Details

Time bar (total: 4.9s)

sample36.0ms

Algorithm
intervals
Results
15.0ms277×body80valid
5.0ms91×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: 16.9b

Counts
2 → 1

localize117.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(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
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (- 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)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0246646
1890606
23700588
35001584

prune267.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New70575
Fresh000
Picked101
Done000
Total71576

Merged error: 7.2b

Counts
76 → 5

localize116.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.6b
(/ (* a c) b)
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
8×add-log-exp
7×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-sub neg-log flip-+
Counts
4 → 81
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
22.0ms
(/ (* a c) b)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0489748
12180661
25002653

prune327.0ms

Filtered
93 candidates to 68 candidates (73.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New91293
Fresh044
Picked101
Done000
Total92698

Merged error: 5.9b

Counts
98 → 6

localize114.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ c b) (/ b a))
0.1b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-sqr-sqrt
11×times-frac
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 associate-/r*
4×difference-of-squares
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+ distribute-lft-out--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num frac-sub cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
12.0ms
(- (/ c b) (/ b a))
11.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(- (/ c b) (/ b a))
186.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0440791
11642695
25001681

prune308.0ms

Filtered
88 candidates to 67 candidates (76.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh145
Picked101
Done000
Total85994

Merged error: 5.8b

Counts
94 → 9

localize122.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
4.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
20.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity 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×associate-/l* unswap-sqr
4×distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod div-inv
2×flip3-- sqrt-div sum-log flip-- associate-/l/ distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative flip-+
Counts
4 → 119
Calls
4 calls:
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
14.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
55.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07871471
136641286
250021241

prune530.0ms

Filtered
131 candidates to 97 candidates (74.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1301131
Fresh088
Picked101
Done000
Total1319140

Merged error: 5.8b

Counts
140 → 9

regimes232.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.8b against oracle of 6.6b and baseline of 21.4b

bsearch197.0ms

Steps
ItersRangePoint
7
6.66182219120084e+105
6.051047097450507e+107
4.678783870646951e+107
7
2.9616153673195096e-176
8.660844906217239e-175
2.9914658520063943e-176
5
-1.3368392339655721e+157
-5.498919035160523e+156
-5.571070222109471e+156

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06372
16372

end0.0ms

sample894.0ms

Algorithm
intervals
Results
468.0ms8745×body80valid
153.0ms2942×body80nan