Details

Time bar (total: 55.6s)

sample202.0ms

Algorithm
intervals
Results
52.0ms166×body160valid
35.0ms45×body80valid
32.0ms474×pre80true
32.0ms218×body80nan
22.0ms45×body320valid

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize31.0ms

Local error

Found 4 expressions with local error:

41.4b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite175.0ms

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
117.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
35.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series407.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
101.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4)))
59.0ms
(- (* b b) (* (* c a) 4))

simplify5.3s

Counts
49 → 88
Calls
49 calls:
Slowest
598.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
368.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
310.0ms
(/ (* (* (- (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)))
278.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
230.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 2) 2) (* (* a a) a)))

prune956.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

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

prune52.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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
23.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms
(/ (* a c) b)

series63.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
28.0ms
(/ (* a c) b)

simplify11.7s

Counts
37 → 59
Calls
37 calls:
Slowest
1.6s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 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 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 2) 2) (* (* a a) a)))
960.0ms
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune634.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 5.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×times-frac
76×add-cbrt-cube add-exp-log
60×*-un-lft-identity add-cube-cbrt
48×sqrt-prod
28×prod-exp cbrt-unprod
26×cbrt-undiv div-exp
22×associate-*r* associate-*l*
13×associate-/r*
9×unswap-sqr
7×associate-/l*
6×pow1
5×associate-*r/ div-inv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l/
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 195
Calls
4 calls:
Slowest
45.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 a))
30.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
8.0ms
(/ a (sqrt b))
4.0ms
(/ c (sqrt b))

series198.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(/ c (sqrt b))
52.0ms
(/ a (sqrt b))
45.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
44.0ms
(/ (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* 2 a))

simplify27.1s

Counts
206 → 207
Calls
206 calls:
Slowest
2.0s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (/ (* (* c c) c) (* (* (sqrt b) (sqrt b)) (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.8s
(/ (* (* (* -2 -2) -2) (* (/ (* (* a a) a) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.8s
(/ (* (* (* -2 -2) -2) (* (/ (* (* a a) a) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.7s
(/ (* (* (* -2 (* (/ a (sqrt b)) (/ c (sqrt b)))) (* -2 (* (/ a (sqrt b)) (/ c (sqrt b))))) (* -2 (* (/ a (sqrt b)) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune2.1s

Pruning

33 alts after pruning (32 fresh and 1 done)

Merged error: 5.0b

regimes706.0ms

Accuracy

0% (6.8b remaining)

Error of 11.8b against oracle of 5.0b and baseline of 11.8b

bsearch2.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.6s8280×body80nan
1.5s4842×body160valid
997.0ms16280×pre80true
734.0ms1419×body320valid
227.0ms1739×body80valid