Details

Time bar (total: 6.9s)

sample44.0ms

Algorithm
intervals
Results
19.0ms282×body80valid
6.0ms81×body80nan

simplify8.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize112.0ms

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))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

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:
26.0ms
(+ (- b) (sqrt (- (* 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)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Counts
75 → 75

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize106.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.8b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 77
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
10.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
22.0ms
(/ (* a c) b)
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Counts
89 → 89

prune373.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize111.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.4b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
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
4×sqrt-prod
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div diff-log associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
168.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
115.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify89.0ms

Counts
127 → 127

prune657.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.7b

localize120.0ms

Local error

Found 4 expressions with local error:

6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
6.2b
(cbrt (/ a (* (cbrt b) (cbrt b))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 63
Calls
4 calls:
7.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
7.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
10.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
153.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
149.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Counts
75 → 75

prune510.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.7b

regimes329.0ms

Accuracy

91.6% (1.2b remaining)

Error of 8.1b against oracle of 6.9b and baseline of 20.8b

bsearch213.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
1.3910222191204909e+74
8
-1.173014798652874e+100
-8.67642318333193e+96
-1.1200838301149146e+100

simplify2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
858.0ms8755×body80valid
550.0ms2933×body80nan