Details

Time bar (total: 4.8s)

sample43.0ms

Algorithm
intervals
Results
19.0ms275×body80valid
5.0ms85×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

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: 20.7b

Counts
2 → 1

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

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))
11.0ms
(- (- 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)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0227581
1878551
23814541
35002538

prune262.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New621072
Fresh000
Picked101
Done000
Total631073

Merged error: 7.0b

Counts
73 → 10

localize114.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
6.1b
(/ (* a c) b)
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

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 add-log-exp
6×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 83
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
18.0ms
(/ (* a c) b)
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0478774
12145683
25002678

prune314.0ms

Filtered
95 candidates to 67 candidates (70.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New89695
Fresh369
Picked101
Done000
Total9312105

Merged error: 5.9b

Counts
105 → 12

localize108.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b
(- (* b b) (* (* 4.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
11.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0362863
11529768
25001759

prune281.0ms

Filtered
88 candidates to 63 candidates (71.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh4711
Picked101
Done000
Total8812100

Merged error: 5.7b

Counts
100 → 12

localize123.0ms

Local error

Found 4 expressions with local error:

2.3b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

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-/l*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×neg-sub0 flip3-- sqrt-div diff-log div-sub flip-- associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- frac-times associate-+l- associate-+r- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative flip-+
Counts
4 → 121
Calls
4 calls:
16.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07761487
136251298
250011254

prune446.0ms

Filtered
133 candidates to 96 candidates (72.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1321133
Fresh01111
Picked101
Done000
Total13312145

Merged error: 5.7b

Counts
145 → 12

regimes239.0ms

Accuracy

88.4% (1.8b remaining)

Error of 8.0b against oracle of 6.2b and baseline of 21.4b

bsearch167.0ms

Steps
ItersRangePoint
7
4.4312058130773924e+95
1.951780157010812e+97
8.668740171701315e+95
9
-8.211399685419546e+34
-2.0557429965048975e+28
-8.122404781735759e+34

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06357
16357

end0.0ms

sample1.0s

Algorithm
intervals
Results
593.0ms8699×body80valid
189.0ms2958×body80nan