Details

Time bar (total: 4.6s)

sample40.0ms

Algorithm
intervals
Results
18.0ms276×body80valid
6.0ms92×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

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: 20.9b

Counts
2 → 1

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune292.0ms

Filtered
78 candidates to 62 candidates (79.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New69978
Fresh000
Picked101
Done000
Total70979

Merged error: 8.6b

Counts
79 → 9

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
4.3b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.7b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff
Counts
4 → 88
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
61.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0454743
12159659
25002652

prune349.0ms

Filtered
100 candidates to 73 candidates (73.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New928100
Fresh538
Picked101
Done000
Total9811109

Merged error: 7.8b

Counts
109 → 11

localize113.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
9×add-exp-log add-cube-cbrt add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
5.0ms
(* (* 4.0 a) c)
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 4.0 a) c)
96.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0337530
11440479
25002467

prune319.0ms

Filtered
92 candidates to 71 candidates (77.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New88492
Fresh4610
Picked101
Done000
Total9310103

Merged error: 7.7b

Counts
103 → 10

localize120.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt c)
0.9b
(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
1.0b
(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
24.7b
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt fma-def add-log-exp
9×add-cube-cbrt
5×pow1
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube log1p-expm1-u
3×cbrt-prod distribute-lft-neg-in sqrt-prod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg pow1/3 diff-log prod-diff neg-log flip-+
Counts
4 → 73
Calls
4 calls:
1.0ms
(cbrt c)
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
4.0ms
(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
4.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series427.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt c)
96.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
65.0ms
(- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
89.0ms
(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0308850
11236747
25001690

prune314.0ms

Filtered
85 candidates to 73 candidates (85.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New85085
Fresh099
Picked011
Done000
Total851095

Merged error: 7.7b

Counts
95 → 10

regimes210.0ms

Accuracy

88.1% (1.7b remaining)

Error of 8.2b against oracle of 6.5b and baseline of 20.9b

bsearch138.0ms

Steps
ItersRangePoint
7
0.008549975533169097
1.4731263457460937
1.4443031837246074
6
-2.8573914020723285e+158
-3.9930817527980913e+157
-4.0541474925789433e+157

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05663
15663

end0.0ms

sample1.0s

Algorithm
intervals
Results
580.0ms8726×body80valid
184.0ms2883×body80nan