Details

Time bar (total: 1.9m)

sample241.0ms

Algorithm
intervals
Results
52.0ms209×body80nan
36.0ms96×body320valid
24.0ms465×pre80true
24.0ms109×body160valid
7.0ms13×body640valid
4.0ms38×body80valid

simplify176.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.1b

localize34.0ms

Local error

Found 4 expressions with local error:

31.2b
(- (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)))

rewrite190.0ms

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
96.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
62.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
132.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
81.0ms
(sqrt (- (* b b) (* (* c a) 4)))
45.0ms
(- (* b b) (* (* c a) 4))

simplify12.8s

Counts
105 → 88
Calls
105 calls:
Slowest
612.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
419.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
409.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
371.0ms
(sqrt (+ (* (* b b) (* b b)) (+ (* (* (* c a) 4) (* (* c a) 4)) (* (* b b) (* (* c a) 4)))))
368.0ms
(/ (* (* (- (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)))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize7.0ms

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

prune54.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.7b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

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))
8.0ms
(/ (* a c) b)

series53.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
28.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
25.0ms
(/ (* a c) b)

simplify16.0s

Counts
65 → 59
Calls
65 calls:
Slowest
1.7s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s
(/ (* (* (* -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 a) (* 2 a)) (* 2 a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
890.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune528.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.6b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
249×add-cbrt-cube add-exp-log
142×prod-exp cbrt-unprod
89×pow1
56×cbrt-undiv div-exp
54×add-sqr-sqrt
50×times-frac
39×*-un-lft-identity pow-prod-down add-cube-cbrt
27×associate-*l*
24×associate-*l/
22×pow-prod-up
16×frac-times associate-*r/
15×associate-*r*
13×swap-sqr
7×cbrt-div
6×pow-plus unswap-sqr
5×cube-unmult div-inv
4×pow2 pow-sqr insert-posit16 add-log-exp
3×*-commutative
1×cbrt-prod pow1/3 rem-cbrt-cube
Counts
4 → 245
Calls
4 calls:
Slowest
171.0ms
(cbrt (* (* (/ a b) (* (/ a b) (/ a b))) (* c (* c c))))
163.0ms
(* (* (/ a b) (* (/ a b) (/ a b))) (* c (* c c)))
54.0ms
(* (/ a b) (* (/ a b) (/ a b)))
25.0ms
(* (/ a b) (/ a b))

series307.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (* (/ a b) (* (/ a b) (/ a b))) (* c (* c c)))
62.0ms
(* (/ a b) (* (/ a b) (/ a b)))
60.0ms
(cbrt (* (* (/ a b) (* (/ a b) (/ a b))) (* c (* c c))))
45.0ms
(* (/ a b) (/ a b))

simplify1.2m

Counts
281 → 257
Calls
281 calls:
Slowest
1.2s
(* (* (* (/ a b) (* (/ a b) (/ a b))) (* (/ a b) (* (/ a b) (/ a b)))) (* (/ a b) (* (/ a b) (/ a b))))
1.1s
(* (* (/ (* (* a a) a) (* (* b b) b)) (* (* (* (/ a b) (/ a b)) (/ a b)) (/ (* (* a a) a) (* (* b b) b)))) (* (* (* c c) c) (* (* (* c c) (* c c)) (* c c))))
925.0ms
(* (* (/ (* (* a a) a) (* (* b b) b)) (* (/ (* (* a a) a) (* (* b b) b)) (/ (* (* a a) a) (* (* b b) b)))) (* (* (* c c) c) (* (* (* c c) (* c c)) (* c c))))
882.0ms
(* (* (/ (* (* a a) a) (* (* b b) b)) (* (/ (* (* a a) a) (* (* b b) b)) (/ (* (* a a) a) (* (* b b) b)))) (* (* (* c (* c c)) (* c (* c c))) (* c (* c c))))
860.0ms
(* (* (/ (* (* a a) a) (* (* b b) b)) (* (/ (* (* a a) a) (* (* b b) b)) (/ (* (* a a) a) (* (* b b) b)))) (* (* (* c c) c) (* (* (* c c) c) (* (* c c) c))))

prune2.9s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 2.6b

regimes495.0ms

Accuracy

0% (3.4b remaining)

Error of 5.9b against oracle of 2.6b and baseline of 5.9b

bsearch1.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.6s3661×body320valid
1.5s16273×pre80true
1.5s8273×body80nan
977.0ms2959×body160valid
299.0ms503×body640valid
144.0ms877×body80valid