Details

sample522.0ms

Algorithm

halfpoints

Results

simplify203.0ms

Calls

1 calls:

Slowest

203.0ms

(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize93.0ms

Local error

Found 4 expressions with local error:

56.8b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
27×	`add-cube-cbrt`
25×	`associate-*l/`
14×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
8×	`pow1` `add-log-exp`
6×	`associate-/r` `associate-r*`
5×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `flip--`
1×	`+-commutative` `sum-log` `sub-neg` `diff-log`

Calls

4 calls:

Slowest

99.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
89.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
29.0ms	(- (exp x) (exp (- x)))
12.0ms	(+ (exp x) (exp (- x)))

series340.0ms

Calls

4 calls:

Slowest

141.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
80.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
80.0ms	(- (exp x) (exp (- x)))
38.0ms	(+ (exp x) (exp (- x)))

simplify8.0s

Calls

100 calls:

Slowest

1.0s	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
407.0ms	(* (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (cos y))
362.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
315.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
312.0ms	(* (/ (- (exp x) (exp (- x))) (* (cbrt 2) (cbrt 2))) (sin y))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize155.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 x)
0.1b	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
0.1b	(* x (* 1/3 x))
0.1b	(* (pow x 5) 1/60)

rewrite4.2s

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
57×	`associate-l`
46×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
24×	`associate-r`
22×	`times-frac`
21×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`distribute-lft-out`
15×	`pow1` `associate-*l/`
10×	`unswap-sqr`
9×	`prod-exp`
7×	`cbrt-unprod` `associate-/l*`
6×	`pow-prod-down`
5×	`*-commutative`
4×	`unpow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv`

Calls

4 calls:

Slowest

4.2s	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
24.0ms	(* x (* 1/3 x))
11.0ms	(* (pow x 5) 1/60)
5.0ms	(* 1/3 x)

series223.0ms

Calls

4 calls:

Slowest

114.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
55.0ms	(* (pow x 5) 1/60)
35.0ms	(* x (* 1/3 x))
19.0ms	(* 1/3 x)

simplify11.2s

Calls

112 calls:

Slowest

550.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
535.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)
530.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
526.0ms	(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) 1)
500.0ms	(* (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sin y))

prune2.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize150.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 x)
0.3b	(/ (sin y) (/ 2 (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
0.1b	(* x (* 1/3 x))
0.1b	(* (pow x 5) 1/60)

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

191×	`*-un-lft-identity`
165×	`times-frac`
101×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
68×	`associate-l`
52×	`distribute-lft-out`
34×	`associate-/r*`
21×	`associate-r` `add-exp-log` `associate-/r/`
18×	`add-cbrt-cube`
13×	`pow1`
8×	`unswap-sqr`
7×	`prod-exp`
6×	`associate-/l*`
5×	`pow-prod-down` `cbrt-unprod` `div-inv`
4×	`unpow-prod-down` `flip3-+` `*-commutative` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`clear-num` `frac-2neg` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Calls

4 calls:

Slowest

1.6s	(/ (sin y) (/ 2 (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
28.0ms	(* x (* 1/3 x))
11.0ms	(* (pow x 5) 1/60)
5.0ms	(* 1/3 x)

series394.0ms

Calls

4 calls:

Slowest

256.0ms	(/ (sin y) (/ 2 (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
63.0ms	(* (pow x 5) 1/60)
53.0ms	(* x (* 1/3 x))
20.0ms	(* 1/3 x)

simplify44.7s

Calls

269 calls:

Slowest

971.0ms	(/ (sqrt 2) (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
902.0ms	(/ (cbrt (sin y)) (sqrt (/ 2 (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))))
700.0ms	(/ (* (* (sin y) (sin y)) (sin y)) (/ (* (* 2 2) 2) (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))))
576.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)
561.0ms	(cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))

prune4.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize154.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

13500×	`times-frac`
9100×	`*-un-lft-identity`
5054×	`add-sqr-sqrt`
5052×	`add-cube-cbrt`
3288×	`sqrt-prod`
2027×	`associate-l`
2024×	`distribute-lft-out`
784×	`associate-/r/`
400×	`associate-/l*`
287×	`div-inv`
256×	`associate-/r*`
84×	`flip3-+` `flip-+`
55×	`clear-num` `frac-2neg`
43×	`add-exp-log`
34×	`add-cbrt-cube`
28×	`div-exp` `associate-/l/`
19×	`cbrt-undiv`
6×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`1-exp` `associate-r`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Calls

4 calls:

Slowest

1.6s	(/ (/ (sin y) (/ (sqrt 2) 1)) (/ (sqrt 2) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
1.1s	(/ (sqrt 2) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))
11.0ms	(/ (sin y) (/ (sqrt 2) 1))
10.0ms	(* 1/3 x)

series790.0ms

Calls

4 calls:

Slowest

428.0ms	(/ (/ (sin y) (/ (sqrt 2) 1)) (/ (sqrt 2) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
217.0ms	(/ (sqrt 2) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))
117.0ms	(/ (sin y) (/ (sqrt 2) 1))
27.0ms	(* 1/3 x)