Details

Time bar (total: 18.6s)

sample127.0ms

Algorithm
intervals
Results
33.0ms178×body80valid
29.0ms38×body2560valid
20.0ms28×body1280valid
12.0ms97×body80nan
10.0ms20×body640valid
2.0ms5×body320valid
2.0ms2×body5120valid
2.0ms6×body160valid

simplify146.0ms

Calls
1 calls:
Slowest
146.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

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)

rewrite47.0ms

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
20.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
13.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
10.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series533.0ms

Calls
4 calls:
Slowest
139.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
137.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
135.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
122.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.4s

Calls
31 calls:
Slowest
537.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
214.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
54.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
48.0ms
(* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)))
46.0ms
(sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b)))))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 33.2b

localize15.0ms

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)

rewrite65.0ms

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
25.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
23.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
13.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series520.0ms

Calls
4 calls:
Slowest
165.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
130.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
112.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

simplify2.3s

Calls
39 calls:
Slowest
587.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
345.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
222.0ms
(* (* (* (/ (- (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)))
182.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
179.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (log (/ 1 a)))

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 33.2b

localize27.0ms

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)))))

rewrite47.0ms

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
20.0ms
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))
20.0ms
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series533.0ms

Calls
4 calls:
Slowest
154.0ms
(sqrt (fma c (* -4 a) (* b b)))
141.0ms
(- (* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b))))) b)
138.0ms
(sqrt (fma c (* -4 a) (* b b)))
99.0ms
(* (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))))

simplify1.4s

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))))))
51.0ms
(+ (log (sqrt (sqrt (fma c (* -4 a) (* b b))))) (log (sqrt (sqrt (fma c (* -4 a) (* b b))))))
49.0ms
(sqrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))
48.0ms
(sqrt (sqrt (sqrt (fma c (* -4 a) (* b b)))))
47.0ms
(* (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (sqrt (fma c (* -4 a) (* b b))))))

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 33.2b

localize16.0ms

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)

rewrite60.0ms

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
27.0ms
(/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)
24.0ms
(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) a)
6.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series592.0ms

Calls
4 calls:
Slowest
176.0ms
(/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)
170.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
124.0ms
(/ (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2) a)
121.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Calls
31 calls:
Slowest
479.0ms
(- (* (sqrt (fma c (* a -4) (* b b))) (sqrt (fma c (* a -4) (* b b)))) (* b b))
131.0ms
(- (pow (sqrt (fma c (* a -4) (* b b))) 3) (pow b 3))
73.0ms
(* (cbrt (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2)))
56.0ms
(sqrt (/ (- (sqrt (fma c (* a -4) (* b b))) b) 2))
50.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)

prune915.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 33.2b

regimes402.0ms

Accuracy

94.3% (0.3b remaining)

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

bsearch140.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s916×body1280valid
1.1s1093×body2560valid
919.0ms5797×body80valid
484.0ms2941×body80nan
292.0ms453×body640valid
122.0ms240×body320valid
105.0ms110×body5120valid
31.0ms120×body160valid