Details

sample473.0ms

Algorithm: halfpoints

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	991
5	235
4	118
3	83
2	48
1	30
0	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.4b	(- (exp x) (exp (- x)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 99

Calls

4 calls:

9.0ms	(+ (exp x) (exp (- x)))
44.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
48.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
10.0ms	(- (exp x) (exp (- x)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (exp x) (exp (- x)))
75.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
117.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
48.0ms	(- (exp x) (exp (- x)))

simplify1.4s

Counts

111 → 111

Iterations

Iter	Nodes
done	5002
2	2321
1	517
0	199

prune890.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow x 5))
0.1b	(* x (* x x))
0.1b	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
0.1b	(* 1/3 (* x (* x x)))

rewrite730.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
28×	`add-sqr-sqrt` `add-exp-log`
25×	`add-cbrt-cube`
22×	`associate-l`
17×	`*-un-lft-identity` `add-cube-cbrt`
14×	`prod-exp`
12×	`associate-r` `cbrt-unprod`
10×	`times-frac` `pow-prod-down`
6×	`unswap-sqr`
5×	`pow-prod-up`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
2×	`sqr-pow`
1×	`pow2` `pow-to-exp` `cbrt-undiv` `pow-plus` `cube-unmult` `div-exp` `associate-*l/` `pow-exp` `pow-sqr` `div-inv`

Counts

4 → 102

Calls

4 calls:

9.0ms	(* 1/60 (pow x 5))
12.0ms	(* x (* x x))
634.0ms	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
72.0ms	(* 1/3 (* x (* x x)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 1/60 (pow x 5))
65.0ms	(* x (* x x))
167.0ms	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
66.0ms	(* 1/3 (* x (* x x)))

simplify1.5s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	2192
1	455
0	181

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize182.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

621.0ms	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
509.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
520.0ms	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
6.0ms	(/ 1 (sqrt 2.0))

series673.0ms

Counts

4 → 10

Calls

4 calls:

176.0ms	(* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
327.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
169.0ms	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify3.7s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	4528
1	721
0	256

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1128×	`sqrt-prod`
1116×	`times-frac`
592×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
79×	`add-exp-log`
49×	`add-cbrt-cube`
37×	`associate-/l*`
32×	`div-exp`
25×	`prod-exp`
24×	`associate-/r*`
23×	`pow1` `div-inv`
20×	`sqrt-pow1`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
14×	`pow-flip`
10×	`pow1/2` `pow-div`
5×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/` `associate-/l/`
2×	`inv-pow`
1×	`frac-times` `flip3-+` `associate-r` `associate-r/` `-commutative` `flip-+`

Counts

4 → 767

Calls

4 calls:

570.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
553.0ms	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
26.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(/ 1 (sqrt (sqrt 2.0)))

series1000.0ms

Counts

4 → 8

Calls

4 calls:

332.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
667.0ms	(/ (+ (+ (* 1/3 (* x (* x x))) (* x 2)) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify2.3s

Counts

775 → 775

Iterations

Iter	Nodes
done	5000
1	1867
0	616

prune5.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample13.1s

Algorithm: halfpoints