Details

Time bar (total: 14.2s)

sample39.0ms

Algorithm
intervals
Results
12.0ms202×body80valid
5.0ms25×body1280valid
4.0ms256×pre80true
2.0ms14×body640valid
1.0ms8×body320valid
1.0ms7×body160valid

simplify52.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214
done500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite906.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
184.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
655.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
58.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series800.0ms

Counts
3 → 9
Calls
3 calls:
399.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
306.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
94.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782
done50011782

prune515.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.5b
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0b
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
8.0b
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
80×add-exp-log add-cbrt-cube
61×*-un-lft-identity
58×times-frac
49×add-sqr-sqrt
41×add-cube-cbrt sqrt-prod
34×cbrt-undiv div-exp
27×associate-*r*
24×prod-exp cbrt-unprod
14×associate-/r*
13×associate-*l*
10×distribute-lft-out
8×sqrt-div associate-/r/
6×pow1 add-log-exp
5×flip3-+ flip-+ associate-/l/
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l*
3×unswap-sqr
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×+-commutative flip3-- fma-def div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 187
Calls
4 calls:
162.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
198.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
723.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
283.0ms
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
364.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
159.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
252.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
301.0ms
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify66.0ms

Counts
199 → 199
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010765004
150014219
done50014219

prune623.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0b
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
8.0b
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
8.4b
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

rewrite936.0ms

Algorithm
rewrite-expression-head
Rules
62×add-exp-log add-cbrt-cube
58×*-un-lft-identity
51×times-frac
48×add-sqr-sqrt
40×add-cube-cbrt
33×sqrt-prod
27×associate-*r*
25×cbrt-undiv div-exp
20×prod-exp cbrt-unprod
16×cbrt-prod
13×associate-*l*
11×fma-def
9×distribute-lft-out
7×associate-/r*
6×pow1 sqrt-div associate-/r/ add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×cube-div cbrt-div div-inv associate-/l* unswap-sqr
2×cube-mult frac-times unpow-prod-down unpow3 cube-prod associate-*r/ associate-*l/ associate-/l/ sqr-pow
1×+-commutative flip3-- frac-2neg pow1/3 div-sub pow-prod-down clear-num sum-log *-commutative flip-- rem-cbrt-cube
Counts
4 → 178
Calls
4 calls:
195.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
713.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
18.0ms
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
3.0ms
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

series1.0s

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
254.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
311.0ms
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3)) 1.0)
296.0ms
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 3))

simplify66.0ms

Counts
190 → 190
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010344673
150014299
done50014299

prune727.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
6.0b
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3)) 1.0)
8.4b
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
382×times-frac
246×associate-*r*
218×*-un-lft-identity
211×sqrt-prod
196×add-sqr-sqrt
164×add-cube-cbrt
127×cbrt-div
119×cbrt-prod
97×add-exp-log add-cbrt-cube
84×sqrt-div associate-/r/
64×flip3-+ flip-+
45×cbrt-undiv div-exp
42×frac-times
30×prod-exp cbrt-unprod
27×distribute-lft-out
22×associate-*r/ associate-*l/
13×associate-*l*
12×div-inv
11×fma-def
10×unswap-sqr
6×pow1 add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cube-div
2×cube-mult unpow-prod-down pow1/3 unpow3 cube-prod sqr-pow
1×+-commutative pow-prod-down sum-log *-commutative rem-cbrt-cube
Counts
4 → 382
Calls
4 calls:
61.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.2s
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
15.0ms
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3)) 1.0)
2.0ms
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
263.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
318.0ms
(+ (cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3)) 1.0)
315.0ms
(cbrt (pow (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 3))

simplify170.0ms

Counts
394 → 394
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0262416114
1500215097
done500215097

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

regimes308.0ms

Accuracy

13.3% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 12.2b

bsearch94.0ms

Steps
ItersRangePoint
10
3.6798278606000456e+102
4.598624050959069e+119
6.237473251530061e+106

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05240
15240
done5240

end0.0ms

sample888.0ms

Algorithm
intervals
Results
273.0ms6386×body80valid
111.0ms523×body1280valid
110.0ms8000×pre80true
94.0ms563×body640valid
44.0ms334×body320valid
16.0ms194×body160valid