Details

Time bar (total: 14.6s)

sample24.0ms

Algorithm
intervals
Results
10.0ms256×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite617.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
583×*-un-lft-identity
339×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
28×flip3-+ flip-+
27×div-inv
19×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
4×associate-/l/
3×pow1 frac-2neg clear-num add-log-exp
Counts
3 → 450
Calls
3 calls:
173.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
261.0ms
(/ (/ (/ (+ (+ (+ 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)))

series354.0ms

Counts
3 → 9
Calls
3 calls:
133.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm
egg-herbie
Counts
459 → 459
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0143912925
1500212452

prune924.0ms

Filtered
459 candidates to 269 candidates (58.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize14.0ms

Local error

Found 3 expressions with local error:

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))
4.8b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
5500×times-frac
3738×*-un-lft-identity
2184×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/
131×flip3-+ flip-+
130×div-inv
17×associate-/r*
13×distribute-neg-frac
12×add-exp-log add-cbrt-cube
5×cbrt-undiv div-exp
4×associate-/l/
3×pow1 frac-2neg div-sub distribute-frac-neg clear-num add-log-exp
2×neg-sub0
Counts
3 → 2555
Calls
3 calls:
285.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
447.0ms
(/ (/ (- (/ (+ (+ (+ 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))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series509.0ms

Counts
3 → 9
Calls
3 calls:
212.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
218.0ms
(/ (/ (- (/ (+ (+ (+ 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))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify748.0ms

Algorithm
egg-herbie
Counts
2564 → 2564
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0500184614

prune6.1s

Filtered
2564 candidates to 1534 candidates (59.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
4.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.7b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.8b
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite597.0ms

Algorithm
rewrite-expression-head
Rules
175×times-frac
126×*-un-lft-identity
122×add-sqr-sqrt
94×add-cube-cbrt
87×associate-*r*
70×sqrt-prod
16×distribute-lft-out
15×add-exp-log add-cbrt-cube
10×flip3-+ sqrt-div associate-/r/ flip-+
8×pow1 unswap-sqr
7×associate-*l* associate-/l*
5×div-inv
4×cbrt-undiv div-exp add-log-exp
3×prod-exp associate-/r* cbrt-unprod
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-/l/
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 201
Calls
4 calls:
111.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
350.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
144.0ms
(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify118.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08763857
140833425
250023314

prune539.0ms

Filtered
213 candidates to 140 candidates (65.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.9b

localize26.0ms

Local error

Found 4 expressions with local error:

1.6b
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (- (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
5.1b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.1b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.1b
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
87×*-un-lft-identity
81×add-sqr-sqrt add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
18×add-exp-log div-inv
16×associate-/r*
12×cbrt-prod
11×add-cbrt-cube
9×div-exp
8×neg-mul-1
7×associate-/l*
6×cbrt-div
5×cbrt-undiv
4×pow1 flip3-+ flip-+ add-log-exp
3×pow1/3 distribute-lft-out
2×sqrt-div 1-exp prod-exp associate-/r/ distribute-neg-frac
1×frac-2neg clear-num cbrt-unprod associate-/l/
Counts
4 → 198
Calls
4 calls:
102.0ms
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (- (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
33.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series441.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (- (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
63.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify102.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
09625015
136524432
250014304

prune678.0ms

Filtered
210 candidates to 122 candidates (58.1%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.9b

regimes76.0ms

Accuracy

42.2% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 3.9b

bsearch66.0ms

Steps
ItersRangePoint
8
3.1136003103388986e+91
6.7696059868838e+95
2.3451858201965897e+92

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05237
17037
27337
37737
47737

end0.0ms

sample548.0ms

Algorithm
intervals
Results
304.0ms8000×body80valid
100.0ms8000×pre80true