Details

Time bar (total: 40.0s)

sample56.0ms

Algorithm
intervals
Results
32.0ms256×body80valid
5.0ms256×pre80true

simplify640.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
01435
13335
211931
359331
done500131

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

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))
5.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

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:
508.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
759.0ms
(/ (/ (/ (+ (+ (+ 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))
426.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series549.0ms

Counts
3 → 9
Calls
3 calls:
209.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
234.0ms
(/ (/ (/ (+ (+ (+ 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))
105.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify881.0ms

Counts
465 → 465
Iterations

Useful iterations: done (845.0ms)

IterNodesCost
058625879
1148125086
done500121722

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize43.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.1b
(/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
5.0b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

rewrite472.0ms

Algorithm
rewrite-expression-head
Rules
3900×times-frac
2576×*-un-lft-identity
1600×add-sqr-sqrt add-cube-cbrt
1140×distribute-lft-neg-in distribute-rgt-neg-in
488×distribute-lft-out
156×neg-mul-1
152×associate-/l*
102×div-inv
18×associate-/r*
12×add-exp-log add-cbrt-cube
5×cbrt-undiv div-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg div-sub distribute-frac-neg clear-num log1p-expm1-u distribute-neg-frac add-log-exp
2×neg-sub0 flip3-+ associate-/r/ flip-+
Counts
3 → 1688
Calls
3 calls:
42.0ms
(/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
145.0ms
(/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
35.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

series714.0ms

Counts
3 → 9
Calls
3 calls:
314.0ms
(/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
292.0ms
(/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0)))
108.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))

simplify2.6s

Counts
1697 → 1697
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01890103089
14761100163
done500298768

prune5.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))))
0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
5.0b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

rewrite577.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
80×sqrt-prod
70×times-frac
60×add-sqr-sqrt
54×add-cube-cbrt
22×distribute-lft-out
13×associate-/r*
11×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 → 169
Calls
4 calls:
28.0ms
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))))
334.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
184.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
21.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
341.0ms
(/ (+ (fma 1.0 2.0 (+ alpha beta)) 1.0) (sqrt (+ 1.0 (fma alpha beta (+ alpha beta)))))
155.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
74.0ms
(sqrt (+ 1.0 (fma alpha beta (+ alpha beta))))

simplify1.7s

Counts
181 → 181
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02714932
15924280
225174117
done50004110

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.9b

localize22.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
5.0b
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
17.0b
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
17.0b
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
7038×times-frac
4584×*-un-lft-identity
2820×add-sqr-sqrt
2808×add-cube-cbrt
2700×sqrt-prod
2048×distribute-lft-neg-in distribute-rgt-neg-in
888×distribute-lft-out
296×neg-mul-1
172×div-inv
8×add-exp-log add-cbrt-cube associate-/l*
6×pow1 rem-sqrt-square associate-/r*
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u associate-/l/ distribute-neg-frac add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 2800
Calls
4 calls:
23.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
27.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
338.0ms
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
333.0ms
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
153.0ms
(/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))
360.0ms
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))
353.0ms
(sqrt (/ (/ (- (/ (+ 1.0 (fma alpha beta (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))) (- (+ (fma 1.0 2.0 (+ alpha beta)) 1.0))))

simplify1.9s

Counts
2812 → 2812
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03229189862
done5000185412

prune14.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.9b

regimes154.0ms

Accuracy

18.6% (2.1b remaining)

Error of 3.2b against oracle of 1.2b and baseline of 3.7b

bsearch63.0ms

Steps
ItersRangePoint
6
1.5868579472363918e+47
1.3781639916158979e+48
5.601169561552346e+47

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03790
15490
25790
done5790

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.0s8000×body80valid
241.0ms8000×pre80true