Details

sample471.0ms

Algorithm

halfpoints

Results

simplify187.0ms

Calls

1 calls:

Slowest

187.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize90.0ms

Local error

Found 3 expressions with local error:

57.7b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(+ (exp x) (exp (- x)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`associate-l`
16×	`times-frac`
13×	`add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
5×	`pow1`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`associate-r` `insert-posit16`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv` `flip--` `distribute-lft-out`

Calls

3 calls:

Slowest

79.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
21.0ms	(- (exp x) (exp (- x)))
9.0ms	(+ (exp x) (exp (- x)))

series192.0ms

Calls

3 calls:

Slowest

99.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
49.0ms	(- (exp x) (exp (- x)))
43.0ms	(+ (exp x) (exp (- x)))

simplify3.4s

Calls

46 calls:

Slowest

931.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
258.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
251.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
168.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
147.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

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

48.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
18.0ms	(* (pow x 5) 1/60)
17.0ms	(* x (* 1/3 x))
8.0ms	(* 1/3 x)

series246.0ms

Calls

4 calls:

Slowest

124.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
54.0ms	(* (pow x 5) 1/60)
44.0ms	(* x (* 1/3 x))
24.0ms	(* 1/3 x)

simplify8.5s

Calls

72 calls:

Slowest

542.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
525.0ms	(/ (* (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)
507.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt 2) (cbrt 2)))
477.0ms	(/ (* (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))
474.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize117.0ms

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

rewrite196.0ms

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

99.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
81.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
7.0ms	(* 1/3 x)
5.0ms	(/ 1 (sqrt 2))

series505.0ms

Calls

4 calls:

Slowest

291.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
189.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
25.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify24.5s

Calls

162 calls:

Slowest

1.2s	(* (/ (* (* 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))))
1.1s	(* (* (* (/ 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))))
895.0ms	(- (log (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (log (sqrt 2)))
723.0ms	(* (/ (* (* 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))))
609.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))

prune3.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize133.0ms

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))

rewrite125.0ms

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

73.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
29.0ms	(* (* x 1/3) x)
11.0ms	(* x 1/3)
9.0ms	(/ 2 (sin y))

series223.0ms

Calls

4 calls:

Slowest

119.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
46.0ms	(* (* x 1/3) x)
31.0ms	(/ 2 (sin y))
27.0ms	(* x 1/3)

simplify23.2s

Calls

154 calls:

Slowest

593.0ms	(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (sqrt (/ 2 (sin y))))
576.0ms	(- (log (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (log (/ 2 (sin y))))
563.0ms	(/ (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (sqrt (/ 2 (sin y))))
539.0ms	(/ (* (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (cbrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))))) 2)
539.0ms	(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (/ (sqrt 2) 1))

prune3.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes583.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch8.0ms

end0.0ms

sample11.5s

Algorithm

halfpoints

Results