Details

Time bar (total: 5.8s)

sample45.0ms

Algorithm
intervals
Results
23.0ms282×body80valid
6.0ms91×body80nan

simplify16.0ms

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: 19.9b

Counts
2 → 1

localize113.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune298.0ms

Filtered
78 candidates to 62 candidates (79.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New70878
Fresh000
Picked101
Done000
Total71879

Merged error: 5.8b

Counts
79 → 8

localize117.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b b) (* (* 4.0 a) c))
3.1b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.5b
(/ (* a c) b)
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt
8×times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out
3×sqrt-prod
2×flip3-- distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 85
Calls
4 calls:
4.0ms
(- (* 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)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 4.0 a) c))
180.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
18.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0418685
12079598
25001591

prune329.0ms

Filtered
97 candidates to 70 candidates (72.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New93497
Fresh347
Picked101
Done000
Total978105

Merged error: 4.5b

Counts
105 → 8

localize125.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b b) (* (* 4.0 a) c))
3.1b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
5.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
33×times-frac
30×add-exp-log *-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
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
3×sqrt-prod div-inv
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip--
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 123
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
15.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
205.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
52.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify87.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07141403
136361218
250021168

prune539.0ms

Filtered
135 candidates to 99 candidates (73.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1332135
Fresh077
Picked101
Done000
Total1349143

Merged error: 4.5b

Counts
143 → 9

localize133.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b b) (* (* 4.0 a) c))
3.1b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) b)))
4.1b
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
63×add-sqr-sqrt times-frac
47×add-cbrt-cube
37×*-un-lft-identity
36×cbrt-prod
31×associate-*r*
29×cbrt-undiv add-cube-cbrt div-exp
25×prod-exp cbrt-unprod
12×unswap-sqr
11×associate-*l*
7×pow1
6×add-log-exp
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u div-inv distribute-lft-out
3×sqrt-prod
2×flip3-- distribute-rgt-neg-in sqrt-div associate-/r/ flip--
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 158
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) b)))
32.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
216.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) b)))
48.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010262897
150012456

prune715.0ms

Filtered
170 candidates to 126 candidates (74.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1700170
Fresh088
Picked011
Done000
Total1709179

Merged error: 4.5b

Counts
179 → 9

regimes226.0ms

Accuracy

93.7% (0.9b remaining)

Error of 7.8b against oracle of 6.9b and baseline of 21.0b

bsearch227.0ms

Steps
ItersRangePoint
10
1.5450168366677492e+128
2.0521185469434633e+142
3.8440821224174866e+136
11
-3.334524116472281e+99
-2.3662890435539516e+79
-2.527728060421314e+94

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06172
16172

end0.0ms

sample1.2s

Algorithm
intervals
Results
590.0ms8732×body80valid
340.0ms2977×body80nan