Details

Time bar (total: 50.2s)

sample208.0ms

Algorithm
intervals
Results
66.0ms268×body80nan
51.0ms164×body160valid
36.0ms524×pre80true
15.0ms32×body320valid
10.0ms60×body80valid

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize48.0ms

Local error

Found 4 expressions with local error:

38.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
90.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
30.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
100.0ms
(sqrt (- (* b b) (* (* c a) 4)))
82.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
81.0ms
(- (* b b) (* (* c a) 4))

simplify6.0s

Counts
49 → 88
Calls
49 calls:
Slowest
647.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
572.0ms
(- b (* 2 (/ (* a c) b)))
443.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
309.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
287.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune99.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (* -2 (/ (* a c) b)) (* 2 a))
0.2b
(/ (* a c) b)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
39×add-cbrt-cube add-exp-log
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
2×pow1 clear-num frac-2neg insert-posit16 div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
Slowest
16.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms
(/ (* a c) b)

series58.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
21.0ms
(/ (* a c) b)

simplify11.5s

Counts
37 → 59
Calls
37 calls:
Slowest
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
944.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune609.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.6b

localize24.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ (* -2 (* a c)) (* (* 2 a) b))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
37×add-cbrt-cube add-exp-log
18×prod-exp cbrt-unprod
9×cbrt-undiv div-exp
1×add-sqr-sqrt pow1 clear-num associate-/r* frac-2neg *-un-lft-identity times-frac add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
Counts
1 → 32
Calls
1 calls:
Slowest
58.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

series35.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
35.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

simplify22.8s

Counts
23 → 35
Calls
23 calls:
Slowest
2.7s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.7s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.7s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.3s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 2) 2) (* (* a a) a)) (* (* b b) b)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* b b) b)))

prune234.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 5.6b

regimes591.0ms

Accuracy

6.5% (6.4b remaining)

Error of 11.5b against oracle of 5.1b and baseline of 11.9b

bsearch34.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.3s4781×body160valid
1.2s8239×body80nan
1.1s16239×pre80true
633.0ms1429×body320valid
318.0ms1790×body80valid