Details

Time bar (total: 9.0s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113
done500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize17.0ms

Local error

Found 3 expressions with local error:

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))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
3 → 456
Calls
3 calls:
324.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
476.0ms
(/ (/ (/ (+ (+ (+ 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))
280.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series384.0ms

Counts
3 → 9
Calls
3 calls:
142.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
157.0ms
(/ (/ (/ (+ (+ (+ 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))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify121.0ms

Counts
465 → 465
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0145512992
1500112037
done500112037

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b
(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.1b
(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite832.0ms

Algorithm
rewrite-expression-head
Rules
196×times-frac
167×add-exp-log
145×add-sqr-sqrt
128×*-un-lft-identity
102×div-exp
100×add-cube-cbrt
61×add-cbrt-cube
44×associate-*l*
40×prod-exp
30×1-exp
29×cbrt-undiv
20×associate-/r*
16×associate-*r*
15×rec-exp
14×unswap-sqr
12×cbrt-unprod div-inv
9×distribute-lft-out
8×associate-/l*
7×pow1
5×associate-/l/
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times flip3-+ associate-*r/ associate-*l/ flip-+
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 284
Calls
4 calls:
9.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
300.0ms
(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
261.0ms
(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
247.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
146.0ms
(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
160.0ms
(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
85.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify61.0ms

Counts
296 → 296
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011904080
150013500
done50013500

prune612.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite623.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
165.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
202.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
124.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
125.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series432.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify70.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05412716
119602543
250012472
done50012472

prune558.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ 1 (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite756.0ms

Algorithm
rewrite-expression-head
Rules
82×*-un-lft-identity
74×sqrt-prod
69×add-sqr-sqrt
67×times-frac
51×add-cube-cbrt
27×associate-*r*
15×add-exp-log distribute-lft-out
11×add-cbrt-cube
10×sqrt-div
8×pow1
7×flip3-+ flip-+ associate-/l*
6×associate-/r*
5×associate-*l* unswap-sqr
4×expm1-log1p-u prod-exp associate-/r/ log1p-expm1-u add-log-exp
3×div-exp
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ cbrt-unprod hypot-def div-inv associate-/l/
1×rec-exp sqrt-undiv frac-2neg 1-exp associate-*r/ pow-prod-down clear-num un-div-inv *-commutative
Counts
4 → 172
Calls
4 calls:
297.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ 1 (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
202.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
123.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
127.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series438.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ 1 (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
108.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
53.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify86.0ms

Counts
184 → 184
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06682469
132132239
250012198
done50012198

prune593.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

regimes117.0ms

Accuracy

93.1% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 3.7b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03434
13434
done3434

end0.0ms

sample557.0ms

Algorithm
intervals
Results
287.0ms8000×body80valid
88.0ms8000×pre80true