Details

Time bar (total: 7.7s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify87.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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)))

rewrite630.0ms

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
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
171.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
268.0ms
(/ (/ (/ (+ (+ (+ 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))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
138.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms
(/ (/ (/ (+ (+ (+ 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))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify132.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0153413079
1500112129

prune1.2s

Filtered
487 candidates to 297 candidates (61.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
0.1b
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite529.0ms

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-*r*
40×prod-exp
30×1-exp
29×cbrt-undiv
20×associate-/r*
18×associate-*l*
15×rec-exp
14×unswap-sqr
12×cbrt-unprod div-inv
9×distribute-lft-out
8×associate-/r/ associate-/l*
7×pow1
6×associate-/l/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 290
Calls
4 calls:
5.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
217.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
146.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
164.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
172.0ms
(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
74.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012994373
150013561

prune724.0ms

Filtered
302 candidates to 173 candidates (57.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.8b

localize23.0ms

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))))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite348.0ms

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:
90.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
110.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series437.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (+ 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))))
54.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05412716
119602543
250012472

prune614.0ms

Filtered
189 candidates to 109 candidates (57.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-prod
57×*-un-lft-identity
46×add-sqr-sqrt
42×times-frac
37×add-cube-cbrt
10×sqrt-div distribute-lft-out
7×pow1 associate-/l*
6×add-exp-log associate-/r* add-cbrt-cube
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
2×associate-/r/ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 131
Calls
4 calls:
110.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series255.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify109.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03401846
110831731
245981682
350011682

prune588.0ms

Filtered
143 candidates to 92 candidates (64.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

regimes93.0ms

Accuracy

52.5% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch48.0ms

Steps
ItersRangePoint
7
2.928539913264705e+160
1.678957329733711e+162
1.4537693536698273e+162

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03118
13118

end0.0ms

sample525.0ms

Algorithm
intervals
Results
296.0ms8000×body80valid
94.0ms8000×pre80true