Details

Time bar (total: 36.8s)

sample34.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
4.0ms256×pre80true

simplify78.0ms

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: 3.1b

localize11.0ms

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

rewrite581.0ms

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:
12.0ms
(+ (+ alpha beta) (* beta alpha))
161.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
241.0ms
(/ (/ (/ (+ (+ (+ 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))
136.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series373.0ms

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)))
145.0ms
(/ (/ (/ (+ (+ (+ 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))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify135.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0151213008
1500112540

prune978.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

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

rewrite1.1s

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))
267.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
415.0ms
(/ (/ (- (/ (+ (+ (+ 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))
135.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* beta alpha))
209.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
216.0ms
(/ (/ (- (/ (+ (+ (+ 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))
71.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify708.0ms

Algorithm
egg-herbie
Counts
2580 → 2580
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500184699

prune6.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.7b

localize20.0ms

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))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite405.0ms

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:
180.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
57.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series399.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ (+ (+ (+ alpha beta) (* 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))))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify67.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05072619
119282448
250012394

prune451.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.7s

Algorithm
rewrite-expression-head
Rules
9712×times-frac
6616×*-un-lft-identity
4074×sqrt-prod
3802×add-sqr-sqrt
3762×add-cube-cbrt
3000×distribute-lft-neg-in distribute-rgt-neg-in
1642×associate-*r*
1427×distribute-lft-out
500×neg-mul-1
428×associate-/r/
417×associate-/l*
409×associate-*l*
216×flip3-+ flip-+
214×div-inv
20×distribute-neg-frac
15×add-exp-log add-cbrt-cube
12×unswap-sqr
10×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 4213
Calls
4 calls:
451.0ms
(/ (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))
7.4s
(* (sqrt (/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))) (/ (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)))
134.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
133.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(/ (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))
216.0ms
(* (sqrt (/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))) (/ (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)))
75.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Algorithm
egg-herbie
Counts
4225 → 4225
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05002153321

prune12.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

regimes79.0ms

Accuracy

55.2% (1.1b remaining)

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

bsearch87.0ms

Steps
ItersRangePoint
10
2.623187409837306e+205
6.055558237187944e+215
1.1856454375998788e+206

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05237
17037
27337
37737
47737

end0.0ms

sample870.0ms

Algorithm
intervals
Results
576.0ms8000×body80valid
143.0ms8000×pre80true