Details

Time bar (total: 35.4s)

sample69.0ms

Algorithm
intervals
Results
19.0ms205×body80valid
10.0ms256×pre80true
9.0ms20×body1280valid
6.0ms16×body640valid
4.0ms15×body320valid

simplify2.0s

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.3b

localize56.0ms

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)))
12.3b
(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)
18.7b
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite55.0ms

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:
1.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
15.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
1.0ms
(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)
35.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series802.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
94.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
301.0ms
(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)
258.0ms
(/ (- beta alpha) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify2.8s

Counts
105 → 105
Iterations
IterNodes
done5000
33884
21077
1377
0168

prune736.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize50.0ms

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)))))
0.5b
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

rewrite202.0ms

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:
19.0ms
(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
35.0ms
(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
87.0ms
(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
55.0ms
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

series771.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ beta alpha) (fma i 2 (+ beta alpha)))
122.0ms
(/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))
295.0ms
(* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha)))))
258.0ms
(+ (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ (- beta alpha) (+ 2.0 (fma i 2 (+ beta alpha))))) 1.0)

simplify2.0s

Counts
181 → 181
Iterations
IterNodes
done5001
22441
1717
0242

prune919.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))
0.4b
(/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
0.4b
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
6.8b
(+ (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) 1.0)

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
91×times-frac
88×add-sqr-sqrt
83×add-exp-log
60×sqrt-prod
58×add-cube-cbrt
49×add-cbrt-cube
41×associate-*r*
34×prod-exp
28×div-exp
18×cbrt-unprod
15×cbrt-undiv distribute-lft-out distribute-lft-out-- difference-of-squares
14×associate-/r*
11×pow1
8×associate-/l*
6×frac-times sqrt-div associate-*l/ associate-/r/ add-log-exp
5×rec-exp 1-exp
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×pow-prod-down associate-*r/ div-inv pow-flip
2×clear-num frac-2neg un-div-inv associate-/l/
1×+-commutative sum-log fma-def sqrt-pow1 flip3-- pow1/2 div-sub associate-*l* *-commutative flip-- inv-pow
Counts
4 → 228
Calls
4 calls:
155.0ms
(* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))
18.0ms
(/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
39.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
115.0ms
(+ (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) 1.0)

series900.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))
182.0ms
(/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
187.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
224.0ms
(+ (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) 1.0)

simplify2.7s

Counts
240 → 240
Iterations
IterNodes
done5001
23695
11013
0344

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
0.4b
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
6.8b
(+ (cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))))) 1.0)
11.9b
(cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))))

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
3501×frac-times
1989×associate-*l/
999×cbrt-div associate-*r/
600×un-div-inv
103×*-un-lft-identity
77×add-sqr-sqrt
70×times-frac
48×sqrt-prod
45×add-cube-cbrt
16×distribute-lft-out-- difference-of-squares
14×associate-/r*
13×distribute-lft-out
10×associate-/l*
8×add-cbrt-cube add-exp-log
6×add-log-exp
4×expm1-log1p-u pow1 fma-def sqrt-div associate-/r/ insert-posit16 log1p-expm1-u associate-/l/
3×flip3-+ flip-+
2×cbrt-prod cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
1×+-commutative sum-log pow1/3 pow3 rem-cbrt-cube
Counts
4 → 1165
Calls
4 calls:
25.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
34.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
179.0ms
(+ (cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))))) 1.0)
4.1s
(cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
155.0ms
(/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))
369.0ms
(+ (cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))))) 1.0)
433.0ms
(cbrt (* (* (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))) (* (* (/ (+ beta alpha) (fma i 2 (+ beta alpha))) (/ 1 (sqrt (+ 2.0 (fma i 2 (+ beta alpha)))))) (/ (- beta alpha) (sqrt (+ 2.0 (fma i 2 (+ beta alpha))))))))

simplify3.6s

Counts
1177 → 1177
Iterations
IterNodes
done5000
02577

prune7.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.9b

regimes335.0ms

Accuracy

0% (0.3b remaining)

Error of 12.3b against oracle of 12.0b and baseline of 12.3b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done19
119
015

end0.0ms

sample2.2s

Algorithm
intervals
Results
628.0ms8000×pre80true
604.0ms6361×body80valid
320.0ms529×body1280valid
255.0ms527×body640valid
126.0ms382×body320valid
31.0ms201×body160valid