Details

Time bar (total: 18.6s)

sample28.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify73.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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:
28.0ms
(+ (+ alpha beta) (* beta alpha))
335.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
490.0ms
(/ (/ (/ (+ (+ (+ 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))
300.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (+ alpha beta) (* beta alpha))
150.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
162.0ms
(/ (/ (/ (+ (+ (+ 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))
88.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify124.0ms

Counts
475 → 475

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.7b
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

rewrite924.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
65×*-un-lft-identity
54×add-exp-log
49×add-sqr-sqrt
42×add-cube-cbrt
34×add-cbrt-cube
24×div-exp
18×associate-/r/
15×associate-*r*
14×cbrt-undiv
13×flip3-+ flip-+ associate-/l*
12×prod-exp
11×distribute-lft-out
10×associate-/r*
9×div-inv
7×pow1 associate-/l/
6×cbrt-unprod
4×frac-times rec-exp 1-exp associate-*l* associate-*l/ add-log-exp
3×frac-2neg clear-num unswap-sqr
2×associate-*r/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 181
Calls
4 calls:
35.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
187.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
320.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
375.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
167.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
83.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

simplify123.0ms

Counts
193 → 193

prune469.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.4b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite828.0ms

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:
374.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
209.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
115.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
124.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series439.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
118.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
49.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
55.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify61.0ms

Counts
171 → 171

prune479.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

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)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.3b
(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
3.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.5b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
10323×times-frac
6511×*-un-lft-identity
3883×add-sqr-sqrt
3881×add-cube-cbrt
2904×sqrt-prod
1315×distribute-lft-out
591×associate-/l*
239×associate-/r/
216×sqrt-div
127×div-inv
115×flip3-+ flip-+
20×add-exp-log add-cbrt-cube
11×cbrt-undiv div-exp associate-/r*
6×pow1
4×add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 3044
Calls
4 calls:
759.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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)) 1.0))
188.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
115.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
122.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series561.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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)) 1.0))
275.0ms
(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
62.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.1s

Counts
3056 → 3056

prune7.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.1b

regimes78.0ms

Accuracy

57.6% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.7b

bsearch62.0ms

Steps
ItersRangePoint
8
3.734405037488181e+157
1.4098134330683202e+162
1.3830890874159494e+162

simplify1.0ms

end0.0ms

sample897.0ms

Algorithm
intervals
Results
517.0ms8000×body80valid
161.0ms8000×pre80true