Details

Time bar (total: 10.5s)

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: 3.3b

localize17.0ms

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))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite110.0ms

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:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms
(/ (/ (/ (+ (+ (+ 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))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
133.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms
(/ (/ (/ (+ (+ (+ 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))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (+ 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))))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite51.0ms

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:
15.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
15.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series409.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
106.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
44.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05272718
119402545
250012473

prune566.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.3b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
1.5b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.0b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite622.0ms

Algorithm
rewrite-expression-head
Rules
2200×times-frac
1122×add-sqr-sqrt
1110×*-un-lft-identity
852×add-cube-cbrt
678×associate-*r*
453×sqrt-prod
412×cbrt-prod
185×add-exp-log
140×associate-/r/
121×distribute-lft-out
104×div-exp
90×add-cbrt-cube
75×flip3-+ flip-+
64×cbrt-undiv div-inv
60×unswap-sqr
49×associate-/l*
44×prod-exp
42×associate-*l*
30×cbrt-unprod
26×cbrt-div
24×sqrt-div
13×associate-/r*
10×pow1
9×frac-times
6×rec-exp 1-exp
5×associate-*r/ associate-*l/
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp pow-div
3×frac-2neg clear-num
2×pow-flip sqrt-pow1 pow1/2 inv-pow
1×pow-prod-down *-commutative
Counts
4 → 1122
Calls
4 calls:
16.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
34.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
444.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
19.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
281.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
158.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
100.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify510.0ms

Algorithm
egg-herbie
Counts
1134 → 1134
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500141944

prune3.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
1.9b
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
3.1b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
230×times-frac
176×*-un-lft-identity
144×add-sqr-sqrt
116×add-cube-cbrt
58×associate-*r*
50×add-exp-log
32×add-cbrt-cube
29×distribute-lft-out
24×div-exp
22×associate-/l*
16×associate-*l*
14×associate-/r/
13×cbrt-undiv add-log-exp
11×div-inv
10×prod-exp
9×flip3-+ flip-+
8×unswap-sqr
6×pow1 associate-/r* sum-log cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×rec-exp fma-def 1-exp associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times associate-+l+ associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 261
Calls
4 calls:
8.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
15.0ms
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
37.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
10.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
66.0ms
(/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
154.0ms
(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (/ (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify66.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011004320
150023846

prune704.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes87.0ms

Accuracy

55.3% (1.1b remaining)

Error of 2.1b against oracle of 1.0b and baseline of 3.4b

bsearch114.0ms

Steps
ItersRangePoint
9
1.0328085592141294e+173
2.3460283182453145e+179
1.939570429570971e+178

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07770
17770

end0.0ms

sample525.0ms

Algorithm
intervals
Results
295.0ms8000×body80valid
93.0ms8000×pre80true