Details

Time bar (total: 24.5s)

sample40.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
5.0ms256×pre80true

simplify881.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
31807
2295
160
017

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize48.0ms

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))
37.1b
(/ (/ (* (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))
45.5b
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

rewrite244.0ms

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:
6.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
61.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
98.0ms
(/ (/ (* (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))
74.0ms
(/ (* (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:
87.0ms
(* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta)))
249.0ms
(* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i))
524.0ms
(/ (/ (* (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))
366.0ms
(/ (* (fma (+ beta (+ alpha i)) i (* beta alpha)) (* (+ beta (+ alpha i)) i)) (* (fma 2.0 i (+ alpha beta)) (fma 2.0 i (+ alpha beta))))

simplify555.0ms

Counts
150 → 150
Iterations
IterNodes
done5000
1759
0248

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.4b

localize51.0ms

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 (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
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)))))
36.1b
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
201×*-un-lft-identity
175×times-frac
144×add-sqr-sqrt
94×associate-*l*
89×add-cbrt-cube add-exp-log
88×add-cube-cbrt
52×distribute-lft-out
33×cbrt-undiv div-exp
31×prod-exp cbrt-unprod
22×difference-of-squares
14×associate-*r*
12×associate-/r/
11×pow1 sqrt-prod distribute-lft-out--
10×associate-/r*
8×div-inv associate-/l*
6×frac-times associate-*r/
5×flip3-+ flip-+
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
2×clear-num frac-2neg flip3-- *-commutative flip-- associate-/l/
Counts
4 → 277
Calls
4 calls:
129.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
71.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
157.0ms
(* (/ (/ (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)))))
23.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

series3.9s

Counts
4 → 12
Calls
4 calls:
338.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
238.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
3.1s
(* (/ (/ (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)))))
255.0ms
(/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))

simplify571.0ms

Counts
289 → 289
Iterations
IterNodes
done5000
11321
0417

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.3b

localize68.0ms

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 (+ 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))) (/ i (fma i 2.0 (+ alpha beta)))))

rewrite385.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
107×add-sqr-sqrt
91×times-frac
61×add-cbrt-cube add-exp-log
51×add-cube-cbrt
49×associate-*l*
39×distribute-lft-out
22×prod-exp cbrt-unprod difference-of-squares
19×cbrt-undiv div-exp
14×associate-*r*
11×pow1 sqrt-prod distribute-lft-out--
9×associate-/r*
8×associate-/l*
6×frac-times associate-*r/
5×div-inv
4×expm1-log1p-u pow-prod-down associate-*l/ associate-/r/ log1p-expm1-u add-log-exp unswap-sqr associate-/l/
3×flip3-- flip--
2×clear-num frac-2neg *-commutative
1×flip3-+ div-sub flip-+
Counts
4 → 219
Calls
4 calls:
127.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
76.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
22.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
147.0ms
(* (/ (- (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)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
385.0ms
(* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta))))
253.0ms
(/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
279.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
851.0ms
(* (/ (- (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)))))

simplify530.0ms

Counts
231 → 231
Iterations
IterNodes
done5000
1979
0312

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 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 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))))))
1.2b
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))))

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
42×*-un-lft-identity times-frac
33×add-cube-cbrt
28×associate-*r*
26×log-prod exp-sum
18×associate-*l*
16×add-cbrt-cube
14×add-exp-log
9×pow1
6×unswap-sqr
5×div-inv
4×expm1-log1p-u exp-prod prod-exp associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp difference-of-squares
3×frac-times cbrt-undiv log-div associate-/r* flip3-- exp-diff div-exp associate-*l/ flip-- distribute-lft-out associate-/l*
2×flip3-+ pow-prod-down associate-*r/ *-commutative sqrt-prod flip-+ distribute-lft-out-- associate-/l/
1×clear-num frac-2neg div-sub log-pow rem-exp-log
Counts
4 → 149
Calls
4 calls:
12.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
99.0ms
(* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta))))
439.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))))))
132.0ms
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
307.0ms
(/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta)))
160.0ms
(* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta))))
820.0ms
(* (/ (- (fma 0.5 i (* 0.125 (/ 1.0 i))) (* 0.25 (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))))))
422.0ms
(exp (log (/ (* (+ (+ i alpha) beta) (/ i (fma i 2.0 (+ alpha beta)))) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))))

simplify1.8s

Counts
161 → 161
Iterations
IterNodes
done5000
24764
1786
0304

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.3b

regimes601.0ms

Accuracy

45.3% (3.2b remaining)

Error of 10.7b against oracle of 7.5b and baseline of 13.4b

bsearch133.0ms

Steps
ItersRangePoint
9
2.997562247900697e+97
3.916531947114467e+103
3.0530456069661542e+100

simplify5.0ms

Iterations
IterNodes
done48
148
037

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s8000×body80valid
328.0ms8000×pre80true