Details

Time bar (total: 1.3m)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify80.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03317
111417
256317
3416417
4500217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b
(/ (/ (+ (+ (+ 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))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×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 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
105.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
323.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
473.0ms
(/ (/ (/ (+ (+ (+ 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))
275.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
130.0ms
(/ (/ (+ (+ (+ 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))
68.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify136.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0149213034
1500212552

prune978.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b
(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.7s

Algorithm
rewrite-expression-head
Rules
79305×times-frac
44568×*-un-lft-identity
31140×sqrt-prod
27018×add-sqr-sqrt add-cube-cbrt
8775×distribute-lft-out
4222×associate-/r/
2144×div-inv
2081×flip3-+ flip-+
326×associate-/r*
75×associate-/l*
66×sqrt-div
15×add-exp-log add-cbrt-cube
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
Counts
4 → 16931
Calls
4 calls:
441.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
948.0ms
(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
277.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
277.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series536.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
144.0ms
(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
68.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify10.0s

Algorithm
egg-herbie
Counts
16943 → 16943
Iterations

Useful iterations: 0 (147.0ms)

IterNodesCost
0166851163626

prune51.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
9.4b
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
161×times-frac
132×sqrt-prod
115×*-un-lft-identity
96×add-sqr-sqrt
85×add-cube-cbrt
15×distribute-lft-out
10×associate-/r/
8×flip3-+ flip-+
7×pow1
6×add-exp-log rem-sqrt-square add-cbrt-cube
5×sqrt-div div-inv
4×associate-/l* add-log-exp
3×sqrt-pow1 pow1/2 associate-/r*
2×associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num
Counts
4 → 168
Calls
4 calls:
109.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
109.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
272.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
188.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify100.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
09043769
130583565
250013467

prune709.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
9.4b
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite774.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
132×sqrt-prod
109×*-un-lft-identity
102×add-sqr-sqrt
84×add-cube-cbrt
15×associate-*r*
13×add-exp-log
12×distribute-lft-out
10×associate-/r/
9×pow1 flip3-+ add-cbrt-cube flip-+
6×rem-sqrt-square
5×sqrt-div div-inv
4×associate-*l* prod-exp add-log-exp
3×sqrt-pow1 pow1/2 unswap-sqr
2×frac-times div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative
Counts
4 → 176
Calls
4 calls:
110.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
110.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
358.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
186.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
43.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
74.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
155.0ms
(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify116.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
010073827
139713586
250023476

prune743.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

regimes74.0ms

Accuracy

53.9% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.7b

bsearch86.0ms

Steps
ItersRangePoint
10
6.334284910020751e+152
7.013797287950175e+165
1.0008115820787637e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04249
14249

end0.0ms

sample543.0ms

Algorithm
intervals
Results
278.0ms8000×body80valid
85.0ms8000×pre80true