Details

Time bar (total: 17.5s)

sample155.0ms

Algorithm
intervals
Results
36.0ms38×body2560valid
32.0ms20×body640valid
28.0ms178×body80valid
21.0ms28×body1280valid
14.0ms97×body80nan
2.0ms5×body320valid
2.0ms6×body160valid
2.0ms2×body5120valid

simplify120.0ms

Calls
1 calls:
Slowest
119.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize37.0ms

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)

rewrite64.0ms

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
24.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
24.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series449.0ms

Calls
4 calls:
Slowest
125.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
120.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
112.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
93.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.2s

Calls
31 calls:
Slowest
480.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
190.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
49.0ms
(sqrt (- (sqrt (fma c (* -4 a) (* b b))) b))
43.0ms
(* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)))
41.0ms
(sqrt (sqrt (fma c (* -4 a) (* b b))))

prune867.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.2b

localize6.0ms

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)

rewrite37.0ms

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
17.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
11.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series463.0ms

Calls
4 calls:
Slowest
141.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
118.0ms
(sqrt (fma c (* -4 a) (* b b)))
107.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
97.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

simplify1.9s

Calls
39 calls:
Slowest
486.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
325.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
168.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
161.0ms
(* (* (* (/ (- (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)))
158.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (log (/ 1 a)))

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 33.2b

localize14.0ms

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)))))

rewrite20.0ms

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
9.0ms
(- (* (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)))

series434.0ms

Calls
4 calls:
Slowest
125.0ms
(sqrt (fma c (* -4 a) (* b b)))
108.0ms
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))
105.0ms
(sqrt (fma c (* -4 a) (* b b)))
96.0ms
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)

simplify1.1s

Calls
49 calls:
Slowest
154.0ms
(* (* (* (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))))))
49.0ms
(sqrt (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))))
46.0ms
(* (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))))
46.0ms
(sqrt (sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b))))))
44.0ms
(sqrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 33.2b

localize1.0ms

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)

rewrite44.0ms

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
24.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
12.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
6.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series482.0ms

Calls
4 calls:
Slowest
140.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
136.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
111.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
95.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.3s

Calls
31 calls:
Slowest
563.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
193.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
72.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
54.0ms
(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
50.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))

prune967.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.2b

regimes530.0ms

Accuracy

94.3% (0.3b remaining)

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

bsearch128.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.5s1093×body2560valid
1.1s916×body1280valid
866.0ms5797×body80valid
427.0ms2941×body80nan
279.0ms453×body640valid
128.0ms110×body5120valid
123.0ms240×body320valid
29.0ms120×body160valid