Details

Time bar (total: 15.9s)

sample84.0ms

Algorithm
intervals
Results
37.0ms285×body80valid
11.0ms98×body80nan

simplify175.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize145.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
72 → 72

prune423.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize146.0ms

Local error

Found 4 expressions with local error:

8.2b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls
4 calls:
15.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
70 → 70

prune630.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize152.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.4b
(/ (* a c) b)
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite166.0ms

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 associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 81
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
11.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
288.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
33.0ms
(/ (* a c) b)
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify831.0ms

Counts
93 → 93

prune525.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize132.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.6b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
21.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite794.0ms

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-/r*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 119
Calls
4 calls:
38.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
685.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series577.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
301.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
131 → 131

prune637.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes409.0ms

Accuracy

90.4% (1.4b remaining)

Error of 8.0b against oracle of 6.6b and baseline of 20.8b

bsearch292.0ms

Steps
ItersRangePoint
10
2.1111705398262576e+94
5.238272520421586e+105
9.00908844538866e+104
8
-3.3488929396586777e+52
-8.270377620091702e+49
-2.662744446675922e+52

simplify898.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
858.0ms8684×body80valid
738.0ms2870×body80nan