Details

Time bar (total: 5.6s)

sample41.0ms

Algorithm
intervals
Results
19.0ms282×body80valid
6.0ms91×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: 19.9b

Counts
2 → 1

localize122.0ms

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)))

rewrite16.0ms

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 flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
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)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0149476
1576446
22486444
35001440

prune249.0ms

Filtered
66 candidates to 50 candidates (75.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New58866
Fresh000
Picked101
Done000
Total59867

Merged error: 5.8b

Counts
67 → 8

localize122.0ms

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 div-exp 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 diff-log flip-+
Counts
4 → 75
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)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
18.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0392629
11966544
25001541

prune367.0ms

Filtered
87 candidates to 60 candidates (69.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New83487
Fresh347
Picked101
Done000
Total87895

Merged error: 4.5b

Counts
95 → 8

localize124.0ms

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)))

rewrite44.0ms

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×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 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 113
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (* 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)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
209.0ms
(/ (* 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)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06871327
135201144
250011103

prune483.0ms

Filtered
125 candidates to 89 candidates (71.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1232125
Fresh077
Picked101
Done000
Total1249133

Merged error: 4.5b

Counts
133 → 9

localize131.0ms

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)))

rewrite68.0ms

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×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 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) b)))
25.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
213.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) b)))
53.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09992793
150022344

prune667.0ms

Filtered
160 candidates to 117 candidates (73.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1600160
Fresh088
Picked011
Done000
Total1609169

Merged error: 4.5b

Counts
169 → 9

regimes227.0ms

Accuracy

93.7% (0.9b remaining)

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

bsearch234.0ms

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

sample1.0s

Algorithm
intervals
Results
586.0ms8732×body80valid
190.0ms2977×body80nan