Details

Time bar (total: 5.1m)

sample108.0ms

Algorithm
intervals
Results
28.0ms29×body2560valid
23.0ms187×body80valid
18.0ms32×body1280valid
10.0ms94×body80nan
7.0ms16×body640valid
3.0ms7×body320valid
1.0ms2×body5120valid

simplify157.0ms

Calls
1 calls:
Slowest
157.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize22.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* 3 a) c)))
0.8b
(- (* b b) (* (* 3 a) c))
0.5b
(* (* 3 a) c)
0.4b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))

rewrite675.0ms

Algorithm
rewrite-expression-head
Rules
207×add-sqr-sqrt
93×*-un-lft-identity
72×times-frac
56×difference-of-squares
54×associate-*l*
47×unswap-sqr
43×add-cube-cbrt
37×sqrt-prod
27×associate-*r*
25×distribute-lft-out--
15×*-commutative
14×add-cbrt-cube add-exp-log
12×associate-/r*
10×pow1
6×swap-sqr associate-/l* add-log-exp
4×prod-exp cbrt-unprod insert-posit16
3×flip3-- pow-prod-down flip--
2×cbrt-undiv sqrt-div div-exp associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-inv
Calls
4 calls:
Slowest
554.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
54.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
32.0ms
(* (* 3 a) c)
32.0ms
(- (* b b) (* (* 3 a) c))

series317.0ms

Calls
4 calls:
Slowest
145.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
97.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
54.0ms
(- (* b b) (* (* 3 a) c))
20.0ms
(* (* 3 a) c)

simplify20.2s

Calls
261 calls:
Slowest
588.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
397.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
395.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
374.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
287.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

localize39.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
0.8b
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
0.4b
(/ (- (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))) b) (* 3 a))
0.3b
(* (cbrt 3) a)

rewrite3.2s

Algorithm
rewrite-expression-head
Rules
1823×add-sqr-sqrt
1053×unswap-sqr
396×difference-of-squares
334×cbrt-prod
208×sqrt-prod
158×swap-sqr
122×*-commutative
100×*-un-lft-identity
72×times-frac
47×associate-*l*
42×add-cube-cbrt
27×distribute-lft-out--
24×associate-*r*
12×associate-/r* add-cbrt-cube
11×add-exp-log
7×pow1
6×associate-/l* add-log-exp
4×insert-posit16
3×flip3-- cbrt-unprod flip--
2×cbrt-undiv sqrt-div div-exp prod-exp associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub pow-prod-down div-inv
Calls
4 calls:
Slowest
2.8s
(/ (- (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))) b) (* 3 a))
243.0ms
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
136.0ms
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
12.0ms
(* (cbrt 3) a)

series587.0ms

Calls
4 calls:
Slowest
237.0ms
(/ (- (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))) b) (* 3 a))
181.0ms
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
104.0ms
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
64.0ms
(* (cbrt 3) a)

simplify2.5m

Calls
769 calls:
Slowest
748.0ms
(/ (- (sqrt (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))) (sqrt b)) (* (sqrt 3) (sqrt a)))
580.0ms
(/ (- (sqrt (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))) (sqrt b)) (* (cbrt 3) a))
573.0ms
(- (sqrt (* b b)) (* (* (cbrt (sqrt 3)) (cbrt (sqrt 3))) (* (sqrt (* (cbrt 3) a)) (sqrt c))))
559.0ms
(/ (+ (sqrt (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))) (sqrt b)) (* 3 (* (cbrt a) (cbrt a))))
554.0ms
(/ (- (sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))) b) (* (sqrt 3) (sqrt a)))

prune7.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize40.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
0.8b
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
0.3b
(* (cbrt 3) a)
0.2b
(* (* (cbrt 3) a) c)

rewrite478.0ms

Algorithm
rewrite-expression-head
Rules
1740×add-sqr-sqrt
1053×unswap-sqr
370×difference-of-squares
339×cbrt-prod
195×sqrt-prod
158×swap-sqr
117×*-commutative
48×associate-*l*
45×*-un-lft-identity
14×add-cbrt-cube distribute-lft-out--
13×add-cube-cbrt
12×pow1
11×add-exp-log
9×associate-*r*
7×cbrt-unprod
6×add-log-exp
4×pow-prod-down prod-exp insert-posit16
2×flip3-- sqrt-div flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Calls
4 calls:
Slowest
286.0ms
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
137.0ms
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
28.0ms
(* (* (cbrt 3) a) c)
6.0ms
(* (cbrt 3) a)

series436.0ms

Calls
4 calls:
Slowest
162.0ms
(sqrt (- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c))))
141.0ms
(- (* b b) (* (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) c)))
78.0ms
(* (* (cbrt 3) a) c)
55.0ms
(* (cbrt 3) a)

simplify1.5m

Calls
633 calls:
Slowest
808.0ms
(* (* (* (* (cbrt 3) (cbrt 3)) (cbrt 3)) (* (* a a) a)) (* (* c c) c))
785.0ms
(- (sqrt (* b b)) (* (* (sqrt (cbrt 3)) (sqrt (cbrt 3))) (* (* (sqrt (cbrt 3)) (sqrt a)) (sqrt c))))
608.0ms
(sqrt (+ b (* (* (cbrt (sqrt 3)) (sqrt (cbrt 3))) (* (* (sqrt (cbrt 3)) (sqrt a)) (sqrt c)))))
582.0ms
(* (* (* (* (cbrt 3) a) (* (cbrt 3) a)) (* (cbrt 3) a)) (* (* c c) c))
449.0ms
(- (* (sqrt b) (sqrt b)) (* (* (cbrt (sqrt 3)) (cbrt (sqrt 3))) (* (* (cbrt (sqrt 3)) (sqrt a)) (sqrt c))))

prune7.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.7b

localize43.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (+ (* b b) (* (* c -3) a)))
0.8b
(+ (* b b) (* (* c -3) a))
0.4b
(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
0.2b
(* (* c -3) a)

rewrite792.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
93×*-un-lft-identity
72×times-frac
54×associate-*l*
43×add-cube-cbrt
27×associate-*r*
26×difference-of-squares
22×sqrt-prod
14×add-cbrt-cube add-exp-log
13×distribute-lft-out--
12×associate-/r* distribute-lft-out
11×unswap-sqr
10×pow1
9×*-commutative
6×associate-/l* add-log-exp
4×prod-exp cbrt-unprod insert-posit16
3×pow-prod-down
2×cbrt-undiv flip3-+ sqrt-div div-exp flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-- pow1/2 div-sub div-inv flip--
Calls
4 calls:
Slowest
671.0ms
(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
63.0ms
(sqrt (+ (* b b) (* (* c -3) a)))
33.0ms
(+ (* b b) (* (* c -3) a))
22.0ms
(* (* c -3) a)

series350.0ms

Calls
4 calls:
Slowest
146.0ms
(/ (- (sqrt (+ (* b b) (* (* c -3) a))) b) (* 3 a))
113.0ms
(sqrt (+ (* b b) (* (* c -3) a)))
59.0ms
(+ (* b b) (* (* c -3) a))
31.0ms
(* (* c -3) a)

simplify14.3s

Calls
216 calls:
Slowest
909.0ms
(- (* (sqrt (+ (* b b) (* (* c -3) a))) (sqrt (+ (* b b) (* (* c -3) a)))) (* b b))
461.0ms
(* (* (* (* c -3) (* c -3)) (* c -3)) (* (* a a) a))
416.0ms
(* (* (* (* c c) c) (* (* -3 -3) -3)) (* (* a a) a))
349.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -3) a) (* (* c -3) a))))
296.0ms
(- (pow (sqrt (+ (* b b) (* (* c -3) a))) 3) (pow b 3))

prune2.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.7b

regimes869.0ms

Accuracy

85.2% (4.1b remaining)

Error of 10.1b against oracle of 5.9b and baseline of 33.9b

bsearch147.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.4s1070×body2560valid
822.0ms5833×body80valid
821.0ms2889×body80nan
688.0ms906×body1280valid
419.0ms476×body640valid
129.0ms110×body5120valid
81.0ms226×body320valid
22.0ms89×body160valid