Details

Time bar (total: 17.2s)

sample45.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01753
16052
229548
3183248
done500048

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.5b

localize40.0ms

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))))
38.4b
(/ (/ (* (* 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))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.1s

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:
219.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
193.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
444.0ms
(/ (/ (* (* 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))
249.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
185.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s
(/ (/ (* (* 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))
275.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify898.0ms

Counts
220 → 220
Iterations

Useful iterations: done (883.0ms)

IterNodesCost
036612421
1137011478
done50019638

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.8b

localize45.0ms

Local error

Found 4 expressions with local error:

35.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
36.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
36.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

rewrite480.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
12×associate-/r*
8×associate-/l*
6×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg associate-*r/ clear-num log1p-expm1-u div-inv associate-/l/ add-log-exp
2×flip3-+ prod-exp cbrt-unprod flip-+
Counts
4 → 108
Calls
4 calls:
58.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
402.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
9.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
9.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

series593.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
117.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
184.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
185.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))

simplify885.0ms

Counts
120 → 120
Iterations

Useful iterations: done (881.0ms)

IterNodesCost
01092616
12712574
214392282
done50022270

prune828.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.8b

localize60.0ms

Local error

Found 4 expressions with local error:

35.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
35.4b
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
36.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
36.2b
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×times-frac
25×add-exp-log *-un-lft-identity
24×add-cube-cbrt
21×add-cbrt-cube
13×associate-*r*
9×associate-/r*
7×div-exp
6×pow1 cbrt-undiv prod-exp
5×associate-*r/ associate-/l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp
3×frac-2neg associate-*l* clear-num unswap-sqr
2×flip3-+ flip-+
1×rec-exp 1-exp pow-prod-down un-div-inv *-commutative
Counts
4 → 117
Calls
4 calls:
43.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
52.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
9.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
37.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
137.0ms
(/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta)))
137.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))
149.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))

simplify1.2s

Counts
129 → 129
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01652763
14222639
221472289
done50012281

prune873.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 35.8b

localize75.0ms

Local error

Found 4 expressions with local error:

36.2b
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))
37.0b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.0b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
37.0b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×*-un-lft-identity
15×add-cube-cbrt
13×add-exp-log associate-*r*
11×times-frac
9×cbrt-prod add-cbrt-cube
6×pow1
4×expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×div-exp cbrt-unprod
1×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 77
Calls
4 calls:
15.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series851.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (/ 1 (fma 2.0 i (+ alpha beta))))
279.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
207.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
207.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify831.0ms

Counts
89 → 89
Iterations

Useful iterations: done (827.0ms)

IterNodesCost
01261740
13041629
210781435
done50011407

prune1.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 35.8b

regimes260.0ms

Accuracy

37.6% (2.2b remaining)

Error of 36.8b against oracle of 34.5b and baseline of 38.1b

bsearch94.0ms

Steps
ItersRangePoint
7
4.208907867440382e+224
1.6005123975973089e+226
4.284299083279605e+224

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02592
13192
done3192

end0.0ms

sample2.0s

Algorithm
intervals
Results
859.0ms8000×body80valid
721.0ms8000×pre80true