65 candidates (69.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89493
Fresh044
Picked101
Done011
Total90999

Merged error: 6.7b

Counts
99 → 9

localize124.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
5.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
17.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
213.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07361436
136021249
250021207

prune455.0ms

Filtered
131 candidates to 94 candidates (71.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1283131
Fresh167
Picked101
Done011
Total13010140

Merged error: 6.7b

Counts
140 → 10

regimes215.0ms

Accuracy

92.7% (1.0b remaining)

Error of 7.6b against oracle of 6.7b and baseline of 20.0b

bsearch178.0ms

Steps
ItersRangePoint
8
4.5418805312590315e+84
1.9690305180656607e+89
4.309841870567569e+88
8
-3.270551254255918e+118
-2.131753517190888e+115
-1.169783528148572e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06071
16071

end0.0ms

sample1.0s

Algorithm
intervals
Results
591.0ms8699×body80valid
186.0ms2900×body80nan

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