Details

Time bar (total: 1.5m)

sample155.0ms

Algorithm
intervals
Results
52.0ms305×body80nan
38.0ms149×body160valid
28.0ms561×pre80true
13.0ms107×body80valid

simplify121.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
120.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize42.0ms

Local error

Found 4 expressions with local error:

28.4b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(- (* b b) (* (* c a) 4))
0.3b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite131.0ms

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
75.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
35.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
11.0ms
(sqrt (- (* b b) (* (* c a) 4)))
9.0ms
(- (* b b) (* (* c a) 4))

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
108.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
96.0ms
(sqrt (- (* b b) (* (* c a) 4)))
61.0ms
(- (* b b) (* (* c a) 4))

simplify5.5s

Counts
49 → 88
Calls
49 calls:
Slowest
590.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
387.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
334.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
314.0ms
(/ (* (* (- (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)))
236.0ms
(- b (* 2 (/ (* a c) b)))

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.8b

localize11.0ms

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

prune72.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.8b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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
26.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
15.0ms
(/ (* a c) b)

series62.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
27.0ms
(/ (* a c) b)

simplify11.9s

Counts
37 → 59
Calls
37 calls:
Slowest
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a 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)))
940.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune608.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 8.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))
0.5b
(* (/ (* a c) b) (/ (* a c) b))
0.3b
(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
0.3b
(/ (* a c) b)

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
216×add-cbrt-cube add-exp-log
101×prod-exp cbrt-unprod
70×cbrt-undiv div-exp
30×pow1
19×add-sqr-sqrt
18×times-frac
16×*-un-lft-identity add-cube-cbrt
14×associate-*r*
11×frac-times associate-*l/
8×associate-*l*
7×cbrt-div pow-plus swap-sqr associate-*r/ pow-prod-up
6×div-inv
4×pow-prod-down insert-posit16 add-log-exp
3×pow2 associate-/r* pow-sqr
2×pow3 *-commutative unswap-sqr
1×cbrt-prod clear-num frac-2neg pow1/3 rem-cbrt-cube associate-/l*
Counts
4 → 193
Calls
4 calls:
Slowest
79.0ms
(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))
76.0ms
(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
21.0ms
(* (/ (* a c) b) (/ (* a c) b))
12.0ms
(/ (* a c) b)

series262.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))
73.0ms
(* (/ (* a c) b) (/ (* a c) b))
46.0ms
(cbrt (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))
29.0ms
(/ (* a c) b)

simplify59.8s

Counts
183 → 205
Calls
183 calls:
Slowest
1.6s
(* (* (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b)))
1.5s
(* (* (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b)))
1.5s
(* (* (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)))
1.4s
(* (* (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b)) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b)))
1.4s
(* (* (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b)) (* (* (/ (* a c) b) (/ (* a c) b)) (/ (* a c) b))) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)))

prune2.0s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 8.6b

regimes783.0ms

Accuracy

45.3% (7.6b remaining)

Error of 16.7b against oracle of 9.1b and baseline of 23.0b

bsearch37.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.6s4437×body160valid
1.3s8576×body80nan
1.0s16576×pre80true
514.0ms3563×body80valid