Details

Time bar (total: 10.5s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize12.0ms

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))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite673.0ms

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:
62.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
172.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
258.0ms
(/ (/ (/ (+ (+ (+ 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))
147.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
135.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms
(/ (/ (/ (+ (+ (+ 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))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize18.0ms

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 3.0)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite576.0ms

Algorithm
rewrite-expression-head
Rules
954×times-frac
827×*-un-lft-identity
382×add-sqr-sqrt add-cube-cbrt
253×distribute-lft-out
82×associate-/l*
62×associate-/r/
32×flip3-+ flip-+
31×div-inv
19×add-exp-log add-cbrt-cube
11×associate-/r*
10×cbrt-undiv div-exp
4×associate-/l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
3 → 517
Calls
3 calls:
175.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
214.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series374.0ms

Counts
3 → 9
Calls
3 calls:
139.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify148.0ms

Algorithm
egg-herbie
Counts
526 → 526
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0147113806
1500212874

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.7b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
435×times-frac
247×*-un-lft-identity
159×add-sqr-sqrt add-cube-cbrt
102×add-exp-log
75×sqrt-prod
63×associate-/l*
60×div-exp
58×add-cbrt-cube
50×associate-/r/
46×distribute-lft-out
40×sqrt-div
31×cbrt-undiv
22×flip3-+ flip-+
16×prod-exp associate-/r* div-inv
12×frac-times associate-*r/
8×cbrt-unprod
7×rec-exp 1-exp
6×pow1 associate-*l/
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×pow-flip
2×associate-/l/
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 377
Calls
4 calls:
128.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
53.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
18.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
19.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
160.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
64.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
97.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify108.0ms

Algorithm
egg-herbie
Counts
389 → 389
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013929146
150017795

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.6b
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.7b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))
2.7b
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

rewrite360.0ms

Algorithm
rewrite-expression-head
Rules
1206×times-frac
968×sqrt-prod
600×*-un-lft-identity
412×add-sqr-sqrt add-cube-cbrt
120×associate-/r/
102×sqrt-div
98×distribute-lft-out
78×associate-/l*
52×flip3-+ flip-+
36×div-inv
32×frac-times associate-*r/
24×associate-/r*
16×associate-*l/
12×add-exp-log add-cbrt-cube
4×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u add-log-exp
2×sqrt-undiv associate-/l/
Counts
4 → 704
Calls
4 calls:
134.0ms
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
134.0ms
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))
15.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
204.0ms
(/ (sqrt (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
96.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))
98.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify276.0ms

Algorithm
egg-herbie
Counts
716 → 716
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0102324694
1364823930
2500123018

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

63.4% (1.3b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 3.7b

bsearch65.0ms

Steps
ItersRangePoint
8
1.5587627514452932e+159
6.363818485527949e+161
3.124255727313828e+160

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04939
14939

end0.0ms

sample520.0ms

Algorithm
intervals
Results
294.0ms8000×body80valid
91.0ms8000×pre80true