Details

Time bar (total: 53.0s)

sample127.0ms

Algorithm
intervals
Results
37.0ms35×body2560valid
24.0ms191×body80valid
22.0ms37×body1280valid
12.0ms106×body80nan
9.0ms16×body640valid
1.0ms4×body320valid
1.0ms1×body5120valid
1.0ms4×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
126.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite180.0ms

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
109.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
47.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms
(- (* b b) (* (* 4 a) c))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) (* 2 a))
116.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
104.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
63.0ms
(- (* b b) (* (* 4 a) c))

simplify5.5s

Counts
49 → 88
Calls
49 calls:
Slowest
580.0ms
(- (* (sqrt (- (* b b) (* (* 4 a) c))) (sqrt (- (* b b) (* (* 4 a) c)))) (* b b))
384.0ms
(/ (sqrt (- (* b b) (* (* 4 a) c))) (* 2 a))
380.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
338.0ms
(- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))
285.0ms
(/ (* (* (- (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)))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

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
70.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
66.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(- (* b b) (* (* 4 a) c))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ 1 (/ (* 2 a) (- (sqrt (- (* b b) (* (* 4 a) c))) b)))
130.0ms
(- (sqrt (- (* b b) (* (* 4 a) c))) b)
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
69.0ms
(- (* b b) (* (* 4 a) c))

simplify18.1s

Counts
123 → 134
Calls
123 calls:
Slowest
540.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))))
494.0ms
(/ (sqrt 1) (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))))
482.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (* (sqrt (- (* b b) (* (* 4 a) c))) (sqrt (- (* b b) (* (* 4 a) c)))) (* b b))))
430.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
391.0ms
(/ 1 (/ (* 2 a) (- (pow (sqrt (- (* b b) (* (* 4 a) c))) 3) (pow b 3))))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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
24.0ms
(+ (sqrt (- (* b b) (* (* 4 a) c))) b)
18.0ms
(/ (- 0 (* (* 4 a) c)) (/ a 1/2))
11.0ms
(- (* b b) (* (* 4 a) c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
97.0ms
(+ (sqrt (- (* b b) (* (* 4 a) c))) b)
83.0ms
(- (* b b) (* (* 4 a) c))
81.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(/ (- 0 (* (* 4 a) c)) (/ a 1/2))

simplify12.7s

Counts
123 → 129
Calls
123 calls:
Slowest
435.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
384.0ms
(/ (* (cbrt (- 0 (* (* 4 a) c))) (cbrt (- 0 (* (* 4 a) c)))) (/ (* (cbrt a) (cbrt a)) (* (cbrt 1/2) (cbrt 1/2))))
332.0ms
(- (* 0 0) (* (* (* 4 a) c) (* (* 4 a) c)))
318.0ms
(/ (- 0 (* (* 4 a) c)) (sqrt (/ a 1/2)))
270.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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
30.0ms
(+ (sqrt (- (* b b) (* (* 4 a) c))) b)
30.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
9.0ms
(- (* b b) (* (* 4 a) c))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(* (sqrt 1/2) (* (sqrt 1/2) (/ c -1/4)))
101.0ms
(+ (sqrt (- (* b b) (* (* 4 a) c))) b)
96.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
53.0ms
(- (* b b) (* (* 4 a) c))

simplify3.9s

Counts
36 → 79
Calls
36 calls:
Slowest
613.0ms
(* (* (* (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))))
357.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 4 a) c) (* (* 4 a) c))))
252.0ms
(/ (exp (* b b)) (exp (* (* 4 a) c)))
238.0ms
(- b (* 2 (/ (* a c) b)))
237.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))

prune989.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.3b

regimes257.0ms

Accuracy

94% (1.4b remaining)

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

bsearch289.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.1s1072×body2560valid
999.0ms5821×body80valid
804.0ms935×body1280valid
715.0ms2839×body80nan
258.0ms428×body640valid
152.0ms233×body320valid
121.0ms92×body5120valid
35.0ms127×body160valid