Details

Time bar (total: 10.3s)

sample81.0ms

Algorithm
intervals
Results
39.0ms282×body80valid
9.0ms97×body80nan

simplify13.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize142.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

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:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Counts
75 → 75

prune463.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.7b

localize146.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (* a c) b)
3.6b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

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:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (* a c) b)
60.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms
(/ (* a c) b)
104.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
98.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Counts
89 → 89

prune505.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize136.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
4.3b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite392.0ms

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:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
257.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
81.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
61.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Counts
127 → 127

prune908.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize147.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
3.6b
(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite605.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
67×add-sqr-sqrt
61×times-frac
47×add-cbrt-cube
36×cbrt-prod
33×*-un-lft-identity
31×associate-*r*
29×cbrt-undiv add-cube-cbrt div-exp
25×prod-exp cbrt-unprod
12×unswap-sqr
11×associate-*l*
8×add-log-exp
7×pow1
4×sqrt-prod div-inv
3×flip3-- associate-/r* flip--
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 → 150
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
429.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
164.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))) (* 2 b)))
92.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Counts
162 → 162

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

regimes385.0ms

Accuracy

86.3% (2.0b remaining)

Error of 9.0b against oracle of 7.0b and baseline of 21.7b

bsearch363.0ms

Steps
ItersRangePoint
8
6.830756908302209e+71
2.772849885831336e+75
1.1686313088576502e+75
9
-0.00024022063624403673
-1.822584514918214e-10
-0.00023778849264226667

simplify26.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.7s8769×body80valid
264.0ms2898×body80nan