Details

Time bar (total: 53.6s)

sample125.0ms

Algorithm
intervals
Results
27.0ms191×body80valid
26.0ms35×body2560valid
26.0ms37×body1280valid
13.0ms106×body80nan
9.0ms16×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
1.0ms4×body160valid

simplify134.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
134.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize34.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* b b) (* (* c a) 4)))
0.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.6b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite183.0ms

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
115.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
44.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(sqrt (- (* b b) (* (* c a) 4)))
9.0ms
(- (* b b) (* (* c a) 4))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
123.0ms
(sqrt (- (* b b) (* (* c a) 4)))
116.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
79.0ms
(- (* b b) (* (* c a) 4))

simplify5.3s

Counts
49 → 88
Calls
49 calls:
Slowest
528.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
459.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
330.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
294.0ms
(/ (* (* (- (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)))
252.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune969.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize28.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* b b) (* (* c a) 4)))
0.9b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.6b
(- (* b b) (* (* c a) 4))
0.2b
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×associate-/r* div-exp
10×difference-of-squares
9×associate-/r/
8×sqrt-prod add-log-exp
7×flip3-- flip--
6×pow1
5×cbrt-undiv div-inv distribute-lft-out--
4×insert-posit16
3×rec-exp 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div diff-log
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 cbrt-unprod pow-flip inv-pow
Counts
4 → 122
Calls
4 calls:
Slowest
58.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
41.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(- (* b b) (* (* c a) 4))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
99.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
86.0ms
(sqrt (- (* b b) (* (* c a) 4)))
56.0ms
(- (* b b) (* (* c a) 4))

simplify17.0s

Counts
123 → 134
Calls
123 calls:
Slowest
693.0ms
(/ (cbrt 1) (+ (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (+ (* b b) (* (sqrt (- (* b b) (* (* c a) 4))) b))))
503.0ms
(/ (sqrt 1) (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))))
415.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))))
415.0ms
(/ 1 (/ (* 2 a) (- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))))
357.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize40.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* b b) (* (* c a) 4)))
14.5b
(/ (- 0 (* (* c a) 4)) (/ a 1/2))
0.9b
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
0.6b
(- (* b b) (* (* c a) 4))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
49×*-un-lft-identity
48×add-sqr-sqrt
47×add-cube-cbrt
13×associate-/r*
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
4×insert-posit16
3×cbrt-undiv flip3-- div-exp sqrt-prod flip-- associate-/l*
2×sqrt-div associate-/l/
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-sub distribute-frac-neg associate-/r/ flip-+ distribute-lft-out sub0-neg
Counts
4 → 117
Calls
4 calls:
Slowest
30.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
12.0ms
(/ (- 0 (* (* c a) 4)) (/ a 1/2))
11.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
107.0ms
(sqrt (- (* b b) (* (* c a) 4)))
54.0ms
(- (* b b) (* (* c a) 4))
9.0ms
(/ (- 0 (* (* c a) 4)) (/ a 1/2))

simplify14.5s

Counts
123 → 129
Calls
123 calls:
Slowest
456.0ms
(/ (- 0 (* (* c a) 4)) (/ 1 1/2))
433.0ms
(/ (- 0 (* (* c a) 4)) (/ a 1/2))
421.0ms
(/ (- 0 (* (* c a) 4)) (/ (cbrt a) (sqrt 1/2)))
404.0ms
(/ (- 0 (* (* c a) 4)) (/ (cbrt a) (cbrt 1/2)))
386.0ms
(/ (- 0 (* (* c a) 4)) (/ (cbrt a) 1/2))

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (- (* b b) (* (* c a) 4)))
0.9b
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
0.6b
(- (* b b) (* (* c a) 4))
0.5b
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube add-exp-log
10×pow1
9×*-un-lft-identity
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×associate-*l* sqrt-prod
5×prod-exp cbrt-unprod
4×insert-posit16
3×pow-prod-down
2×flip3-- sqrt-div associate-*r/ flip--
1×cbrt-undiv +-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log div-exp associate-*r* *-commutative flip-+ distribute-lft-out
Counts
4 → 67
Calls
4 calls:
Slowest
48.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
41.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
14.0ms
(- (* b b) (* (* c a) 4))
10.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
106.0ms
(sqrt (- (* b b) (* (* c a) 4)))
96.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
57.0ms
(- (* b b) (* (* c a) 4))

simplify4.2s

Counts
36 → 79
Calls
36 calls:
Slowest
657.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
620.0ms
(* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (* (sqrt 1/2) (sqrt 1/2)) (sqrt 1/2)) (* (* (/ c -1/4) (/ c -1/4)) (/ c -1/4))))
207.0ms
(- b (* 2 (/ (* a c) b)))
205.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))
199.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune932.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes331.0ms

Accuracy

94% (1.4b remaining)

Error of 7.3b against oracle of 5.9b and baseline of 29.4b

bsearch354.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s1072×body2560valid
995.0ms5821×body80valid
720.0ms935×body1280valid
501.0ms2839×body80nan
218.0ms428×body640valid
89.0ms233×body320valid
86.0ms92×body5120valid
33.0ms127×body160valid