Details

Time bar (total: 32.9s)

sample104.0ms

Algorithm
intervals
Results
29.0ms197×body80valid
21.0ms256×pre80true
12.0ms20×body640valid
12.0ms16×body1280valid
7.0ms17×body320valid
2.0ms6×body160valid

simplify603.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize40.0ms

Local error

Found 3 expressions with local error:

17.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.3b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite734.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- insert-posit16 flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 114
Calls
3 calls:
Slowest
525.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
140.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
66.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series846.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
374.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
329.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
143.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts
123 → 123

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize40.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.0b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-cbrt-cube add-exp-log
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×associate-*l* insert-posit16
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 299
Calls
4 calls:
Slowest
406.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
183.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
97.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
39.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series925.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
339.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
251.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
214.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
121.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify2.1s

Counts
311 → 311

prune4.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize88.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.0b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite654.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
131×*-un-lft-identity
96×add-sqr-sqrt
90×associate-*r*
63×add-cube-cbrt
22×distribute-lft-out
13×add-cbrt-cube add-exp-log
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+ add-log-exp
6×pow1
5×div-inv
4×associate-*l* insert-posit16
3×cbrt-undiv +-commutative sum-log div-exp prod-exp cbrt-unprod unswap-sqr
2×frac-times associate-*l/
1×pow-prod-down associate-*r/ *-commutative
Counts
4 → 154
Calls
4 calls:
Slowest
380.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
103.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
84.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
80.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
356.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
276.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
266.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
258.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.6s

Counts
166 → 166

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize61.0ms

Local error

Found 4 expressions with local error:

7.3b
(+ (* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
2.0b
(* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
0.4b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
344×times-frac
273×add-sqr-sqrt
251×*-un-lft-identity
154×associate-*r*
141×add-cube-cbrt
132×sqrt-prod
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
31×associate-*l*
29×distribute-lft-out
25×unswap-sqr
21×distribute-lft-out-- difference-of-squares
20×associate-/r/
19×cbrt-undiv cbrt-unprod
15×flip3-+ flip-+
13×pow1
10×frac-times div-inv
7×rec-exp associate-/r* 1-exp associate-*r/
6×sqrt-div associate-*l/ add-log-exp
4×pow-prod-down insert-posit16
3×pow-flip associate-/l*
2×*-commutative
1×+-commutative clear-num sum-log frac-2neg sqrt-pow1 pow1/2 inv-pow
Counts
4 → 347
Calls
4 calls:
Slowest
526.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
423.0ms
(+ (* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
422.0ms
(* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
92.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
368.0ms
(* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
254.0ms
(+ (* (+ beta alpha) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)
248.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
195.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify1.3s

Counts
359 → 359

prune5.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

regimes394.0ms

Accuracy

6% (5.9b remaining)

Error of 11.8b against oracle of 6.0b and baseline of 12.2b

bsearch431.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s6365×body80valid
724.0ms8000×pre80true
393.0ms552×body640valid
375.0ms504×body1280valid
188.0ms373×body320valid
54.0ms206×body160valid