Details

Time bar (total: 23.1s)

sample107.0ms

Algorithm
intervals
Results
35.0ms201×body80valid
14.0ms256×pre80true
12.0ms14×body1280valid
10.0ms18×body320valid
9.0ms12×body640valid
4.0ms11×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
42315
3458
299
132
016

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
12.9b
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
16.3b
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×*-un-lft-identity
18×add-cube-cbrt
15×times-frac
11×pow1
8×add-cbrt-cube add-exp-log
5×associate-/l*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×associate-/r* swap-sqr associate-*r* associate-*l*
2×associate-/l/
1×pow2 distribute-rgt-in cbrt-undiv clear-num frac-2neg distribute-lft-in pow-plus flip3-- div-sub div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv flip-- unswap-sqr
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
6.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
0.0ms
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
12.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series632.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
87.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
208.0ms
(fma (/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) (+ beta alpha) 1.0)
209.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.3s

Counts
105 → 105
Iterations
IterNodes
done5000
33884
21077
1377
0168

prune705.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
0.0b
(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
0.1b
(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
2.5b
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
72×add-sqr-sqrt
68×times-frac
42×add-cube-cbrt
26×associate-*r*
20×add-cbrt-cube add-exp-log
18×distribute-lft-out
16×associate-*l*
9×associate-/l* distribute-lft-out-- difference-of-squares
7×associate-/r*
6×pow1 cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u flip3-+ prod-exp associate-/r/ cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv unswap-sqr associate-/l/
2×clear-num frac-2neg
1×frac-times +-commutative sum-log fma-def flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 169
Calls
4 calls:
16.0ms
(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
26.0ms
(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
76.0ms
(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
16.0ms
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

series736.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
111.0ms
(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
298.0ms
(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
243.0ms
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

simplify1.8s

Counts
181 → 181
Iterations
IterNodes
done5001
22441
1717
0242

prune928.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
0.1b
(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
1.3b
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
3.4b
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
319×times-frac
290×*-un-lft-identity
215×add-sqr-sqrt
140×add-cube-cbrt
82×associate-*r*
42×distribute-lft-out
33×distribute-lft-out-- difference-of-squares
31×associate-/l*
20×add-cbrt-cube add-exp-log
16×associate-/r/
11×flip3-+ flip-+
10×div-inv
7×cbrt-undiv associate-/r* div-exp
6×pow1 add-log-exp
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log fma-def flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 302
Calls
4 calls:
35.0ms
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
40.0ms
(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
87.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
28.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

series903.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
210.0ms
(/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))
331.0ms
(* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha))))
240.0ms
(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (fma 2 i (+ beta alpha)))) 1.0)

simplify2.8s

Counts
314 → 314
Iterations
IterNodes
done5001
23756
11079
0386

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
0.2b
(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
2.5b
(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
3.3b
(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
28×add-sqr-sqrt
20×times-frac
18×add-cube-cbrt
7×add-exp-log
6×pow1 log-prod add-cbrt-cube distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u exp-prod associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×exp-sum
2×associate-/r/ log-pow associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp rem-log-exp flip-+ fma-udef div-inv flip-- rem-exp-log
Counts
4 → 93
Calls
4 calls:
28.0ms
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
7.0ms
(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
0.0ms
(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
1.0ms
(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
584.0ms
(exp (log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)))
211.0ms
(fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0)
343.0ms
(log (fma (/ (- beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (+ beta alpha) (fma 2 i (+ beta alpha))) 1.0))

simplify2.5s

Counts
105 → 105
Iterations
IterNodes
done5000
34343
2966
1358
0162

prune686.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

regimes372.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.9b and baseline of 12.1b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done23
123
018

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s6380×body80valid
430.0ms538×body640valid
345.0ms8000×pre80true
344.0ms500×body1280valid
204.0ms362×body320valid
58.0ms220×body160valid