Details

Time bar (total: 27.1s)

sample60.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
12.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01753
16052
229548
3183248
done500048

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.0b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 208
Calls
4 calls:
214.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
124.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
359.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
305.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series2.1s

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
148.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.6s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
298.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify716.0ms

Counts
220 → 220
Iterations

Useful iterations: done (706.0ms)

IterNodesCost
036612421
1137011478
done50019638

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
34.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
256×times-frac
209×*-un-lft-identity
181×add-sqr-sqrt
108×add-cube-cbrt
84×associate-*r*
74×add-exp-log add-cbrt-cube
45×distribute-lft-out
41×associate-*l*
35×cbrt-undiv div-exp
26×difference-of-squares
22×div-inv
17×prod-exp cbrt-unprod
13×sqrt-prod distribute-lft-out--
11×associate-/r* associate-/l*
6×pow1 associate-/r/ unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r/ clear-num flip-+ associate-/l/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 291
Calls
4 calls:
94.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
391.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
51.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series4.2s

Counts
4 → 12
Calls
4 calls:
365.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0))))
3.6s
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
105.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
157.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify617.0ms

Counts
303 → 303
Iterations

Useful iterations: done (604.0ms)

IterNodesCost
041814581
1146014151
done500112667

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
34.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite527.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log add-cbrt-cube
81×times-frac
80×*-un-lft-identity
61×add-sqr-sqrt
41×add-cube-cbrt associate-*l*
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod distribute-lft-out
13×associate-*r*
12×associate-/r*
10×div-inv
6×pow1
5×associate-/l/ associate-/l*
4×expm1-log1p-u associate-*r/ associate-/r/ log1p-expm1-u add-log-exp difference-of-squares unswap-sqr
3×frac-2neg clear-num
2×frac-times flip3-+ associate-*l/ sqrt-prod flip-+ distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 190
Calls
4 calls:
182.0ms
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
262.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
53.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
10.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series4.8s

Counts
4 → 12
Calls
4 calls:
3.7s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
846.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))))
140.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
179.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify600.0ms

Counts
202 → 202
Iterations

Useful iterations: done (589.0ms)

IterNodesCost
03149608
110089262
done50007630

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 32.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))))
34.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
34.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
122×times-frac
120×*-un-lft-identity
118×sqrt-prod
65×add-sqr-sqrt add-cube-cbrt
33×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×associate-/r*
15×associate-/l*
13×div-inv
6×cbrt-undiv div-exp
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg associate-*r/ clear-num log1p-expm1-u add-log-exp
3×flip3-+ sqrt-div flip-+
2×prod-exp associate-/r/ cbrt-unprod
1×sqrt-undiv
Counts
4 → 195
Calls
4 calls:
79.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))))
43.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
79.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
10.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series1.4s

Counts
4 → 12
Calls
4 calls:
871.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))) (sqrt (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))))
156.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
170.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
181.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify1.6s

Counts
207 → 207
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02877003
15956544
228696224
done50026217

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 32.5b

regimes272.0ms

Accuracy

39.9% (2.3b remaining)

Error of 36.4b against oracle of 34.1b and baseline of 37.9b

bsearch116.0ms

Steps
ItersRangePoint
8
1.1683988266709735e+214
7.871996106811619e+216
1.1880562151605723e+214

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02467
12967
done2967

end0.0ms

sample2.0s

Algorithm
intervals
Results
931.0ms8000×body80valid
642.0ms8000×pre80true