Details

sample476.0ms

Algorithm

halfpoints

Results

simplify200.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

200.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize108.0ms

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))

rewrite112.0ms

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--`

Counts

3 → 90

Calls

3 calls:

Slowest

64.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
37.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
10.0ms	(- (exp x) (exp (- x)))

series299.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

147.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
87.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
64.0ms	(- (exp x) (exp (- x)))

simplify12.6s

Counts

104 → 99

Calls

104 calls:

Slowest

909.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (sin y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))) (* (/ (- (exp x) (exp (- x))) 2) (sin y)))
800.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
504.0ms	(* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x))))
466.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
406.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (+ (exp x) (exp (- x))) 2) (cos y))) (* (/ (+ (exp x) (exp (- x))) 2) (cos y)))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize171.0ms

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)

rewrite106.0ms

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`

Counts

4 → 97

Calls

4 calls:

Slowest

66.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
26.0ms	(* x (* 1/3 x))
8.0ms	(* (pow x 5) 1/60)
5.0ms	(* 1/3 x)

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
59.0ms	(* (pow x 5) 1/60)
29.0ms	(* x (* 1/3 x))
19.0ms	(* 1/3 x)

simplify15.4s

Counts

111 → 109

Calls

111 calls:

Slowest

645.0ms	(* (cbrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sin y))
644.0ms	(sqrt (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y)))
533.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
523.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sin y))
506.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize166.0ms

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)))

rewrite180.0ms

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`

Counts

4 → 162

Calls

4 calls:

Slowest

104.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
63.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
6.0ms	(/ 1 (sqrt 2))
5.0ms	(* 1/3 x)

series465.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

270.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
167.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
28.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify35.8s

Counts

209 → 172

Calls

209 calls:

Slowest

996.0ms	(* (/ (* (* 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))))
982.0ms	(* (* (* (/ 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))))
640.0ms	(/ (sqrt 2) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))))
605.0ms	(* (/ (* (* 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))))
597.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 1))

prune3.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize131.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

Slowest

73.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2))) (/ 2 (sin y)))
15.0ms	(* 1/3 (* x x))
8.0ms	(* (pow x 5) 1/60)
4.0ms	(/ 2 (sin y))

series575.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(/ 2 (sin y))
121.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2))) (/ 2 (sin y)))
70.0ms	(* (pow x 5) 1/60)
28.0ms	(* 1/3 (* x x))

simplify32.9s

Counts

211 → 159

Calls

211 calls:

Slowest

535.0ms	(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2)))) 1)
534.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2))) (/ 1 1))
522.0ms	(* (* (* (pow x 5) 1/60) (* (pow x 5) 1/60)) (* (pow x 5) 1/60))
488.0ms	(/ (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2))) 1)
476.0ms	(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* 1/3 (* x x)) 2)))) 2)

prune3.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch5.0ms

end0.0ms

sample11.7s

Algorithm

halfpoints

Results