Details

Time bar (total: 34.6s)

sample41.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
5.0ms256×pre80true

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
017485
160460
2280435
31614435
done5007435

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
0.0b
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
35.8b
(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))
47.2b
(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
22×times-frac
21×add-sqr-sqrt
17×cbrt-undiv div-exp prod-exp cbrt-unprod
16×pow1
15×*-un-lft-identity add-cube-cbrt
11×associate-/l*
8×associate-*r/
6×associate-*l* associate-/r/
5×distribute-rgt-in associate-/r* distribute-lft-in
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u div-inv add-log-exp difference-of-squares
3×flip3-- swap-sqr flip-- associate-/l/
2×clear-num frac-2neg flip3-+ *-commutative flip-+ fma-udef
1×pow2 pow-plus pow-sqr pow-prod-up unswap-sqr
Counts
4 → 136
Calls
4 calls:
5.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
64.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
90.0ms
(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))
75.0ms
(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
216.0ms
(* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i)))
472.0ms
(/ (/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))
881.0ms
(/ (* (fma beta alpha (* i (+ (+ alpha beta) i))) (* i (+ (+ alpha beta) i))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))

simplify3.3s

Counts
148 → 148
Iterations

Useful iterations: done (3.3s)

IterNodesCost
025865981
174058974
2329256023
done501655958

prune940.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))
0.1b
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
34.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
231×times-frac
155×add-sqr-sqrt
142×*-un-lft-identity
98×add-cube-cbrt
74×add-cbrt-cube add-exp-log
58×associate-*l*
40×associate-*r*
35×cbrt-undiv div-exp
24×associate-/r/
18×difference-of-squares
17×prod-exp cbrt-unprod
16×associate-/l*
15×div-inv
13×associate-/r* distribute-lft-out
9×sqrt-prod distribute-lft-out--
8×flip3-- flip--
6×pow1 unswap-sqr
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*r/ associate-/l/
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 280
Calls
4 calls:
51.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))
206.0ms
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
54.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
11.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
361.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))
861.0ms
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
255.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
429.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify3.4s

Counts
292 → 292
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0447177755
11416166457
done5000164470

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))) (fma 2.0 i (+ alpha beta)))
0.1b
(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
34.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
91×times-frac
85×add-cbrt-cube add-exp-log
76×add-sqr-sqrt
68×*-un-lft-identity
44×add-cube-cbrt
40×cbrt-undiv div-exp associate-*r*
21×prod-exp cbrt-unprod
18×associate-*l*
13×associate-/r*
12×associate-/r/
10×difference-of-squares
8×div-inv
7×distribute-lft-out
6×pow1
5×sqrt-prod associate-/l* distribute-lft-out-- associate-/l/
4×expm1-log1p-u flip3-- associate-*r/ log1p-expm1-u flip-- add-log-exp unswap-sqr
3×clear-num frac-2neg flip3-+ flip-+
2×frac-times associate-*l/
1×pow-prod-down *-commutative
Counts
4 → 200
Calls
4 calls:
123.0ms
(/ (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))) (fma 2.0 i (+ alpha beta)))
158.0ms
(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
42.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
11.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series3.7s

Counts
4 → 12
Calls
4 calls:
841.0ms
(/ (* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))) (fma 2.0 i (+ alpha beta)))
2.2s
(* (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (/ (/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
252.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
395.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify3.1s

Counts
212 → 212
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0360125724
11175116028
done5000112465

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
0.1b
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))))
0.2b
(* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
34.5b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

rewrite474.0ms

Algorithm
rewrite-expression-head
Rules
336×*-un-lft-identity
333×times-frac
236×add-sqr-sqrt
143×add-cube-cbrt
113×associate-*r*
88×distribute-lft-out
71×add-cbrt-cube add-exp-log
61×associate-*l*
42×difference-of-squares
26×cbrt-undiv div-exp
24×prod-exp cbrt-unprod
21×sqrt-prod distribute-lft-out--
16×associate-/r/
11×pow1
10×associate-/r* div-inv
8×associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u flip3-- pow-prod-down associate-*r/ log1p-expm1-u flip-- add-log-exp
3×unswap-sqr
2×clear-num frac-2neg *-commutative associate-/l/
1×frac-times associate-*l/
Counts
4 → 328
Calls
4 calls:
89.0ms
(/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
172.0ms
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))))
172.0ms
(* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
22.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

series2.0s

Counts
4 → 12
Calls
4 calls:
243.0ms
(/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
893.0ms
(* (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))) (* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta)))))
393.0ms
(* i (/ (/ (+ (+ alpha beta) i) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) (fma 2.0 i (+ alpha beta))))
462.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))

simplify3.8s

Counts
340 → 340
Iterations

Useful iterations: done (3.7s)

IterNodesCost
0471179151
11416167305
done5000163506

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 27.6b

regimes370.0ms

Accuracy

44.1% (5.1b remaining)

Error of 33.8b against oracle of 28.7b and baseline of 37.9b

bsearch192.0ms

Steps
ItersRangePoint
7
1.0039621938915216e+154
1.9524761169176419e+155
1.3095997644368501e+154
4
6.507028279409348e+146
1.035883662374499e+147
6.59041040993646e+146
5
1.471982168198973e+142
3.5205365678208034e+142
3.4734203445964717e+142

simplify48.0ms

Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
0431588
1581588
done581588

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8000×body80valid
248.0ms8000×pre80true