Details

sample36.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5007
3	1614
2	280
1	60
0	17

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.2b	(/ (/ (* (* 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))
45.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite638.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
38×	`add-sqr-sqrt`
32×	`frac-times`
28×	`associate-*r/`
24×	`*-un-lft-identity` `add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
9×	`pow1` `associate-/l/`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down`
2×	`distribute-rgt-in` `associate-+r+` `clear-num` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `fma-def` `flip3--` `associate-l` `*-commutative` `flip--`

Counts

4 → 187

Calls

4 calls:

18.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
134.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
289.0ms	(/ (/ (* (* 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))
188.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.8s

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
158.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.3s	(/ (/ (* (* 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))
259.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify2.1s

Counts

199 → 199

Iterations

Iter	Nodes
done	5001
1	1260
0	347

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 32.3b

localize48.0ms

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)))
0.2b	(* (/ (/ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

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-cbrt-cube` `add-exp-log`
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×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 372

Calls

4 calls:

316.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.0s	(* (/ (/ (* 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))))
78.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
128.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.4s

Counts

4 → 12

Calls

4 calls:

427.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.7s	(* (/ (/ (* 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))))
112.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
209.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.9s

Counts

384 → 384

Iterations

Iter	Nodes
done	5001
1	1746
0	509

prune2.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (- (+ (+ 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))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1669×	`times-frac`
1103×	`add-sqr-sqrt`
864×	`*-un-lft-identity`
630×	`add-cube-cbrt`
290×	`associate-r`
220×	`add-exp-log`
210×	`difference-of-squares`
128×	`div-exp`
107×	`associate-/r/`
105×	`sqrt-prod` `distribute-lft-out--`
101×	`associate-/r*`
100×	`add-cbrt-cube`
58×	`div-inv`
53×	`cbrt-undiv`
51×	`flip3-+` `prod-exp` `flip-+`
42×	`associate-l`
21×	`cbrt-unprod`
15×	`rec-exp` `1-exp`
14×	`unswap-sqr`
9×	`distribute-lft-out`
7×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-*r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 887

Calls

4 calls:

187.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
1.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
64.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
155.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.4s

Counts

4 → 12

Calls

4 calls:

531.0ms	(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
3.5s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
123.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
196.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.1s

Counts

899 → 899

Iterations

Iter	Nodes
done	5000
1	3771
0	1052

prune6.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 32.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
0.1b	(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
32.6b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.1b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

14802×	`times-frac`
7254×	`*-un-lft-identity`
6816×	`add-sqr-sqrt`
4236×	`add-cube-cbrt`
1524×	`associate-/r/`
1290×	`difference-of-squares`
864×	`distribute-lft-out`
784×	`div-inv`
743×	`flip3-+` `flip-+`
645×	`sqrt-prod` `distribute-lft-out--`
101×	`associate-/r*`
65×	`add-cbrt-cube` `add-exp-log`
46×	`associate-/l*`
42×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`associate-+r+` `associate-*r/`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in`

Counts

4 → 4241

Calls

4 calls:

29.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
707.0ms	(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
90.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
148.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.9s

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* beta alpha) (* i (+ (+ alpha beta) i)))
3.6s	(/ (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
134.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
184.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify8.3s

Counts

4253 → 4253

Iterations

Iter	Nodes
done	5001
0	4571

prune24.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 32.2b

regimes267.0ms

Accuracy

37.2% (2.3b remaining)

Error of 36.1b against oracle of 33.8b and baseline of 37.4b

bsearch72.0ms

Steps

Iters	Range		Point
8	1.5761988857549511e+195	9.744806586651462e+197	6.52967490975705e+195

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

929.0ms	8000×	body	80	valid
596.0ms	8000×	pre	80	true