Details

Time bar (total: 18.3s)

sample118.0ms

Algorithm
intervals
Results
30.0ms38×body2560valid
25.0ms178×body80valid
19.0ms28×body1280valid
12.0ms97×body80nan
11.0ms20×body640valid
2.0ms5×body320valid
2.0ms6×body160valid
1.0ms2×body5120valid

simplify131.0ms

Calls
1 calls:
Slowest
131.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize24.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma c (* -4 a) (* b b)))
1.5b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×associate-/l*
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×div-sub div-inv associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×rem-sqrt-square sub-neg pow1/2
Calls
4 calls:
Slowest
26.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
12.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series365.0ms

Calls
4 calls:
Slowest
103.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
93.0ms
(sqrt (fma c (* -4 a) (* b b)))
92.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
78.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify1.2s

Calls
31 calls:
Slowest
500.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
170.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
64.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
51.0ms
(* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)))
47.0ms
(sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))

prune989.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.2b

localize8.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma c (* -4 a) (* b b)))
1.5b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
0.2b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×flip3-- flip-- associate-/l/
1×frac-times rem-sqrt-square clear-num sub-neg frac-2neg pow1/2 div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ un-div-inv *-commutative cbrt-unprod
Calls
4 calls:
Slowest
24.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
21.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series451.0ms

Calls
4 calls:
Slowest
120.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
115.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
109.0ms
(sqrt (fma c (* -4 a) (* b b)))
107.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)

simplify2.2s

Calls
39 calls:
Slowest
590.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
332.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
201.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (log (/ 1 a)))
180.0ms
(* (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
160.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 33.2b

localize13.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma c (* -4 a) (* b b)))
25.3b
(sqrt (fma c (* -4 a) (* b b)))
12.7b
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
0.5b
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×pow1 associate-*r* associate-*l*
6×add-cbrt-cube pow1/2 add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow-prod-down pow-prod-up
1×pow2 sub-neg rem-square-sqrt pow-plus flip3-- fma-neg sqrt-unprod prod-exp *-commutative cbrt-unprod flip--
Calls
4 calls:
Slowest
13.0ms
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
8.0ms
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series428.0ms

Calls
4 calls:
Slowest
125.0ms
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
107.0ms
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))
102.0ms
(sqrt (fma c (* -4 a) (* b b)))
95.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.2s

Calls
49 calls:
Slowest
165.0ms
(* (* (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (* (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) (sqrt (sqrt (fma c (* -4 a) (* b b))))))
48.0ms
(sqrt (sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b))))))
48.0ms
(sqrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))
45.0ms
(+ (log (sqrt (sqrt (fma c (* -4 a) (* b b))))) (log (sqrt (sqrt (fma c (* -4 a) (* b b))))))
45.0ms
(sqrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 33.2b

localize15.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma c (* a -4) (* b b)))
1.5b
(- (sqrt (fma c (* a -4) (* b b))) b)
0.2b
(/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)
0.1b
(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) a)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
7×associate-/l*
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×div-sub div-inv associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×rem-sqrt-square sub-neg pow1/2
Calls
4 calls:
Slowest
11.0ms
(/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)
11.0ms
(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) a)
10.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series402.0ms

Calls
4 calls:
Slowest
111.0ms
(/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)
105.0ms
(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) a)
96.0ms
(sqrt (fma c (* a -4) (* b b)))
90.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)

simplify1.3s

Calls
31 calls:
Slowest
547.0ms
(- (* (sqrt (fma c (* a -4) (* b b))) (sqrt (fma c (* a -4) (* b b)))) (* b b))
176.0ms
(- (pow (sqrt (fma c (* a -4) (* b b))) 3) (pow b 3))
68.0ms
(* (cbrt (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)))
44.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
43.0ms
(/ (sqrt (fma c (* a -4) (* b b))) 2)

prune959.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.2b

regimes511.0ms

Accuracy

94.3% (0.3b remaining)

Error of 29.2b against oracle of 28.9b and baseline of 33.8b

bsearch145.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.2s1093×body2560valid
964.0ms5797×body80valid
957.0ms916×body1280valid
791.0ms453×body640valid
526.0ms240×body320valid
419.0ms2941×body80nan
147.0ms110×body5120valid
34.0ms120×body160valid