Details

Time bar (total: 31.6s)

sample284.0ms

Algorithm
intervals
Results
69.0ms108×body320valid
39.0ms300×body80nan
39.0ms556×pre80true
25.0ms99×body160valid
7.0ms17×body640valid
4.0ms32×body80valid

simplify508.0ms

Calls
1 calls:
Slowest
507.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize31.0ms

Local error

Found 4 expressions with local error:

27.3b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.0b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×pow1 flip3-- insert-posit16 flip--
3×times-frac sqrt-prod associate-/l*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* frac-2neg pow1/2 diff-log div-sub div-exp div-inv
Calls
4 calls:
Slowest
39.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
15.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
5.0ms
(sqrt (- (* b b) (* (* c a) 4)))
3.0ms
(- (* b b) (* (* c a) 4))

series452.0ms

Calls
4 calls:
Slowest
160.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
113.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
105.0ms
(sqrt (- (* b b) (* (* c a) 4)))
73.0ms
(- (* b b) (* (* c a) 4))

simplify3.7s

Calls
32 calls:
Slowest
582.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
456.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* c a) 4) 3)))
275.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
273.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
252.0ms
(/ (* (* (- (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)))

prune851.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize5.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

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

series0.0ms

Calls
0 calls:
Slowest

simplify0.0ms

Calls
0 calls:
Slowest

prune51.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×add-cbrt-cube add-exp-log
2×add-sqr-sqrt pow1 clear-num frac-2neg *-un-lft-identity add-cube-cbrt insert-posit16 div-inv associate-/l* add-log-exp
1×cbrt-undiv associate-/r* times-frac div-exp associate-*r/ associate-/l/
Calls
2 calls:
Slowest
9.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
6.0ms
(/ (* a c) b)

series75.0ms

Calls
2 calls:
Slowest
40.0ms
(/ (* a c) b)
35.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify1.2s

Calls
11 calls:
Slowest
718.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
148.0ms
(/ (/ (* a c) b) a)
143.0ms
(- (log (* -2 (/ (* a c) b))) (log (* 2 a)))
25.0ms
(* -1 (/ c b))
25.0ms
(* -1 (/ c b))

prune373.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
28×distribute-neg-frac
24×associate-*l*
20×pow1
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-*r*
12×distribute-lft-neg-in distribute-rgt-neg-in
11×frac-times add-cbrt-cube associate-*r/ add-exp-log
8×div-inv
7×cbrt-div associate-*l/
5×pow-prod-up
4×associate-/r* pow-prod-down prod-exp distribute-rgt-neg-out cbrt-unprod insert-posit16 add-log-exp
3×distribute-lft-neg-out neg-mul-1
2×pow2 pow-plus cube-unmult *-commutative
1×cbrt-prod clear-num frac-2neg pow1/3 sqr-neg associate-/r/ rem-cbrt-cube
Calls
4 calls:
Slowest
30.0ms
(* (- (/ (/ c (/ b a)) a)) (* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a))))
23.0ms
(cbrt (* (- (/ (/ c (/ b a)) a)) (* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a)))))
15.0ms
(* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a)))
0.0ms
(/ c (/ b a))

series199.0ms

Calls
4 calls:
Slowest
77.0ms
(cbrt (* (- (/ (/ c (/ b a)) a)) (* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a)))))
58.0ms
(* (- (/ (/ c (/ b a)) a)) (* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a))))
38.0ms
(* (- (/ (/ c (/ b a)) a)) (- (/ (/ c (/ b a)) a)))
25.0ms
(/ c (/ b a))

simplify15.6s

Calls
89 calls:
Slowest
532.0ms
(cbrt (* (- (/ c (/ b a))) (* (- (/ (/ c (/ b a)) a)) (- (/ c (/ b a))))))
511.0ms
(* (cbrt (- (/ (/ c (/ b a)) a))) (cbrt (- (/ (/ c (/ b a)) a))))
500.0ms
(* (- (/ c (/ b a))) (* (- (/ c (/ b a))) (- (/ c (/ b a)))))
497.0ms
(sqrt (- (/ (/ c (/ b a)) a)))
494.0ms
(sqrt (- (/ (/ c (/ b a)) a)))

prune1.2s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 3.0b

regimes396.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch2.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.2s8317×body80nan
1.6s3651×body320valid
987.0ms16317×pre80true
809.0ms2919×body160valid
310.0ms537×body640valid
197.0ms893×body80valid