Details

Time bar (total: 6.8s)

sample55.0ms

Algorithm
intervals
Results
23.0ms273×body80valid
7.0ms76×body80nan

simplify8.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

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:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms
(- (- 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)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Counts
75 → 75

prune313.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize106.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
6.5b
(/ (* a c) b)
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

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 add-log-exp
6×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 83
Calls
4 calls:
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
10.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
21.0ms
(/ (* a c) b)
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Counts
95 → 95

prune372.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize99.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
8×add-exp-log add-cbrt-cube
7×times-frac associate-/r* add-log-exp
6×add-cube-cbrt sqrt-prod distribute-lft-out-- difference-of-squares
4×pow1
3×flip3-- distribute-rgt-neg-in flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/r/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 64
Calls
3 calls:
47.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series349.0ms

Counts
3 → 9
Calls
3 calls:
190.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify38.0ms

Counts
73 → 73

prune290.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize106.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
25.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite741.0ms

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-/l*
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in div-inv
2×neg-sub0 flip3-- sqrt-div diff-log div-sub flip-- associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- frac-times associate-+l- associate-+r- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative flip-+
Counts
4 → 121
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
661.0ms
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
88.0ms
(/ (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)) (* 2.0 a))
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Counts
133 → 133

prune592.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

regimes240.0ms

Accuracy

91.6% (1.2b remaining)

Error of 7.7b against oracle of 6.5b and baseline of 20.8b

bsearch165.0ms

Steps
ItersRangePoint
5
1.0433798175544735e+152
3.237299440315181e+152
1.1155337065557208e+152
8
-1.173014798652874e+100
-8.67642318333193e+96
-1.1200838301149146e+100

simplify1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s8717×body80valid
268.0ms2914×body80nan