Details

Time bar (total: 20.5s)

sample58.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
7.0ms256×pre80true

simplify674.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
01435
13335
211931
359331
done500131

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
179.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
434.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
769.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
485.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
159.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
228.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
117.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify933.0ms

Counts
488 → 488
Iterations

Useful iterations: done (902.0ms)

IterNodesCost
061126134
1153724802
done500021940

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ (+ alpha beta) (fma beta alpha 1.0))) (sqrt (fma 1.0 2.0 (+ alpha beta)))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ alpha beta) (fma beta alpha 1.0)))

rewrite656.0ms

Algorithm
rewrite-expression-head
Rules
390×times-frac
346×*-un-lft-identity
277×sqrt-prod
211×add-sqr-sqrt
205×add-cube-cbrt
83×distribute-lft-out
58×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/l*
8×sqrt-div
6×pow1 div-inv
4×cbrt-undiv expm1-log1p-u flip3-+ div-exp flip-+ log1p-expm1-u add-log-exp
3×associate-/r/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def associate-/l/
1×sqrt-undiv
Counts
4 → 341
Calls
4 calls:
331.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
83.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ (+ alpha beta) (fma beta alpha 1.0))) (sqrt (fma 1.0 2.0 (+ alpha beta)))))
169.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ alpha beta) (fma beta alpha 1.0)))

series869.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
548.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (/ (sqrt (+ (+ alpha beta) (fma beta alpha 1.0))) (sqrt (fma 1.0 2.0 (+ alpha beta)))))
81.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
81.0ms
(sqrt (+ (+ alpha beta) (fma beta alpha 1.0)))

simplify825.0ms

Counts
353 → 353
Iterations

Useful iterations: done (807.0ms)

IterNodesCost
045513356
1113311889
done500011592

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))))
0.0b
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.6b
(/ (/ (/ 1 1) 1) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
2.9b
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
604×*-un-lft-identity
548×times-frac
250×add-exp-log
233×add-sqr-sqrt
228×distribute-lft-out
224×add-cube-cbrt
200×div-exp
100×associate-*l*
74×add-cbrt-cube
68×1-exp
53×associate-/l*
48×prod-exp
40×cbrt-undiv
23×associate-/r* div-inv
16×rec-exp
12×cbrt-unprod
6×pow1
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×flip3-+ associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 476
Calls
4 calls:
210.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))))
255.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
73.0ms
(/ (/ (/ 1 1) 1) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
91.0ms
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

series981.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))))
359.0ms
(* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
255.0ms
(/ (/ (/ 1 1) 1) (* (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
135.0ms
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

simplify1.6s

Counts
488 → 488
Iterations

Useful iterations: done (1.6s)

IterNodesCost
059919271
1211017583
done500016150

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
0.1b
(/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.1b
(* (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
2.9b
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

rewrite680.0ms

Algorithm
rewrite-expression-head
Rules
302×*-un-lft-identity
290×times-frac
168×add-sqr-sqrt
140×add-cube-cbrt
96×distribute-lft-out
67×associate-*r*
54×add-exp-log
34×add-cbrt-cube
29×associate-/l*
26×div-exp
19×associate-*l*
16×associate-/r/
14×cbrt-undiv
12×div-inv
11×associate-/r*
10×prod-exp
9×flip3-+ flip-+
8×unswap-sqr
7×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 312
Calls
4 calls:
76.0ms
(/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
97.0ms
(/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
317.0ms
(* (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
156.0ms
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
120.0ms
(/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
270.0ms
(* (/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ alpha beta) (fma 2.0 1.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
111.0ms
(/ (+ (+ alpha beta) (fma beta alpha 1.0)) (fma 1.0 2.0 (+ alpha beta)))

simplify752.0ms

Counts
324 → 324
Iterations

Useful iterations: done (728.0ms)

IterNodesCost
035710014
111409431
done50008707

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes124.0ms

Accuracy

66% (1.2b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 3.8b

bsearch139.0ms

Steps
ItersRangePoint
8
4.640840902156564e+159
7.514763735460967e+162
4.714456171199346e+159

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
03680
14976
done4976

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
237.0ms8000×pre80true