Details

Time bar (total: 24.4s)

sample68.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
8.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
done5001
31807
2295
160
017

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
0.1b
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
37.8b
(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
45.6b
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
28×add-sqr-sqrt
26×times-frac
22×prod-exp cbrt-unprod
20×*-un-lft-identity add-cube-cbrt
19×cbrt-undiv div-exp
16×pow1
7×div-inv
6×associate-*l* associate-/l* difference-of-squares
5×associate-/r*
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ associate-*r/ log1p-expm1-u add-log-exp
3×swap-sqr associate-/l/
2×clear-num frac-2neg flip3-+ associate-/r/ *-commutative flip-+ fma-udef
1×pow2 distribute-rgt-in distribute-lft-in pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 138
Calls
4 calls:
12.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
69.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
105.0ms
(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
91.0ms
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

series1.1s

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
225.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
445.0ms
(/ (/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))) (- (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))) 1.0))
372.0ms
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify529.0ms

Counts
150 → 150
Iterations
IterNodes
done5000
1759
0248

prune981.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
0.0b
(/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))
36.8b
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
217×*-un-lft-identity
144×add-sqr-sqrt
120×add-cube-cbrt
82×add-cbrt-cube add-exp-log
58×associate-*l*
46×distribute-lft-out
32×cbrt-undiv div-exp
27×prod-exp cbrt-unprod
26×associate-/l*
18×associate-/r/
13×associate-/r*
12×difference-of-squares
11×div-inv
9×pow1 flip3-+ flip-+
6×sqrt-prod distribute-lft-out--
5×frac-times associate-*r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/ associate-/l/
1×flip3-- associate-*r* *-commutative flip--
Counts
4 → 294
Calls
4 calls:
64.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
36.0ms
(/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
167.0ms
(* (/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))
21.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

series4.2s

Counts
4 → 12
Calls
4 calls:
258.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
388.0ms
(/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
3.3s
(* (/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))
238.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

simplify689.0ms

Counts
306 → 306
Iterations
IterNodes
done5001
11273
0425

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
0.0b
(/ i (fma i 2.0 (+ alpha beta)))
0.0b
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
64×add-sqr-sqrt
57×times-frac
51×add-cbrt-cube add-exp-log
40×add-cube-cbrt
21×distribute-lft-out
18×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
13×associate-*l*
12×associate-/r* difference-of-squares
11×associate-/l*
9×pow1
6×sqrt-prod distribute-lft-out--
5×frac-times associate-*r/
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp associate-/l/
3×clear-num frac-2neg pow-prod-down associate-*l/
2×flip3-- associate-/r/ flip--
1×flip3-+ div-sub associate-*r* *-commutative flip-+
Counts
4 → 173
Calls
4 calls:
62.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
7.0ms
(/ i (fma i 2.0 (+ alpha beta)))
23.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
145.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
145.0ms
(/ i (fma i 2.0 (+ alpha beta)))
280.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
867.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))

simplify1.7s

Counts
185 → 185
Iterations
IterNodes
done5001
24140
1785
0279

prune1.7s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 6.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
0.0b
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (exp (log (/ i (fma i 2.0 (+ alpha beta)))))))
1.3b
(exp (log (/ i (fma i 2.0 (+ alpha beta)))))

rewrite251.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
64×add-sqr-sqrt
57×times-frac
40×add-cube-cbrt
29×add-cbrt-cube
25×add-exp-log
21×distribute-lft-out
13×log-prod associate-*l* exp-sum
12×difference-of-squares
10×pow1 prod-exp cbrt-unprod
9×associate-/r*
8×associate-/l*
7×cbrt-undiv div-exp
6×sqrt-prod distribute-lft-out--
5×frac-times log-div exp-diff associate-*r/
4×expm1-log1p-u exp-prod log1p-expm1-u div-inv add-log-exp associate-/l/
3×pow-prod-down associate-*l/
2×clear-num frac-2neg flip3-- associate-/r/ flip--
1×flip3-+ div-sub associate-*r* log-pow *-commutative flip-+ rem-exp-log
Counts
4 → 164
Calls
4 calls:
64.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
18.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
158.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (exp (log (/ i (fma i 2.0 (+ alpha beta)))))))
5.0ms
(exp (log (/ i (fma i 2.0 (+ alpha beta)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
267.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
307.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
798.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (exp (log (/ i (fma i 2.0 (+ alpha beta)))))))
120.0ms
(exp (log (/ i (fma i 2.0 (+ alpha beta)))))

simplify1.6s

Counts
176 → 176
Iterations
IterNodes
done5001
23657
1794
0314

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.9b

regimes850.0ms

Accuracy

45.7% (3.0b remaining)

Error of 10.1b against oracle of 7.0b and baseline of 12.6b

bsearch120.0ms

Steps
ItersRangePoint
7
1.342640657450137e+130
6.131967184752214e+131
6.919336700596673e+130

simplify13.0ms

Iterations
IterNodes
done55
255
153
039

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s8000×body80valid
295.0ms8000×pre80true