Details

Time bar (total: 56.7s)

sample136.0ms

Algorithm
intervals
Results
49.0ms35×body2560valid
24.0ms191×body80valid
19.0ms37×body1280valid
11.0ms106×body80nan
8.0ms16×body640valid
1.0ms1×body5120valid
1.0ms4×body320valid
1.0ms4×body160valid

simplify574.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
574.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize54.0ms

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))

rewrite153.0ms

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
96.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
31.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
10.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
121.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
100.0ms
(sqrt (- (* b b) (* (* c a) 4)))
81.0ms
(- (* b b) (* (* c a) 4))

simplify5.6s

Counts
49 → 88
Calls
49 calls:
Slowest
649.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
440.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
390.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
343.0ms
(/ (* (* (- (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)))
296.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize39.0ms

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)))

rewrite139.0ms

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
59.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
52.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
14.0ms
(- (* b b) (* (* c a) 4))
11.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* c a) 4))) b)))
98.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
95.0ms
(sqrt (- (* b b) (* (* c a) 4)))
75.0ms
(- (* b b) (* (* c a) 4))

simplify17.7s

Counts
123 → 134
Calls
123 calls:
Slowest
458.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))))
436.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))))
391.0ms
(/ (sqrt 1) (/ (* 2 a) (- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))))
388.0ms
(/ (* (* 1 1) 1) (/ (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b))))
380.0ms
(/ (sqrt 1) (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))))

prune1.5s

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))

rewrite51.0ms

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
22.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
11.0ms
(/ (- 0 (* (* c a) 4)) (/ a 1/2))
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))
7.0ms
(- (* b b) (* (* c a) 4))

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(sqrt (- (* b b) (* (* c a) 4)))
84.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
48.0ms
(- (* b b) (* (* c a) 4))
13.0ms
(/ (- 0 (* (* c a) 4)) (/ a 1/2))

simplify15.7s

Counts
123 → 129
Calls
123 calls:
Slowest
486.0ms
(/ (sqrt (- 0 (* (* c a) 4))) (/ a 1/2))
454.0ms
(/ (- 0 (* (* c a) 4)) (/ 1 1/2))
431.0ms
(/ (- 0 (* (* c a) 4)) (/ (cbrt a) (sqrt 1/2)))
425.0ms
(/ (- 0 (* (* c a) 4)) (/ (cbrt a) (cbrt 1/2)))
422.0ms
(/ (- 0 (* (* c a) 4)) (/ (sqrt a) (sqrt 1/2)))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize42.0ms

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)))

rewrite106.0ms

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
44.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
32.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
15.0ms
(- (* b b) (* (* c a) 4))
15.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
121.0ms
(+ (sqrt (- (* b b) (* (* c a) 4))) b)
102.0ms
(sqrt (- (* b b) (* (* c a) 4)))
63.0ms
(- (* b b) (* (* c a) 4))

simplify3.8s

Counts
36 → 79
Calls
36 calls:
Slowest
596.0ms
(* (* (* (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))))
302.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
283.0ms
(- b (* 2 (/ (* a c) b)))
254.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))
247.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes351.0ms

Accuracy

94% (1.4b remaining)

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

bsearch346.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.4s5821×body80valid
1.2s935×body1280valid
1.0s1072×body2560valid
522.0ms2839×body80nan
295.0ms428×body640valid
132.0ms233×body320valid
88.0ms92×body5120valid
33.0ms127×body160valid