Details

Time bar (total: 25.1s)

sample154.0ms

Algorithm
intervals
Results
53.0ms194×body80valid
20.0ms35×body2560valid
11.0ms28×body1280valid
7.0ms79×body80nan
4.0ms11×body640valid
2.0ms4×body5120valid
1.0ms5×body320valid
1.0ms4×body160valid

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
68.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize21.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite393.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
209.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
104.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms
(sqrt (- (* b_2 b_2) (* a c)))
27.0ms
(- (* b_2 b_2) (* a c))

series596.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(sqrt (- (* b_2 b_2) (* a c)))
159.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
134.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(- (* b_2 b_2) (* a c))

simplify4.3s

Counts
73 → 100
Calls
73 calls:
Slowest
449.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
333.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
295.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
277.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
265.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize20.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
72.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
43.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
94.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
80.0ms
(sqrt (- (* b_2 b_2) (* a c)))
56.0ms
(- (* b_2 b_2) (* a c))

simplify4.3s

Counts
73 → 100
Calls
73 calls:
Slowest
428.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
320.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
310.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
284.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))
230.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
47.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(sqrt (- (* b_2 b_2) (* a c)))
91.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts
38 → 76
Calls
38 calls:
Slowest
310.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
268.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
258.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
209.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
184.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune800.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.5b

localize44.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×sqrt-prod add-log-exp
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
68.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
103.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
74.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.9s

Counts
38 → 76
Calls
38 calls:
Slowest
358.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
321.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
283.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
221.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
221.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune884.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.5b

regimes406.0ms

Accuracy

83.7% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.1b

bsearch89.0ms

end13.0ms

sample3.9s

Algorithm
intervals
Results
1.0s950×body1280valid
885.0ms1024×body2560valid
834.0ms5880×body80valid
321.0ms2988×body80nan
209.0ms437×body640valid
108.0ms226×body320valid
87.0ms109×body5120valid
47.0ms121×body160valid