Details

Time bar (total: 26.2s)

sample50.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
6.0ms256×pre80true

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
done5001
31807
2295
160
017

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize55.0ms

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))
37.7b
(/ (/ (* (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))
45.9b
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite298.0ms

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:
11.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
67.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
106.0ms
(/ (/ (* (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))
104.0ms
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

series1.2s

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
214.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
501.0ms
(/ (/ (* (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))
380.0ms
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify546.0ms

Counts
150 → 150
Iterations
IterNodes
done5000
1759
0248

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 35.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ i (fma i 2.0 (+ alpha beta)))
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)))))
35.7b
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
165×*-un-lft-identity
115×add-sqr-sqrt add-cube-cbrt
82×add-cbrt-cube add-exp-log
58×associate-*l*
32×cbrt-undiv div-exp
27×prod-exp cbrt-unprod
25×distribute-lft-out
24×associate-/l*
16×associate-/r/
11×div-inv
10×associate-/r*
9×pow1
8×flip3-+ flip-+
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/
1×associate-*r* *-commutative associate-/l/
Counts
4 → 264
Calls
4 calls:
6.0ms
(/ i (fma i 2.0 (+ alpha beta)))
28.0ms
(/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
163.0ms
(* (/ (/ (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)))))
22.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

series4.2s

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ i (fma i 2.0 (+ alpha beta)))
398.0ms
(/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
3.4s
(* (/ (/ (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)))))
282.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

simplify633.0ms

Counts
276 → 276
Iterations
IterNodes
done5000
11169
0388

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.9b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
78×add-sqr-sqrt
70×times-frac
61×add-cbrt-cube add-exp-log
49×associate-*l*
46×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×distribute-lft-out
14×associate-*r*
11×pow1
10×difference-of-squares
6×frac-times associate-/r* associate-*r/ associate-/l*
5×sqrt-prod div-inv distribute-lft-out--
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
2×clear-num frac-2neg associate-/r/ *-commutative
1×flip3-- flip--
Counts
4 → 186
Calls
4 calls:
132.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
4.0ms
(/ i (fma i 2.0 (+ alpha beta)))
4.0ms
(/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta)))
105.0ms
(* (/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 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)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
401.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
139.0ms
(/ i (fma i 2.0 (+ alpha beta)))
304.0ms
(/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta)))
848.0ms
(* (/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 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)))))

simplify2.3s

Counts
198 → 198
Iterations
IterNodes
done5000
24669
1786
0270

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.9b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta)))
0.0b
(* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta))))
0.1b
(* (/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0)))))))
1.5b
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0))))))

rewrite534.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
38×*-un-lft-identity
36×times-frac
33×add-cube-cbrt
23×associate-*r*
18×associate-*l*
16×log-prod add-cbrt-cube exp-sum
14×add-exp-log
9×pow1
6×unswap-sqr
5×div-inv
4×expm1-log1p-u exp-prod prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×frac-times cbrt-undiv log-div associate-/r* exp-diff div-exp associate-*l/ distribute-lft-out associate-/l*
2×flip3-+ pow-prod-down associate-*r/ *-commutative flip-+
1×clear-num frac-2neg log-pow rem-exp-log
Counts
4 → 136
Calls
4 calls:
4.0ms
(/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta)))
86.0ms
(* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta))))
355.0ms
(* (/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0)))))))
84.0ms
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta)))
153.0ms
(* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta))))
861.0ms
(* (/ (fma i 0.5 (fma (/ 1.0 i) 0.125 (- (* 0.25 (sqrt 1.0))))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0)))))))
384.0ms
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (fma 2.0 i (- (+ alpha beta) (sqrt 1.0))))))

simplify2.5s

Counts
148 → 148
Iterations
IterNodes
done5001
23953
1649
0265

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

regimes665.0ms

Accuracy

43.8% (3.1b remaining)

Error of 10.5b against oracle of 7.4b and baseline of 13.0b

bsearch48.0ms

Steps
ItersRangePoint
3
1.9535558302743353e+91
2.517074866955258e+91
2.4818549271627002e+91

simplify16.0ms

Iterations
IterNodes
done63
263
159
041

end0.0ms

sample1.7s

Algorithm
intervals
Results
984.0ms8000×body80valid
284.0ms8000×pre80true