Details

Time bar (total: 22.7s)

sample101.0ms

Algorithm
intervals
Results
24.0ms26×body1280valid
23.0ms38×body2560valid
18.0ms174×body80valid
9.0ms101×body80nan
7.0ms22×body640valid
2.0ms7×body320valid
2.0ms3×body5120valid
0.0ms2×body160valid

simplify108.0ms

Calls
1 calls:
Slowest
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.2b

localize25.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(- (* b b) (* (* 3 a) c))
0.6b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 fma-def times-frac insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod distribute-lft-out
2×neg-sub0 flip3-+ flip3-- sqrt-div associate-+l- flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sum-log sub-neg frac-2neg pow1/2 fma-neg diff-log div-sub div-exp prod-diff div-inv
Calls
4 calls:
Slowest
22.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
3.0ms
(- (* b b) (* (* 3 a) c))

series412.0ms

Calls
4 calls:
Slowest
116.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
112.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
103.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
81.0ms
(- (* b b) (* (* 3 a) c))

simplify4.2s

Calls
40 calls:
Slowest
586.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
448.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
268.0ms
(+ (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 3 a) c))) 3))
248.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
242.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(- (* b b) (* (* 3 a) c))
0.6b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(* (* 3 a) c)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity add-log-exp
7×add-sqr-sqrt
6×add-cube-cbrt
4×expm1-log1p-u pow1 fma-def add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×sqrt-prod
2×flip3-- sqrt-div flip--
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sum-log sub-neg flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff *-commutative associate-+l- flip-+ distribute-lft-out
Calls
4 calls:
Slowest
19.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
6.0ms
(- (* b b) (* (* 3 a) c))
5.0ms
(* (* 3 a) c)

series338.0ms

Calls
4 calls:
Slowest
131.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
113.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
70.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)

simplify2.1s

Calls
25 calls:
Slowest
482.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
244.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
188.0ms
(- b (* 3/2 (/ (* a c) b)))
173.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
130.0ms
(* (exp (- b)) (exp (sqrt (- (* b b) (* (* 3 a) c)))))

prune969.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma (* a c) -3 (* b b)))
1.3b
(fma (* a c) -3 (* b b))
0.6b
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
0.2b
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u pow1 fma-def times-frac insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod distribute-lft-out
2×neg-sub0 flip3-+ associate-+l- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sum-log frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
34.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
10.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
1.0ms
(sqrt (fma (* a c) -3 (* b b)))
0.0ms
(fma (* a c) -3 (* b b))

series464.0ms

Calls
4 calls:
Slowest
142.0ms
(sqrt (fma (* a c) -3 (* b b)))
142.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
101.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
79.0ms
(fma (* a c) -3 (* b b))

simplify2.3s

Calls
35 calls:
Slowest
314.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -3 (* b b))) (sqrt (fma (* a c) -3 (* b b)))))
262.0ms
(+ (pow (- b) 3) (pow (sqrt (fma (* a c) -3 (* b b))) 3))
260.0ms
(/ (* (* (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
124.0ms
(- (log (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (log (* 3 a)))
116.0ms
(- (* 3/2 (/ (* a c) b)) (* 2 b))

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.8b

localize4.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma (* a c) -3 (* b b)))
1.3b
(fma (* a c) -3 (* b b))
0.6b
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
0.2b
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
6×add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u pow1 fma-def times-frac insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod distribute-lft-out
2×neg-sub0 flip3-+ associate-+l- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sum-log frac-2neg pow1/2 div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
18.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
5.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
1.0ms
(sqrt (fma (* a c) -3 (* b b)))
0.0ms
(fma (* a c) -3 (* b b))

series484.0ms

Calls
4 calls:
Slowest
178.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
111.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
105.0ms
(sqrt (fma (* a c) -3 (* b b)))
90.0ms
(fma (* a c) -3 (* b b))

simplify2.3s

Calls
35 calls:
Slowest
317.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -3 (* b b))) (sqrt (fma (* a c) -3 (* b b)))))
274.0ms
(/ (* (* (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
250.0ms
(+ (pow (- b) 3) (pow (sqrt (fma (* a c) -3 (* b b))) 3))
120.0ms
(- (log (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (log (* 3 a)))
116.0ms
(* -3/2 (/ (* a c) b))

prune985.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.8b

regimes1.1s

Accuracy

83% (4.7b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.0b

bsearch244.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.0s1075×body2560valid
931.0ms5843×body80valid
806.0ms2973×body80nan
612.0ms882×body1280valid
242.0ms463×body640valid
131.0ms105×body5120valid
112.0ms227×body320valid
30.0ms121×body160valid