Details

Time bar (total: 14.1s)

sample128.0ms

Algorithm
intervals
Results
33.0ms201×body80valid
31.0ms31×body2560valid
21.0ms26×body1280valid
13.0ms87×body80nan
7.0ms11×body640valid
4.0ms3×body5120valid
2.0ms3×body320valid
1.0ms2×body160valid

simplify178.0ms

Calls
1 calls:
Slowest
178.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize21.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma b b (* (* a c) -4)))
1.0b
(fma b b (* (* a c) -4))
0.5b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
20.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
13.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series216.0ms

Calls
4 calls:
Slowest
72.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
60.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
44.0ms
(fma b b (* (* a c) -4))
40.0ms
(sqrt (fma b b (* (* a c) -4)))

simplify1.3s

Calls
26 calls:
Slowest
246.0ms
(- b (* 2 (/ (* a c) b)))
164.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
103.0ms
(- (* 2 (/ (* a c) b)) b)
89.0ms
(- (pow b 2) (* 4 (* a c)))
69.0ms
(* -2 (/ (* a c) b))

prune907.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
12.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series236.0ms

Calls
4 calls:
Slowest
91.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
50.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
49.0ms
(fma (* a c) -4 (* b b))
46.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify730.0ms

Calls
26 calls:
Slowest
93.0ms
(- (pow b 2) (* 4 (* a c)))
90.0ms
(- (pow b 2) (* 4 (* a c)))
82.0ms
(- (pow b 2) (* 4 (* a c)))
62.0ms
(* (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
55.0ms
(/ (/ (sqrt (fma (* a c) -4 (* b b))) 2) a)

prune971.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
5×pow1 associate-/r* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×associate-/r/ div-inv
1×rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
6.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
0.0ms
(fma (* a c) -4 (* b b))

series234.0ms

Calls
4 calls:
Slowest
94.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
51.0ms
(sqrt (fma (* a c) -4 (* b b)))
50.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
38.0ms
(fma (* a c) -4 (* b b))

simplify818.0ms

Calls
27 calls:
Slowest
84.0ms
(- (pow b 2) (* 4 (* a c)))
78.0ms
(cbrt (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
63.0ms
(/ 1 (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))
62.0ms
(- (pow b 2) (* 4 (* a c)))
59.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))

prune848.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (fma (* a c) -4 (* b b)))
19.5b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.8b
(fma (* a c) -4 (* b b))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow1/2 fma-udef
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))
0.0ms
(fma (* a c) -4 (* b b))

series198.0ms

Calls
4 calls:
Slowest
61.0ms
(sqrt (fma (* a c) -4 (* b b)))
60.0ms
(sqrt (fma (* a c) -4 (* b b)))
43.0ms
(fma (* a c) -4 (* b b))
34.0ms
(fma (* a c) -4 (* b b))

simplify673.0ms

Calls
20 calls:
Slowest
89.0ms
(- (pow b 2) (* 4 (* a c)))
85.0ms
(- (pow b 2) (* 4 (* a c)))
82.0ms
(- (pow b 2) (* 4 (* a c)))
70.0ms
(- (pow b 2) (* 4 (* a c)))
54.0ms
(- (pow b 2) (* 4 (* a c)))

prune930.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes337.0ms

Accuracy

83.3% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.5b

bsearch178.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.6s1021×body2560valid
949.0ms5887×body80valid
777.0ms926×body1280valid
492.0ms112×body5120valid
462.0ms3030×body80nan
317.0ms456×body640valid
125.0ms220×body320valid
67.0ms117×body160valid