Details

Time bar (total: 1.2m)

sample108.0ms

Algorithm
intervals
Results
24.0ms39×body2560valid
20.0ms185×body80valid
18.0ms32×body1280valid
18.0ms95×body80nan
6.0ms15×body640valid
3.0ms10×body320valid
1.0ms3×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
139.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize27.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (- (* b b) (* (* 3 a) c)))
1.6b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.0b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
31.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
13.0ms
(* (* 3 a) c)
10.0ms
(- (* b b) (* (* 3 a) c))
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
95.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
66.0ms
(- (* b b) (* (* 3 a) c))
22.0ms
(* (* 3 a) c)

simplify10.0s

Counts
84 → 76
Calls
84 calls:
Slowest
663.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
546.0ms
(* (* (* (* 3 a) c) (* (* 3 a) c)) (* (* 3 a) c))
543.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
442.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
386.0ms
(- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))

prune964.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize45.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (+ (* b b) (* (* c -3) a)))
1.6b
(- (sqrt (+ (* b b) (* (* c -3) a))) b)
1.0b
(+ (* b b) (* (* c -3) a))
0.2b
(* (* c -3) a)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative flip-- distribute-lft-out--
Counts
4 → 63
Calls
4 calls:
Slowest
39.0ms
(- (sqrt (+ (* b b) (* (* c -3) a))) b)
26.0ms
(* (* c -3) a)
12.0ms
(+ (* b b) (* (* c -3) a))
12.0ms
(sqrt (+ (* b b) (* (* c -3) a)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(- (sqrt (+ (* b b) (* (* c -3) a))) b)
95.0ms
(sqrt (+ (* b b) (* (* c -3) a)))
78.0ms
(+ (* b b) (* (* c -3) a))
34.0ms
(* (* c -3) a)

simplify7.9s

Counts
82 → 75
Calls
82 calls:
Slowest
839.0ms
(- (* (sqrt (+ (* b b) (* (* c -3) a))) (sqrt (+ (* b b) (* (* c -3) a)))) (* b b))
607.0ms
(* (* (* (* c -3) a) (* (* c -3) a)) (* (* c -3) a))
528.0ms
(exp (+ (* b b) (* (* c -3) a)))
474.0ms
(* (* (* (* c -3) (* c -3)) (* c -3)) (* (* a a) a))
431.0ms
(- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a)))

prune940.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

localize68.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a))))
1.6b
(- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b)
1.0b
(+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))
0.6b
(cbrt a)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log sqrt-prod insert-posit16
3×cbrt-prod
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 pow1/3 diff-log flip-- distribute-lft-out--
Counts
4 → 56
Calls
4 calls:
Slowest
55.0ms
(- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b)
22.0ms
(+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))
11.0ms
(sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a))))
1.0ms
(cbrt a)

series604.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(cbrt a)
136.0ms
(- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b)
134.0ms
(sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a))))
80.0ms
(+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))

simplify10.2s

Counts
78 → 68
Calls
78 calls:
Slowest
908.0ms
(- (pow (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) 3) (pow b 3))
553.0ms
(sqrt (- (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a))))
524.0ms
(- (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))
453.0ms
(* (exp (* b b)) (exp (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a))))
381.0ms
(* (* (- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b) (- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b)) (- (sqrt (+ (* b b) (* (* (* c -3) (* (cbrt a) (cbrt a))) (cbrt a)))) b))

prune872.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

localize31.0ms

Local error

Found 4 expressions with local error:

21.8b
(sqrt (+ (* (* c -3) a) (* b b)))
8.5b
(/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))
3.6b
(/ (/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (* 3 a))
1.4b
(+ b (sqrt (+ (* (* c -3) a) (* b b))))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
45×add-cbrt-cube add-exp-log
22×times-frac
21×*-un-lft-identity
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
12×add-sqr-sqrt
11×add-cube-cbrt associate-/l*
6×associate-/r/ add-log-exp
5×pow1 associate-/r* flip3-+ flip-+ distribute-lft-out
4×insert-posit16 div-inv
3×sqrt-prod
2×clear-num frac-2neg sqrt-div
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 106
Calls
4 calls:
Slowest
108.0ms
(/ (/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (* 3 a))
79.0ms
(/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))
33.0ms
(sqrt (+ (* (* c -3) a) (* b b)))
26.0ms
(+ b (sqrt (+ (* (* c -3) a) (* b b))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
275.0ms
(/ (/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (* 3 a))
246.0ms
(/ (* (* c -3) a) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))
143.0ms
(+ b (sqrt (+ (* (* c -3) a) (* b b))))
98.0ms
(sqrt (+ (* (* c -3) a) (* b b)))

simplify33.5s

Counts
138 → 118
Calls
138 calls:
Slowest
1.9s
(/ (/ (* (* (* (* c c) c) (* (* -3 -3) -3)) (* (* a a) a)) (* (* (+ b (sqrt (+ (* (* c -3) a) (* b b)))) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))) (* (* (* 3 3) 3) (* (* a a) a)))
1.9s
(/ (/ (* (* (* (* c c) c) (* (* -3 -3) -3)) (* (* a a) a)) (* (* (+ b (sqrt (+ (* (* c -3) a) (* b b)))) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.9s
(/ (/ (* (* (* (* c -3) (* c -3)) (* c -3)) (* (* a a) a)) (* (* (+ b (sqrt (+ (* (* c -3) a) (* b b)))) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.7s
(/ (/ (* (* (* (* c -3) a) (* (* c -3) a)) (* (* c -3) a)) (* (* (+ b (sqrt (+ (* (* c -3) a) (* b b)))) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.6s
(/ (/ (* (* (* (* c -3) a) (* (* c -3) a)) (* (* c -3) a)) (* (* (+ b (sqrt (+ (* (* c -3) a) (* b b)))) (+ b (sqrt (+ (* (* c -3) a) (* b b))))) (+ b (sqrt (+ (* (* c -3) a) (* b b)))))) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.7b

regimes733.0ms

Accuracy

94.1% (1.2b remaining)

Error of 10.3b against oracle of 9.1b and baseline of 29.3b

bsearch408.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.4s1078×body2560valid
798.0ms5868×body80valid
713.0ms901×body1280valid
413.0ms2895×body80nan
290.0ms445×body640valid
135.0ms227×body320valid
94.0ms103×body5120valid
25.0ms103×body160valid