Details

Time bar (total: 13.3s)

sample23.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify79.0ms

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: 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)))

rewrite107.0ms

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:
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series368.0ms

Counts
3 → 9
Calls
3 calls:
140.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms
(/ (/ (/ (+ (+ (+ 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))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify130.0ms

Algorithm
egg-herbie
Counts
459 → 459
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0143912925
1500212452

prune953.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize18.0ms

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)))

rewrite436.0ms

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:
28.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
113.0ms
(/ (/ (- (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series679.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
219.0ms
(/ (/ (- (/ (+ (+ (+ 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))
233.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify735.0ms

Algorithm
egg-herbie
Counts
2564 → 2564
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500184614

prune6.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.9b

localize15.0ms

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))))

rewrite97.0ms

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:
14.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
8.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms
(* (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))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
46.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
142.0ms
(* (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))))

simplify120.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08763857
140833425
250023314

prune561.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.9b

localize25.0ms

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))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
390×times-frac
233×distribute-lft-neg-in distribute-rgt-neg-in
193×*-un-lft-identity
187×add-sqr-sqrt add-cube-cbrt
114×sqrt-prod
36×neg-mul-1
35×div-inv
18×associate-/l*
16×associate-/r*
12×cbrt-prod
6×add-exp-log cbrt-div add-cbrt-cube
4×pow1 flip3-+ flip-+ add-log-exp
3×pow1/3 distribute-neg-frac distribute-lft-out
2×sqrt-div associate-/r/
1×cbrt-undiv neg-sub0 frac-2neg div-sub distribute-frac-neg div-exp clear-num associate-/l/
Counts
4 → 381
Calls
4 calls:
17.0ms
(/ (- (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1)) (- (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series422.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (- (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1)) (- (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
66.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms
(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify117.0ms

Algorithm
egg-herbie
Counts
393 → 393
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0137011172
1500210106

prune1.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.9b

regimes68.0ms

Accuracy

42.2% (1.5b remaining)

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

bsearch65.0ms

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

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04935
16535
26835
37235
47235

end0.0ms

sample535.0ms

Algorithm
intervals
Results
301.0ms8000×body80valid
92.0ms8000×pre80true