Details

sample509.0ms

Algorithm

halfpoints

Results

simplify159.0ms

Calls

1 calls:

Slowest

158.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize78.0ms

Local error

Found 3 expressions with local error:

58.4b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
22×	`add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`insert-posit16` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

3 calls:

Slowest

65.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
51.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
21.0ms	(- (exp x) (exp (- x)))

series235.0ms

Calls

3 calls:

Slowest

97.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
81.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
57.0ms	(- (exp x) (exp (- x)))

simplify5.5s

Calls

72 calls:

Slowest

928.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
417.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
329.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
297.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
251.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize114.0ms

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)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`associate-l`
21×	`add-exp-log`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
13×	`pow1`
10×	`times-frac` `associate-r`
9×	`prod-exp`
7×	`cbrt-unprod`
6×	`unswap-sqr`
5×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `div-exp` `associate-*l/` `pow-exp` `div-inv`

Calls

4 calls:

Slowest

54.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
14.0ms	(* x (* 1/3 x))
12.0ms	(* 1/3 x)
8.0ms	(* (pow x 5) 1/60)

series254.0ms

Calls

4 calls:

Slowest

117.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
86.0ms	(* (pow x 5) 1/60)
33.0ms	(* x (* 1/3 x))
17.0ms	(* 1/3 x)

simplify9.1s

Calls

72 calls:

Slowest

605.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)
557.0ms	(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) (sqrt 2))
547.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
541.0ms	(/ (* (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)
520.0ms	(* (/ (* (* (+ (* 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))) (* (* 2 2) 2)) (* (* (sin y) (sin y)) (sin y)))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize121.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
51×	`add-sqr-sqrt` `add-exp-log`
49×	`*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
31×	`add-cbrt-cube`
25×	`associate-l`
21×	`prod-exp`
13×	`pow1` `div-exp`
12×	`associate-/r*`
11×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow` `unswap-sqr`

Calls

4 calls:

Slowest

72.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
67.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
6.0ms	(* 1/3 x)
5.0ms	(/ 1 (sqrt 2))

series488.0ms

Calls

4 calls:

Slowest

297.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
174.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
17.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify24.4s

Calls

162 calls:

Slowest

986.0ms	(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 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))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
975.0ms	(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
955.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 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))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
726.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
612.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt 1))

prune3.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/3)
0.2b	(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
0.1b	(* (* x 1/3) x)
0.1b	(/ 2 (sin y))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
59×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
11×	`pow1`
6×	`associate-r` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+` `unswap-sqr`

Calls

4 calls:

Slowest

44.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
27.0ms	(* (* x 1/3) x)
12.0ms	(* x 1/3)
8.0ms	(/ 2 (sin y))

series193.0ms

Calls

4 calls:

Slowest

118.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
31.0ms	(* (* x 1/3) x)
28.0ms	(* x 1/3)
15.0ms	(/ 2 (sin y))

simplify23.9s

Calls

154 calls:

Slowest

591.0ms	(/ (* (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))))) (sqrt (/ 2 (sin y))))
583.0ms	(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (cbrt (/ 2 (sin y))))
567.0ms	(* (* (* (* x 1/3) (* x 1/3)) (* x 1/3)) (* (* x x) x))
557.0ms	(sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))))
551.0ms	(/ (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (cbrt (/ 2 (sin y))))

prune3.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes301.0ms

Accuracy

0% (0.9b remaining)

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

bsearch11.0ms

end0.0ms

sample12.1s

Algorithm

halfpoints

Results