Details

Time bar (total: 16.8s)

sample73.0ms

Algorithm
intervals
Results
41.0ms283×body80valid
8.0ms94×body80nan

simplify155.0ms

Counts
1 → 1
Iterations
IterNodes
done168
7168
6166
5160
4151
3127
274
138
020

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize170.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (* b b) (* (* 4.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
6.0ms
(- (* b b) (* (* 4.0 a) c))
6.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 4.0 a) c))
59.0ms
(- (* b b) (* (* 4.0 a) c))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
66 → 66
Iterations
IterNodes
done5002
32175
2510
1157
062

prune536.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.3b

localize159.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* b b) (* (* 4.0 a) c))
3.5b
(/ (* 2.0 c) (+ (- b) (- (* (* 2.0 c) (/ a b)) b)))
4.8b
(* (* 2.0 c) (/ a b))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
14×times-frac add-cube-cbrt
13×associate-*r*
10×pow1
7×prod-exp cbrt-unprod
6×add-log-exp
5×associate-/r*
4×cbrt-undiv div-exp distribute-lft-out
3×pow-prod-down sqrt-prod
2×distribute-rgt-neg-in flip3-- sqrt-div associate-/r/ div-inv flip--
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* associate-*r/ *-commutative flip-+ associate-/l*
Counts
4 → 87
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(/ (* 2.0 c) (+ (- b) (- (* (* 2.0 c) (/ a b)) b)))
35.0ms
(* (* 2.0 c) (/ a b))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* b b) (* (* 4.0 a) c))
251.0ms
(/ (* 2.0 c) (+ (- b) (- (* (* 2.0 c) (/ a b)) b)))
37.0ms
(* (* 2.0 c) (/ a b))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
99 → 99
Iterations
IterNodes
done5001
22301
1514
0177

prune872.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.3b

localize195.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (* 2.0 c) (/ a b))
9.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt add-cbrt-cube add-exp-log
13×*-un-lft-identity associate-*r* add-cube-cbrt
11×pow1
9×times-frac
8×add-log-exp
6×prod-exp sqrt-prod cbrt-unprod
4×sqrt-div
3×flip3-- pow-prod-down flip--
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-exp
1×associate--l- neg-sub0 sub-neg associate-*l* neg-log associate-*r/ *-commutative div-inv difference-of-squares
Counts
4 → 78
Calls
4 calls:
32.0ms
(* (* 2.0 c) (/ a b))
18.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* 2.0 c) (/ a b))
104.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
101.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
90 → 90
Iterations
IterNodes
done5001
21562
1439
0161

prune914.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize178.0ms

Local error

Found 4 expressions with local error:

9.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative flip3-+ neg-log associate-+l- flip-+
Counts
4 → 58
Calls
4 calls:
12.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
70 → 70
Iterations
IterNodes
done5000
32860
2724
1229
086

prune633.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

regimes542.0ms

Accuracy

92.7% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 20.3b

bsearch243.0ms

Steps
ItersRangePoint
5
6.972240796235003e+85
2.4695855038465726e+86
2.216005534325193e+86
9
-6.117539429929052e+154
-3.6285784997486435e+148
-7.406561173130012e+149

simplify28.0ms

Iterations
IterNodes
done62
162
051

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s8725×body80valid
380.0ms2954×body80nan