Details

Time bar (total: 9.9s)

sample25.0ms

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

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))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

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:
123.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
338.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
490.0ms
(/ (/ (/ (+ (+ (+ 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))
287.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
127.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
142.0ms
(/ (/ (/ (+ (+ (+ 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))
67.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify139.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 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))))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite667.0ms

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:
188.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
210.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
130.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
132.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series388.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
98.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
42.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05272718
119402545
250012473

prune574.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite639.0ms

Algorithm
rewrite-expression-head
Rules
347×times-frac
287×*-un-lft-identity
212×sqrt-prod
189×add-sqr-sqrt
183×add-cube-cbrt
56×distribute-lft-out
55×associate-/r*
17×add-exp-log
14×sqrt-div
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ associate-/l*
7×pow1
6×div-inv
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num hypot-def associate-/l/
1×pow-flip inv-pow
Counts
4 → 321
Calls
4 calls:
191.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
167.0ms
(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
130.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
133.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series390.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
98.0ms
(/ 1 (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
42.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08925793
145075290
250015281

prune802.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize25.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.7b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.8b
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite853.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
36×flip3-+ flip-+
32×frac-times
26×associate-/r/
25×add-exp-log
18×sqrt-div
16×associate-*l/
15×add-cbrt-cube
13×*-un-lft-identity
12×cbrt-prod
10×associate-*r/
9×prod-exp cbrt-unprod
8×associate-/l/
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 distribute-lft-out
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 109
Calls
4 calls:
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
668.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
54.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
474.0ms
(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (* (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08912842
133732539
250012475

prune654.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes80.0ms

Accuracy

37% (1.6b remaining)

Error of 3.0b against oracle of 1.3b and baseline of 3.9b

bsearch75.0ms

Steps
ItersRangePoint
9
2.9801746589989353e+86
4.795377564182692e+91
1.8347442425532666e+88

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04643
14643

end0.0ms

sample703.0ms

Algorithm
intervals
Results
435.0ms8000×body80valid
88.0ms8000×pre80true