Details

sample69.0ms

Algorithm

intervals

Results

41.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify5.4s

Counts: 1 → 1

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.9b

localize60.0ms

Local error

Found 4 expressions with local error:

46.2b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
39.4b	(/ (/ (* (* 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))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite672.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`*-un-lft-identity` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 212

Calls

4 calls:

Slowest

276.0ms	(/ (/ (* (* 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))
162.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
121.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
109.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(/ (/ (* (* 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))
232.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
165.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
101.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify4.0s

Counts: 224 → 224

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 37.6b

localize57.0ms

Local error

Found 4 expressions with local error:

37.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 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))))
0.0b	(* i (+ (+ alpha beta) 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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 272

Calls

4 calls:

Slowest

768.0ms	(* (/ (/ (* 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))))
158.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
96.0ms	(* i (+ (+ alpha beta) i))
86.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

Slowest

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))))
142.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
101.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
41.0ms	(* i (+ (+ alpha beta) i))

simplify1.2s

Counts: 284 → 284

prune4.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.6b

localize68.0ms

Local error

Found 4 expressions with local error:

37.4b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.4b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

2499×	`times-frac`
1610×	`add-sqr-sqrt`
1254×	`*-un-lft-identity`
938×	`add-cube-cbrt`
921×	`sqrt-prod`
900×	`associate-r`
298×	`difference-of-squares`
149×	`distribute-lft-out--`
92×	`associate-/r/`
89×	`add-cbrt-cube` `add-exp-log`
76×	`sqrt-div`
49×	`div-inv`
46×	`cbrt-undiv` `div-exp`
45×	`flip3-+` `flip-+`
42×	`associate-l`
21×	`prod-exp` `cbrt-unprod`
16×	`unswap-sqr`
9×	`distribute-lft-out`
8×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `pow-prod-down` `associate-l/` `-commutative` `flip--` `associate-/l*`

Counts

4 → 1069

Calls

4 calls:

Slowest

909.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
68.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
10.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
6.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.5s

Counts

4 → 12

Calls

4 calls:

Slowest

3.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
106.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
106.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
73.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify6.4s

Counts: 1081 → 1081

prune21.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 37.6b

localize53.0ms

Local error

Found 4 expressions with local error:

37.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.5b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.3b	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

183×	`times-frac`
161×	`add-sqr-sqrt`
146×	`add-exp-log`
125×	`*-un-lft-identity`
114×	`associate-r`
108×	`sqrt-prod`
106×	`add-cbrt-cube`
89×	`add-cube-cbrt`
63×	`div-exp`
57×	`prod-exp`
41×	`cbrt-undiv`
39×	`cbrt-unprod`
36×	`difference-of-squares`
20×	`associate-/r/`
18×	`distribute-lft-out--`
12×	`flip3-+` `flip-+`
10×	`div-inv`
9×	`pow1` `associate-/r*`
8×	`1-exp`
7×	`associate-/l*`
6×	`associate-/l/`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 275

Calls

4 calls:

Slowest

745.0ms	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
200.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
198.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
76.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts

4 → 12

Calls

4 calls:

Slowest

3.3s	(* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
177.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
150.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
139.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.3s

Counts: 287 → 287

prune5.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 37.6b

regimes250.0ms

Accuracy

39.9% (1.6b remaining)

Error of 35.7b against oracle of 34.2b and baseline of 36.8b

bsearch126.0ms

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
396.0ms	8000×	pre	80	true