Details

Time bar (total: 10.3s)

sample83.0ms

Algorithm
intervals
Results
30.0ms274×body80valid
19.0ms92×body80nan

simplify12.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize142.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(+ (- 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)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log flip-+
Counts
4 → 57
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (* b b) (* (* 4.0 a) c))
124.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify130.0ms

Counts
69 → 69

prune442.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.1b

localize141.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.4b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
8×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×distribute-rgt-neg-in 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* difference-of-squares
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 80
Calls
4 calls:
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
21.0ms
(/ (* a c) b)
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
258.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
25.0ms
(/ (* a c) b)
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Counts
92 → 92

prune575.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

localize163.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity 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×associate-/r* unswap-sqr
4×distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod div-inv
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- 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 → 118
Calls
4 calls:
49.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
53.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
297.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify126.0ms

Counts
130 → 130

prune904.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.6b

localize185.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
67×add-sqr-sqrt
64×times-frac
47×add-cbrt-cube
41×*-un-lft-identity
36×cbrt-prod
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
6×associate-/r*
4×div-inv distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod
2×flip3-- sqrt-div sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- 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 → 153
Calls
4 calls:
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
41.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series1.1s

Counts
4 → 12
Calls
4 calls:
598.0ms
(+ (- 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))))
315.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Counts
165 → 165

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.6b

regimes448.0ms

Accuracy

91.5% (1.2b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 21.4b

bsearch284.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.269665110513951e+61
10
-1.437929939467773e+163
-1.7004475472942417e+152
-1.3404533579516929e+154

simplify45.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8718×body80valid
372.0ms2845×body80nan