Details

Time bar (total: 11.1s)

sample25.0ms

Algorithm
intervals
Results
9.0ms256×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: 3.1b

localize15.0ms

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

rewrite658.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
586×*-un-lft-identity
340×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 associate-/l/
3×frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 465
Calls
4 calls:
56.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
171.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
255.0ms
(/ (/ (/ (+ (+ (+ 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))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
136.0ms
(/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify133.0ms

Algorithm
egg-herbie
Counts
477 → 477
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0149213034
1500212552

prune964.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite534.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cube-cbrt add-cbrt-cube
28×div-exp
18×associate-*r*
16×prod-exp
15×cbrt-undiv associate-*l*
10×associate-/r* associate-/r/
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×flip3-+ flip-+ unswap-sqr
5×rec-exp 1-exp div-inv associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×frac-times associate-*r/ associate-*l/
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 169
Calls
4 calls:
19.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
215.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
149.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 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)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms
(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
149.0ms
(/ (* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 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)))

simplify50.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07642679
150012305

prune379.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 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)))
2.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite806.0ms

Algorithm
rewrite-expression-head
Rules
1517×times-frac
931×*-un-lft-identity
511×add-sqr-sqrt add-cube-cbrt
480×cbrt-prod
266×associate-/r*
210×distribute-lft-out
73×associate-/r/
38×flip3-+ flip-+ div-inv
22×add-exp-log
16×add-cbrt-cube
13×associate-/l*
9×cbrt-undiv div-exp associate-/l/
6×cbrt-div
4×pow1 frac-2neg clear-num add-log-exp
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ associate-*l/
Counts
4 → 642
Calls
4 calls:
308.0ms
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (* (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (/ (+ (+ (+ 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) (cbrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify292.0ms

Algorithm
egg-herbie
Counts
654 → 654
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0241632088
1500131655

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize36.0ms

Local error

Found 4 expressions with local error:

2.1b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 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)))
4.6b
(cbrt (/ (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite546.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
332×*-un-lft-identity
232×add-sqr-sqrt add-cube-cbrt
180×cbrt-prod
138×sqrt-prod
87×cbrt-div
70×associate-/r/
50×distribute-lft-out
49×flip3-+ flip-+
38×associate-/l*
24×frac-times
17×div-inv
13×add-exp-log
12×associate-*r/ associate-*l/ associate-/r* add-cbrt-cube
5×cbrt-undiv div-exp associate-/l/
4×pow1 sqrt-div add-log-exp
3×frac-2neg clear-num
1×pow1/3
Counts
4 → 408
Calls
4 calls:
180.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
52.0ms
(cbrt (/ (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series634.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (cbrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
259.0ms
(cbrt (/ (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify122.0ms

Algorithm
egg-herbie
Counts
420 → 420
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151811104
1500110799

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes77.0ms

Accuracy

54.9% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch33.0ms

Steps
ItersRangePoint
5
1.2761513080479214e+167
3.467445464211409e+167
3.2116744201778903e+167

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03023
13023

end0.0ms

sample526.0ms

Algorithm
intervals
Results
293.0ms8000×body80valid
94.0ms8000×pre80true