Details

Time bar (total: 59.9s)

sample171.0ms

Algorithm
intervals
Results
54.0ms304×body80nan
39.0ms143×body160valid
34.0ms560×pre80true
16.0ms113×body80valid

simplify148.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
148.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize46.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.3b
(- (* b b) (* (* c a) 4))
0.2b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite177.0ms

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
89.0ms
(/ (- (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))
10.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
117.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
84.0ms
(sqrt (- (* b b) (* (* c a) 4)))
68.0ms
(- (* b b) (* (* c a) 4))

simplify5.1s

Counts
49 → 88
Calls
49 calls:
Slowest
557.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
407.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
278.0ms
(/ (* (* (- (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)))
245.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
243.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.9b

localize14.0ms

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

prune73.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.9b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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
19.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms
(/ (* a c) b)

series63.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
39.0ms
(/ (* a c) b)
23.0ms
(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify11.6s

Counts
37 → 59
Calls
37 calls:
Slowest
1.8s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) 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 2) 2) (* (* a a) a)))
1.3s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a 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 a) (* 2 a)) (* 2 a)))
1.0s
(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune491.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (* a c) (/ 1 b))
0.3b
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
120×add-exp-log
70×add-cbrt-cube
64×prod-exp
34×cbrt-unprod
32×div-exp
18×cbrt-undiv
13×associate-*r*
10×times-frac
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×rec-exp 1-exp
4×associate-*r/
3×pow-prod-down
2×un-div-inv insert-posit16 div-inv add-log-exp associate-/l/
1×clear-num associate-/r* frac-2neg associate-*l* *-commutative associate-/l*
Counts
2 → 87
Calls
2 calls:
Slowest
69.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
17.0ms
(* (* a c) (/ 1 b))

series61.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
34.0ms
(/ (* -2 (* (* a c) (/ 1 b))) (* 2 a))
26.0ms
(* (* a c) (/ 1 b))

simplify33.5s

Counts
69 → 93
Calls
69 calls:
Slowest
2.4s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.2s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (/ (* (* 1 1) 1) (* (* b b) b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.1s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 2) 2) (* (* a a) a)))
2.1s
(/ (* (* (* -2 -2) -2) (* (* (* (* a a) a) (* (* c c) c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
2.0s
(/ (* (* (* -2 -2) -2) (* (* (* (* a c) (* a c)) (* a c)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune788.0ms

Pruning

32 alts after pruning (30 fresh and 2 done)

Merged error: 9.7b

regimes727.0ms

Accuracy

45.6% (7.3b remaining)

Error of 16.3b against oracle of 9.1b and baseline of 22.5b

bsearch69.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.7s4522×body160valid
1.6s8486×body80nan
985.0ms16486×pre80true
523.0ms3478×body80valid