Details

Time bar (total: 6.6s)

sample36.0ms

Algorithm
intervals
Results
14.0ms279×body80valid
4.0ms90×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize85.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms
(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

prune272.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.1b
(/ (* a c) b)
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 71
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* b b) (* (* 4.0 a) c))
66.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
18.0ms
(/ (* a c) b)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0396579
11957504
25002502

prune322.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize96.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.0b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
3×flip3-- associate-/r* sqrt-prod flip-- div-inv
2×sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 109
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
162.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* b b) (* (* 4.0 a) c))
47.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
95.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06891267
135381094
250021044

prune577.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize126.0ms

Local error

Found 4 expressions with local error:

3.6b
(cbrt (/ c (cbrt b)))
3.6b
(cbrt (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))) (* 2 b)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
62×cbrt-prod
39×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
9×add-exp-log add-cbrt-cube
5×pow1
4×add-log-exp
3×associate-/r* sqrt-prod div-inv
2×cbrt-undiv cbrt-div flip3-- pow1/3 sqrt-div div-exp associate-/r/ flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod associate-/l*
Counts
4 → 100
Calls
4 calls:
3.0ms
(cbrt (/ c (cbrt b)))
3.0ms
(cbrt (/ c (cbrt b)))
1.2s
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))) (* 2 b)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (/ c (cbrt b)))
150.0ms
(cbrt (/ c (cbrt b)))
66.0ms
(/ (* 2.0 c) (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (* (cbrt (/ c (cbrt b))) (cbrt (/ c (cbrt b))))) (cbrt (/ c (cbrt b))))) (* 2 b)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04421406
117631248
250011188

prune604.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

regimes273.0ms

Accuracy

92.3% (1.1b remaining)

Error of 7.8b against oracle of 6.7b and baseline of 20.9b

bsearch155.0ms

Steps
ItersRangePoint
6
2.905752377093217e+53
1.5130510757279288e+54
1.4394867919093142e+54
9
-3.819893964099896e+158
-6.080633474453611e+152
-7.031354366652439e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06772
16772

end0.0ms

sample954.0ms

Algorithm
intervals
Results
458.0ms8711×body80valid
142.0ms2998×body80nan