Details

Time bar (total: 20.5s)

sample37.0ms

Algorithm
intervals
Results
8.0ms211×body80valid
6.0ms16×body1280valid
4.0ms256×pre80true
3.0ms17×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify54.0ms

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: 21.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite912.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity times-frac
62×add-sqr-sqrt
58×add-cube-cbrt
42×fma-def
24×associate-/r/
21×distribute-lft-out
20×add-exp-log add-cbrt-cube
19×flip3-+ flip-+
18×prod-diff
12×div-inv
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r*
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*r/ associate-*l* associate-*l/ log1p-expm1-u
3×prod-exp cbrt-unprod
2×sub-neg frac-2neg clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 212
Calls
4 calls:
36.0ms
(* (+ alpha beta) (- beta alpha))
178.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
632.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
56.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ alpha beta) (- beta alpha))
248.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
292.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
83.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify46.0ms

Counts
224 → 224
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09372463
150022158
done50022158

prune840.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
0.9b
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
4.7b
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
52×*-un-lft-identity
46×add-sqr-sqrt
39×times-frac
28×add-cube-cbrt
24×associate-*r*
22×prod-exp cbrt-unprod
19×frac-times
18×cbrt-undiv div-exp
17×associate-*l*
13×associate-*l/
11×pow1 associate-*r/ associate-/l/
10×fma-def
9×flip3-- flip-- distribute-lft-out
8×prod-diff
7×distribute-rgt-in distribute-lft-in
6×associate-/r/ add-log-exp
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u div-inv unswap-sqr
3×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
2×sub-neg associate--l+ *-commutative
1×+-commutative frac-2neg clear-num sum-log associate-/l*
Counts
4 → 184
Calls
4 calls:
297.0ms
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
115.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
636.0ms
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
200.0ms
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

series785.0ms

Counts
4 → 12
Calls
4 calls:
259.0ms
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
130.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
305.0ms
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
91.0ms
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

simplify54.0ms

Counts
196 → 196
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010273537
150012963
done50012963

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.5b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.9b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3236
Calls
4 calls:
238.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
27.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
43.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.3s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series678.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
158.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
138.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify425.0ms

Counts
3248 → 3248
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500147194
done500147194

prune9.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.8b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
46.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
182.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series534.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
173.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
284.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify99.0ms

Counts
190 → 190
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07273112
132592892
250022876
done50022876

prune576.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

regimes240.0ms

Accuracy

16.2% (5.5b remaining)

Error of 11.7b against oracle of 6.1b and baseline of 12.7b

bsearch70.0ms

Steps
ItersRangePoint
8
1.598288092058601e+139
7.397337972832879e+141
5.849296461317042e+141

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14326
24326
done4326

end0.0ms

sample860.0ms

Algorithm
intervals
Results
243.0ms6317×body80valid
118.0ms8000×pre80true
102.0ms523×body1280valid
96.0ms609×body640valid
38.0ms336×body320valid
16.0ms215×body160valid