Details

Time bar (total: 30.8s)

sample40.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
5.0ms256×pre80true

simplify649.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
40.9b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
109.0ms
(* i (+ (+ alpha beta) i))
147.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
359.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
235.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.4s

Counts
4 → 12
Calls
4 calls:
28.0ms
(* i (+ (+ alpha beta) i))
128.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.0s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
253.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify747.0ms

Counts
201 → 201

prune875.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
37.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
396.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.1s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
155.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.5s

Counts
4 → 12
Calls
4 calls:
428.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.9s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
105.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
147.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.0s

Counts
376 → 376

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
37.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
220×add-exp-log
136×add-cbrt-cube
91×times-frac div-exp
87×prod-exp
73×add-sqr-sqrt *-un-lft-identity
54×cbrt-undiv
49×add-cube-cbrt cbrt-unprod
43×associate-*l*
39×associate-*r*
18×associate-/r/
11×pow1
10×flip3-+ flip-+
9×rec-exp 1-exp div-inv distribute-lft-out
6×frac-times associate-*r/ associate-*l/ associate-/r* difference-of-squares
4×pow-prod-down associate-/l/ associate-/l* add-log-exp unswap-sqr
3×sqrt-prod distribute-lft-out--
2×frac-2neg clear-num *-commutative
1×flip3-- un-div-inv flip--
Counts
4 → 242
Calls
4 calls:
637.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
1.4s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
84.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
209.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.4s

Counts
4 → 12
Calls
4 calls:
895.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))
3.3s
(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
95.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify981.0ms

Counts
254 → 254

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 37.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
37.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.0b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
291×times-frac
237×add-sqr-sqrt
174×*-un-lft-identity
138×sqrt-prod
120×add-cube-cbrt
96×associate-*r*
90×associate-*l*
37×add-exp-log add-cbrt-cube
36×associate-/r/
30×difference-of-squares
20×flip3-+ flip-+
18×div-inv
15×distribute-lft-out-- unswap-sqr
14×cbrt-undiv div-exp
12×distribute-lft-out
9×associate-/r*
8×prod-exp cbrt-unprod
6×pow1 associate-/l/
5×associate-*r/ associate-/l*
4×add-log-exp
3×frac-2neg clear-num
2×sqrt-div
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 306
Calls
4 calls:
1.3s
(* (/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
108.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
229.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.5s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
124.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
121.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
168.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify891.0ms

Counts
318 → 318

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 37.3b

regimes191.0ms

Accuracy

34.9% (2.4b remaining)

Error of 36.6b against oracle of 34.1b and baseline of 37.9b

bsearch122.0ms

Steps
ItersRangePoint
9
1.0082603371343233e+223
1.1920749407542138e+231
1.0233927319500506e+223

simplify1.0s

end0.0ms

sample2.0s

Algorithm
intervals
Results
848.0ms8000×body80valid
758.0ms8000×pre80true