Details

Time bar (total: 14.4s)

sample25.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
3.0ms256×pre80true

simplify81.0ms

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: 3.6b

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)))

rewrite643.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×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 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
179.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
266.0ms
(/ (/ (/ (+ (+ (+ 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))
151.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ alpha beta) (* beta alpha))
140.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
157.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify136.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151213008
1500112540

prune984.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize14.0ms

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)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
5500×times-frac
3739×*-un-lft-identity
2185×add-sqr-sqrt add-cube-cbrt
1821×distribute-lft-neg-in distribute-rgt-neg-in
777×distribute-lft-out
450×associate-/l*
302×neg-mul-1
260×associate-/r/
132×flip3-+ flip-+
130×div-inv
17×associate-/r*
13×add-exp-log add-cbrt-cube distribute-neg-frac
9×add-log-exp
5×cbrt-undiv div-exp
4×pow1 associate-/l/
3×frac-2neg div-sub distribute-frac-neg clear-num sum-log
2×neg-sub0
1×+-commutative associate-+l+
Counts
4 → 2568
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
293.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
462.0ms
(/ (/ (- (/ (+ (+ (+ 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))
151.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
221.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
228.0ms
(/ (/ (- (/ (+ (+ (+ 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)))

simplify744.0ms

Algorithm
egg-herbie
Counts
2580 → 2580
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0500184699

prune6.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (+ (+ alpha beta) (* 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))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
80×sqrt-prod
70×times-frac
56×add-sqr-sqrt
54×add-cube-cbrt
22×distribute-lft-out
13×associate-/r*
11×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
1×sqrt-undiv
Counts
4 → 159
Calls
4 calls:
199.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
116.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
65.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series424.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
113.0ms
(/ (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))

simplify69.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05072617
119422448
250032394

prune452.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(* (+ alpha beta) (+ alpha beta))
2.3b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite455.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
145×*-un-lft-identity
87×add-sqr-sqrt
85×add-cube-cbrt
29×distribute-lft-out
25×associate-/l*
19×difference-of-squares
16×associate-/r/
15×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
11×pow1 associate-/r*
8×div-inv
6×swap-sqr
5×cbrt-undiv div-exp associate-/l/
4×frac-times associate-*r* associate-*l* add-log-exp
3×frac-2neg clear-num
2×flip3-- associate-*r/ associate-*l/ flip--
1×pow2 distribute-rgt-in distribute-lft-in pow-plus div-sub pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 222
Calls
4 calls:
97.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms
(* (+ alpha beta) (+ alpha beta))
181.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
152.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms
(* (+ alpha beta) (+ alpha beta))
166.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify63.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010394291
150024105

prune627.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.6b

regimes65.0ms

Accuracy

56% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch66.0ms

Steps
ItersRangePoint
8
6.080532357857461e+175
3.1725731237402986e+178
1.4955754255315103e+178

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05140
16740
27040
37440
47440

end0.0ms

sample521.0ms

Algorithm
intervals
Results
292.0ms8000×body80valid
91.0ms8000×pre80true