Details

Time bar (total: 8.8s)

sample35.0ms

Algorithm
intervals
Results
15.0ms283×body80valid
4.0ms81×body80nan

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13538
26537
311437
413637
514837
614937
done14937

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize112.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

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:
12.0ms
(- (- b) (sqrt (- (* 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)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
75 → 75
Iterations

Useful iterations: 3 (599.0ms)

IterNodesCost
01001330
12461186
27661089
329201070
done50001070

prune282.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize118.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- add-log-exp
Counts
4 → 60
Calls
4 calls:
4.0ms
(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)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
72 → 72
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0521140
11301008
2434928
31651928
done5000924

prune339.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.2b

localize122.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.5b
(/ (* a c) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series243.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify673.0ms

Counts
86 → 86
Iterations

Useful iterations: 2 (168.0ms)

IterNodesCost
01731340
14611252
217451078
done50011078

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize118.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
4.3b
(* a (/ c b))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity
15×add-cube-cbrt
14×add-exp-log add-cbrt-cube
13×times-frac associate-*r*
8×add-log-exp
7×pow1
3×cbrt-undiv div-exp associate-*l* prod-exp associate-/r* sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log associate-/r/ flip-- div-inv distribute-lft-out unswap-sqr
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log clear-num *-commutative flip-+ associate-/l*
Counts
4 → 85
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
7.0ms
(* a (/ c b))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(/ (* 2.0 c) (- (* 2.0 (* a (/ c b))) (* 2 b)))
19.0ms
(* a (/ c b))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify758.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (194.0ms)

IterNodesCost
01971431
15261333
218211159
done50001159

prune364.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

regimes185.0ms

Accuracy

91.8% (1.2b remaining)

Error of 8.0b against oracle of 6.8b and baseline of 21.7b

bsearch166.0ms

Steps
ItersRangePoint
7
1.1889782913455773e+76
8.569650126343972e+77
1.454073572953768e+77
9
-2.5095870340849847e+160
-2.2087357092495854e+152
-2.2953165565822647e+153

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
047156
159156
done59156

end0.0ms

sample878.0ms

Algorithm
intervals
Results
461.0ms8726×body80valid
141.0ms2945×body80nan