Details

Time bar (total: 28.5s)

sample97.0ms

Algorithm
intervals
Results
23.0ms197×body80valid
18.0ms28×body2560valid
11.0ms91×body80nan
10.0ms20×body1280valid
9.0ms19×body640valid
4.0ms11×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify166.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.1b

localize19.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 3 a) c)))
1.0b
(- (* b b) (* (* 3 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
77.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
30.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms
(- (* b b) (* (* 3 a) c))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
160.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
111.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
75.0ms
(- (* b b) (* (* 3 a) c))

simplify5.0s

Counts
52 → 106
Calls
52 calls:
Slowest
593.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
338.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
335.0ms
(/ (* (* (+ (- 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)))
276.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
259.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 3) 3) (* (* a a) a)))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.5b

localize29.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 3 a) c)))
1.0b
(- (* b b) (* (* 3 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(* (* 3 a) c)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
26.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
19.0ms
(* (* 3 a) c)
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
8.0ms
(- (* b b) (* (* 3 a) c))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
94.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
56.0ms
(- (* b b) (* (* 3 a) c))
37.0ms
(* (* 3 a) c)

simplify3.4s

Counts
41 → 96
Calls
41 calls:
Slowest
385.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
382.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
378.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
292.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
237.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.5b

localize52.0ms

Local error

Found 4 expressions with local error:

22.1b
(pow (fma b b (* a (* c -3))) (/ 1 2))
1.3b
(fma b b (* a (* c -3)))
0.5b
(+ (- b) (pow (fma b b (* a (* c -3))) (/ 1 2)))
0.2b
(* a (* c -3))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
16×add-sqr-sqrt add-cube-cbrt
13×pow-unpow
10×pow1 fma-def add-exp-log
9×times-frac add-cbrt-cube
8×add-log-exp
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in unpow-prod-down associate-*l* pow-prod-down prod-exp cbrt-unprod
2×sum-log distribute-lft-out
1×neg-sub0 pow-to-exp +-commutative neg-mul-1 pow-pow flip3-+ associate-*r* neg-log pow-exp *-commutative associate-+l- flip-+ fma-udef div-inv sqr-pow
Counts
4 → 90
Calls
4 calls:
Slowest
25.0ms
(+ (- b) (pow (fma b b (* a (* c -3))) (/ 1 2)))
24.0ms
(* a (* c -3))
5.0ms
(pow (fma b b (* a (* c -3))) (/ 1 2))
0.0ms
(fma b b (* a (* c -3)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(+ (- b) (pow (fma b b (* a (* c -3))) (/ 1 2)))
98.0ms
(pow (fma b b (* a (* c -3))) (/ 1 2))
62.0ms
(fma b b (* a (* c -3)))
24.0ms
(* a (* c -3))

simplify3.6s

Counts
49 → 102
Calls
49 calls:
Slowest
421.0ms
(* (exp (- b)) (exp (pow (fma b b (* a (* c -3))) (/ 1 2))))
403.0ms
(* (* (* a a) a) (* (* (* c -3) (* c -3)) (* c -3)))
318.0ms
(pow (* (cbrt (fma b b (* a (* c -3)))) (cbrt (fma b b (* a (* c -3))))) (/ 1 2))
302.0ms
(* (* (* a a) a) (* (* (* c c) c) (* (* -3 -3) -3)))
287.0ms
(+ (- b) (pow (fma b b (* a (* c -3))) (/ 1 2)))

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.4b

localize40.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(fma -3 (* c a) (* b b))
0.5b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
44.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
15.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
113.0ms
(sqrt (fma -3 (* c a) (* b b)))
98.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
59.0ms
(fma -3 (* c a) (* b b))

simplify4.1s

Counts
87 → 114
Calls
87 calls:
Slowest
464.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
338.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
206.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
172.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 3) 3) (* (* a a) a)))
101.0ms
(- (pow b 2) (* 3 (* a c)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

regimes420.0ms

Accuracy

82.7% (4.8b remaining)

Error of 10.1b against oracle of 5.3b and baseline of 33.2b

bsearch180.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s1009×body2560valid
892.0ms5885×body80valid
823.0ms2893×body80nan
682.0ms889×body1280valid
305.0ms469×body640valid
120.0ms259×body320valid
112.0ms99×body5120valid
25.0ms109×body160valid