Details

Time bar (total: 24.7s)

sample135.0ms

Algorithm
intervals
Results
43.0ms38×body2560valid
26.0ms178×body80valid
20.0ms28×body1280valid
13.0ms97×body80nan
10.0ms20×body640valid
2.0ms2×body5120valid
2.0ms5×body320valid
1.0ms6×body160valid

simplify176.0ms

Calls
1 calls:
Slowest
176.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize38.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (- (* b b) (* (* 4 a) c)))
1.5b
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
0.8b
(- (* b b) (* (* 4 a) c))
0.3b
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))

rewrite181.0ms

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
Calls
4 calls:
Slowest
109.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
49.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(- (* b b) (* (* 4 a) c))

series457.0ms

Calls
4 calls:
Slowest
154.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
116.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
82.0ms
(- (* b b) (* (* 4 a) c))

simplify5.6s

Calls
49 calls:
Slowest
624.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (sqrt (- (* b b) (* (* 4 a) c)))) (* b b))
433.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
353.0ms
(- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))
271.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (- (sqrt (- (* b b) (* (* 4 a) c))) b)) (- (sqrt (- (* b b) (* (* 4 a) c))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
256.0ms
(/ (exp (* b b)) (exp (* (* 4 a) c)))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.4b

localize20.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (+ (* b b) (* (* c -4) a)))
1.5b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.8b
(+ (* b b) (* (* c -4) a))
0.3b
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))

rewrite154.0ms

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×insert-posit16
3×distribute-lft-out--
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
87.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
48.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
10.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
7.0ms
(+ (* b b) (* (* c -4) a))

series362.0ms

Calls
4 calls:
Slowest
120.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
101.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
95.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
46.0ms
(+ (* b b) (* (* c -4) a))

simplify4.5s

Calls
49 calls:
Slowest
775.0ms
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
358.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
356.0ms
(- (pow (sqrt (+ (* b b) (* (* c -4) a))) 3) (pow b 3))
324.0ms
(/ (* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
297.0ms
(* (exp (* b b)) (exp (* (* c -4) a)))

prune985.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize38.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (+ (* b b) (* (* c -4) a)))
1.5b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.8b
(+ (* b b) (* (* c -4) a))
0.3b
(/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b))

rewrite106.0ms

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×associate-/r* times-frac sqrt-prod difference-of-squares
5×pow1
4×insert-posit16
3×distribute-lft-out--
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp associate-/r/ flip-+ flip--
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
41.0ms
(/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b))
40.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
12.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
10.0ms
(+ (* b b) (* (* c -4) a))

series586.0ms

Calls
4 calls:
Slowest
298.0ms
(/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b))
122.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
110.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
55.0ms
(+ (* b b) (* (* c -4) a))

simplify3.8s

Calls
50 calls:
Slowest
402.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
270.0ms
(/ (* (* (* 2 2) 2) (* (* a a) a)) (* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
247.0ms
(/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
242.0ms
(- b (* 2 (/ (* a c) b)))
199.0ms
(* (exp (* b b)) (exp (* (* c -4) a)))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.4b

localize11.0ms

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

prune1.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 8.4b

regimes324.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.8b

bsearch216.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.4s5797×body80valid
1.0s1093×body2560valid
710.0ms916×body1280valid
563.0ms240×body320valid
517.0ms2941×body80nan
269.0ms453×body640valid
189.0ms110×body5120valid
33.0ms120×body160valid