Details

Time bar (total: 59.0s)

sample163.0ms

Algorithm
intervals
Results
44.0ms178×body80valid
39.0ms38×body2560valid
24.0ms28×body1280valid
15.0ms97×body80nan
13.0ms20×body640valid
2.0ms5×body320valid
2.0ms2×body5120valid
2.0ms6×body160valid

simplify169.0ms

Calls
1 calls:
Slowest
169.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize23.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma b b (* (* a c) -4)))
1.5b
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0b
(fma b b (* (* a c) -4))
0.2b
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Calls
4 calls:
Slowest
29.0ms
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
8.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series527.0ms

Calls
4 calls:
Slowest
162.0ms
(/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)
137.0ms
(sqrt (fma b b (* (* a c) -4)))
136.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
92.0ms
(fma b b (* (* a c) -4))

simplify5.6s

Calls
111 calls:
Slowest
459.0ms
(- (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (* b b))
347.0ms
(- (pow (sqrt (fma b b (* (* a c) -4))) 3) (pow b 3))
231.0ms
(/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2))
180.0ms
(- b (* 2 (/ (* a c) b)))
130.0ms
(fma (* (cbrt (sqrt (fma b b (* (* a c) -4)))) (cbrt (sqrt (fma b b (* (* a c) -4))))) (cbrt (sqrt (fma b b (* (* a c) -4)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize27.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma b b (* (* a c) -4)))
13.2b
(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
3.4b
(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
1.0b
(fma b b (* (* a c) -4))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
54×add-cbrt-cube add-exp-log
26×times-frac
19×cbrt-undiv div-exp
18×add-sqr-sqrt prod-exp cbrt-unprod
17×*-un-lft-identity add-cube-cbrt
10×associate-*r/ associate-/r/
8×associate-/l*
6×div-inv
5×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef associate-/l/
Calls
4 calls:
Slowest
33.0ms
(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
22.0ms
(/ (* (* a -4) c) (* 2 (+ (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))

series697.0ms

Calls
4 calls:
Slowest
256.0ms
(/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)))
236.0ms
(/ (/ (* (* a -4) c) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) a)
120.0ms
(sqrt (fma b b (* (* a c) -4)))
85.0ms
(fma b b (* (* a c) -4))

simplify28.6s

Calls
100 calls:
Slowest
2.0s
(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 2) 2) (* (* (+ (sqrt (fma b b (* (* a c) -4))) b) (+ (sqrt (fma b b (* (* a c) -4))) b)) (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.8s
(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.8s
(/ (* (* (* (* a a) a) (* (* -4 -4) -4)) (* (* c c) c)) (* (* (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.7s
(/ (* (* (* (* a -4) (* a -4)) (* a -4)) (* (* c c) c)) (* (* (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b)) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))) (* 2 (+ (sqrt (fma b b (* (* a c) -4))) b))))
1.3s
(/ (* (* (* (* a a) a) (* (* -4 -4) -4)) (* (* c c) c)) (* (* (* 2 2) 2) (* (* (+ (sqrt (fma b b (* (* a c) -4))) b) (+ (sqrt (fma b b (* (* a c) -4))) b)) (+ (sqrt (fma b b (* (* a c) -4))) b))))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.3b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
97×times-frac
86×*-un-lft-identity
57×add-sqr-sqrt
56×add-cube-cbrt
15×distribute-lft-out
13×associate-/l*
9×add-cbrt-cube add-exp-log
6×fma-def sqrt-prod div-inv add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp
2×flip3-+ associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 fma-udef associate-/l/
Calls
4 calls:
Slowest
26.0ms
(/ (/ c -1/2) (+ (sqrt (fma b b (* a (* c -4)))) b))
12.0ms
(+ (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)))

series586.0ms

Calls
4 calls:
Slowest
243.0ms
(/ (/ c -1/2) (+ (sqrt (fma b b (* a (* c -4)))) b))
127.0ms
(+ (sqrt (fma b b (* a (* c -4)))) b)
124.0ms
(sqrt (fma b b (* a (* c -4))))
92.0ms
(fma b b (* a (* c -4)))

simplify9.1s

Calls
149 calls:
Slowest
442.0ms
(+ (* (sqrt (fma b b (* a (* c -4)))) (sqrt (fma b b (* a (* c -4))))) (- (* b b) (* (sqrt (fma b b (* a (* c -4)))) b)))
402.0ms
(/ (/ (* (cbrt c) (cbrt c)) (* (cbrt -1/2) (cbrt -1/2))) (* (cbrt (+ (sqrt (fma b b (* a (* c -4)))) b)) (cbrt (+ (sqrt (fma b b (* a (* c -4)))) b))))
292.0ms
(- b (* 2 (/ (* a c) b)))
258.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
201.0ms
(/ (/ (* (cbrt c) (cbrt c)) (sqrt -1/2)) (* (cbrt (+ (sqrt (fma b b (* a (* c -4)))) b)) (cbrt (+ (sqrt (fma b b (* a (* c -4)))) b))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.7b

localize50.0ms

Local error

Found 4 expressions with local error:

25.3b
(sqrt (fma b b (* a (* c -4))))
1.0b
(fma b b (* a (* c -4)))
0.6b
(cbrt c)
0.6b
(cbrt c)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma b b (* a (* c -4))))
1.0ms
(cbrt c)
1.0ms
(cbrt c)
0.0ms
(fma b b (* a (* c -4)))

series1.2s

Calls
4 calls:
Slowest
687.0ms
(cbrt c)
270.0ms
(cbrt c)
136.0ms
(sqrt (fma b b (* a (* c -4))))
75.0ms
(fma b b (* a (* c -4)))

simplify1.0s

Calls
23 calls:
Slowest
178.0ms
(- b (* 2 (/ (* a c) b)))
140.0ms
(* (cbrt -1) (pow (* c -1) 1/3))
126.0ms
(* (cbrt -1) (pow (* c -1) 1/3))
88.0ms
(- (* 2 (/ (* a c) b)) b)
80.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.7b

regimes366.0ms

Accuracy

85.7% (3.4b remaining)

Error of 8.9b against oracle of 5.5b and baseline of 29.4b

bsearch425.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.5s1093×body2560valid
976.0ms5797×body80valid
619.0ms916×body1280valid
434.0ms2941×body80nan
336.0ms453×body640valid
122.0ms240×body320valid
113.0ms110×body5120valid
64.0ms120×body160valid