Details

Time bar (total: 47.5s)

sample127.0ms

Algorithm
intervals
Results
44.0ms159×body160valid
25.0ms276×body80nan
22.0ms532×pre80true
11.0ms41×body320valid
5.0ms56×body80valid

simplify134.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
134.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize27.0ms

Local error

Found 4 expressions with local error:

40.8b
(- (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))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite207.0ms

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
119.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
58.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))
14.0ms
(- (* b b) (* (* c a) 4))

series430.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(sqrt (- (* b b) (* (* c a) 4)))
123.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
99.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
76.0ms
(- (* b b) (* (* c a) 4))

simplify5.7s

Counts
49 → 88
Calls
49 calls:
Slowest
699.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
523.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
366.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
272.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
255.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.2b

localize5.0ms

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

prune55.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.2b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

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
33.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms
(/ (* a c) b)

series60.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
31.0ms
(/ (* a c) b)
29.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.2s

Counts
37 → 59
Calls
37 calls:
Slowest
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 a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -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)))
1.0s
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune489.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ (* -2 (* a c)) (* (* 2 a) b))

rewrite28.0ms

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
28.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

series31.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
31.0ms
(/ (* -2 (* a c)) (* (* 2 a) b))

simplify21.1s

Counts
23 → 35
Calls
23 calls:
Slowest
2.8s
(/ (* (* (* -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)))
2.5s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.0s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 2) 2) (* (* a a) a)) (* (* b b) b)))
2.0s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* b b) b)))

prune258.0ms

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 5.2b

regimes540.0ms

Accuracy

15.3% (6.0b remaining)

Error of 11.2b against oracle of 5.2b and baseline of 12.3b

bsearch68.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.1s8227×body80nan
1.4s4808×body160valid
1.1s16227×pre80true
668.0ms1349×body320valid
267.0ms1843×body80valid