Details

sample459.0ms

Algorithm: halfpoints

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 6 (150.0ms)

Iter	Nodes	Cost
0	16	543
1	30	363
2	48	294
3	79	294
4	111	294
5	178	294
6	432	293
7	1165	293
8	2574	293
done	5001	293

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize105.0ms

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))
57.6b	(- (exp x) (exp (- x)))

rewrite190.0ms

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:

16.0ms	(+ (exp x) (exp (- x)))
73.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
78.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.0ms	(- (exp x) (exp (- x)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (exp x) (exp (- x)))
98.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
133.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
63.0ms	(- (exp x) (exp (- x)))

simplify2.2s

Counts

111 → 111

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	199	45913
1	517	43852
2	1758	39796
done	5001	39717

prune753.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(* 1/60 (pow x 5))
0.1b	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
0.2b	(* (* x x) 1/3)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
33×	`associate-l`
31×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`add-exp-log`
23×	`times-frac`
21×	`add-cbrt-cube`
16×	`associate-r`
13×	`pow1`
10×	`prod-exp`
8×	`cbrt-unprod` `unswap-sqr`
5×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 111

Calls

4 calls:

69.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
10.0ms	(* 1/60 (pow x 5))
28.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
20.0ms	(* (* x x) 1/3)

series299.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
62.0ms	(* 1/60 (pow x 5))
123.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2.0) (sin y))
31.0ms	(* (* x x) 1/3)

simplify2.3s

Counts

123 → 123

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	237	52699
1	598	49974
2	2000	49371
done	5000	49251

prune979.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite160.0ms

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:

41.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
73.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
30.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
5.0ms	(/ 1 (sqrt 2.0))

series700.0ms

Counts

4 → 10

Calls

4 calls:

197.0ms	(* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y))
321.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
182.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify3.9s

Counts

192 → 192

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	255	126500
1	709	117305
2	2260	115098
done	5001	114656

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize161.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite336.0ms

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:

194.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
40.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
16.0ms	(/ 1 (sqrt (sqrt 2.0)))
22.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series477.0ms

Counts

4 → 8

Calls

4 calls:

319.0ms	(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0)) (sin y)))
158.0ms	(/ (+ (* x (+ 2 (* (* x x) 1/3))) (* 1/60 (pow x 5))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify3.2s

Iterations

Useful iterations: 1 (1.2s)

Iter	Nodes	Cost
0	615	539801
1	1760	477746