Details

Time bar (total: 1.0m)

sample82.0ms

Algorithm
intervals
Results
46.0ms256×body80valid
13.0ms256×pre80true

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
411034
31567
2267
158
017

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize45.0ms

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))))
38.9b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
45.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite564.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
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 insert-posit16 add-log-exp
3×distribute-lft-out
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 193
Calls
4 calls:
78.0ms
(* i (+ (+ alpha beta) i))
91.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
234.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
157.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
33.0ms
(* i (+ (+ alpha beta) i))
143.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
275.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify2.7s

Counts
205 → 205
Iterations
IterNodes
26935
11224
0351

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
35.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
36.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
213×times-frac
175×add-sqr-sqrt
145×*-un-lft-identity
101×associate-*r*
92×add-cube-cbrt
67×add-cbrt-cube add-exp-log
45×associate-*l*
30×cbrt-undiv div-exp difference-of-squares
28×associate-/r/
17×prod-exp cbrt-unprod
16×flip3-+ flip-+
15×sqrt-prod distribute-lft-out--
14×div-inv
12×distribute-lft-out
8×pow1
7×unswap-sqr
6×associate-/r*
5×associate-*r/
4×insert-posit16 associate-/l* add-log-exp associate-/l/
2×clear-num frac-2neg pow-prod-down *-commutative
1×distribute-rgt-in frac-times distribute-lft-in flip3-- associate-*l/ flip--
Counts
4 → 264
Calls
4 calls:
61.0ms
(* i (+ (+ alpha beta) i))
782.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
62.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
150.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.6s

Counts
4 → 12
Calls
4 calls:
32.0ms
(* i (+ (+ alpha beta) i))
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
135.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
192.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.3s

Counts
276 → 276
Iterations
IterNodes
26730
11516
0444

prune4.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
36.7b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
902×times-frac
718×*-un-lft-identity
463×add-sqr-sqrt
347×add-cube-cbrt
281×associate-*l*
191×distribute-lft-out
101×associate-*r*
64×add-cbrt-cube add-exp-log
48×associate-/r/
32×cbrt-undiv div-exp
30×difference-of-squares
26×div-inv
24×flip3-+ flip-+
15×sqrt-prod distribute-lft-out--
13×prod-exp cbrt-unprod unswap-sqr
8×pow1 associate-/r*
6×associate-/l*
4×insert-posit16 add-log-exp associate-/l/
3×associate-*r/
2×clear-num frac-2neg pow-prod-down *-commutative
1×distribute-rgt-in frac-times distribute-lft-in flip3-- associate-*l/ flip--
Counts
4 → 520
Calls
4 calls:
96.0ms
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
76.0ms
(* i (+ (+ alpha beta) i))
651.0ms
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
190.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.5s

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
26.0ms
(* i (+ (+ alpha beta) i))
3.2s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
143.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.8s

Counts
532 → 532
Iterations
IterNodes
12531
0732

prune9.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.0b
(/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i)))
0.0b
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
1688×times-frac
1426×*-un-lft-identity
705×add-sqr-sqrt
661×add-cube-cbrt
428×distribute-lft-out
278×associate-*l*
80×associate-/r/
74×associate-/l*
52×add-cbrt-cube add-exp-log
45×div-inv
35×flip3-+ flip-+
30×associate-/r*
26×cbrt-undiv div-exp
24×associate-*r*
8×prod-exp cbrt-unprod unswap-sqr
6×pow1 difference-of-squares
4×insert-posit16 add-log-exp
3×clear-num frac-2neg sqrt-prod distribute-lft-out-- associate-/l/
1×frac-times flip3-- pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 846
Calls
4 calls:
592.0ms
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
195.0ms
(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
57.0ms
(/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i)))
132.0ms
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))

series1.1s

Counts
4 → 12
Calls
4 calls:
580.0ms
(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ alpha beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
350.0ms
(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
119.0ms
(/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i)))
84.0ms
(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))

simplify1.6s

Counts
858 → 858
Iterations
IterNodes
12656
0820

prune13.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.0b

regimes351.0ms

Accuracy

42.2% (8.8b remaining)

Error of 10.9b against oracle of 2.1b and baseline of 17.4b

bsearch115.0ms

Steps
ItersRangePoint
8
8.076566236415723e+137
3.1021573281508808e+140
2.943197667848456e+140

simplify9.0ms

Iterations
IterNodes
245
145
032

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.9s8000×body80valid
364.0ms8000×pre80true