Details

Time bar (total: 1.8m)

sample346.0ms

Algorithm
intervals
Results
76.0ms554×pre80true
49.0ms111×body320valid
40.0ms298×body80nan
29.0ms100×body160valid
7.0ms13×body640valid
6.0ms32×body80valid

simplify198.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
197.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize44.0ms

Local error

Found 4 expressions with local error:

29.4b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(- (* b b) (* (* c a) 4))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite149.0ms

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
94.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
38.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
8.0ms
(sqrt (- (* b b) (* (* c a) 4)))
8.0ms
(- (* b b) (* (* c a) 4))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
124.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
101.0ms
(sqrt (- (* b b) (* (* c a) 4)))
66.0ms
(- (* b b) (* (* c a) 4))

simplify5.3s

Counts
49 → 88
Calls
49 calls:
Slowest
547.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
391.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
305.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
301.0ms
(/ (* (* (- (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)))
284.0ms
(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize9.0ms

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

prune42.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.4b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite48.0ms

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
31.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
15.0ms
(/ (* a c) b)

series60.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
32.0ms
(/ (* a c) b)
28.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.1s

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 c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 2) 2) (* (* a a) a)))
803.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune677.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a))))
0.5b
(* (/ c (/ b a)) (/ c (/ b a)))
0.4b
(* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a)))
0.3b
(/ c (/ b a))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
426×times-frac
263×add-sqr-sqrt
221×*-un-lft-identity add-cube-cbrt
216×add-cbrt-cube add-exp-log
105×cbrt-undiv div-exp
88×associate-*r*
66×prod-exp cbrt-unprod
45×associate-*l*
44×swap-sqr
30×pow1
25×div-inv
13×associate-/r*
12×unswap-sqr
11×frac-times associate-*l/
7×cbrt-div pow-plus associate-*r/ pow-prod-up
6×associate-/r/
4×pow-prod-down insert-posit16 add-log-exp
3×pow2 pow-sqr associate-/l*
2×pow3 *-commutative
1×cbrt-prod clear-num frac-2neg pow1/3 rem-cbrt-cube
Counts
4 → 400
Calls
4 calls:
Slowest
75.0ms
(* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a)))
71.0ms
(cbrt (* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a))))
34.0ms
(* (/ c (/ b a)) (/ c (/ b a)))
11.0ms
(/ c (/ b a))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a)))
94.0ms
(* (/ c (/ b a)) (/ c (/ b a)))
57.0ms
(cbrt (* (* (/ c (/ b a)) (/ c (/ b a))) (/ c (/ b a))))
21.0ms
(/ c (/ b a))

simplify1.3m

Counts
471 → 412
Calls
471 calls:
Slowest
1.1s
(* (* (/ (* (* c c) c) (* (* (/ b a) (/ b a)) (/ b a))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a)))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))))
997.0ms
(* (* (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))) (/ (* (* c c) c) (* (* (/ b a) (/ b a)) (/ b a)))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))))
911.0ms
(* (* (* (* (/ c (/ b a)) (/ c (/ b a))) (* (/ c (/ b a)) (/ c (/ b a)))) (* (/ c (/ b a)) (/ c (/ b a)))) (/ (* (* c c) c) (* (* (/ b a) (/ b a)) (/ b a))))
897.0ms
(* (* (/ (* (* c c) c) (* (* (/ b a) (/ b a)) (/ b a))) (/ (* (* c c) c) (* (* (/ b a) (/ b a)) (/ b a)))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))))
882.0ms
(* (* (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a)))) (/ (* (* c c) c) (/ (* (* b b) b) (* (* a a) a))))

prune4.9s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 2.4b

regimes582.0ms

Accuracy

0% (3.4b remaining)

Error of 6.1b against oracle of 2.7b and baseline of 6.1b

bsearch2.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.0s8228×body80nan
1.7s3645×body320valid
984.0ms16228×pre80true
851.0ms2970×body160valid
270.0ms494×body640valid
145.0ms891×body80valid