Details

Time bar (total: 7.5s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify82.0ms

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: 3.6b

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

rewrite625.0ms

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))
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))
148.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
145.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify133.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 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))))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite345.0ms

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:
89.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
111.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series436.0ms

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))))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05412716
119602543
250012472

prune588.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize23.0ms

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))))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite423.0ms

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:
165.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ 1 (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
112.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series437.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ 1 (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
106.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06682469
132132239
250012198

prune624.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

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))))
3.3b
(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))

rewrite327.0ms

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:
112.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series254.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03401846
110831731
245981682
350011682

prune701.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.6b

regimes63.0ms

Accuracy

54.4% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.8b

bsearch59.0ms

Steps
ItersRangePoint
8
6.080532357857461e+175
3.1725731237402986e+178
6.1364080644475965e+175

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03829
13829

end0.0ms

sample525.0ms

Algorithm
intervals
Results
291.0ms8000×body80valid
96.0ms8000×pre80true