Details

sample414.0ms

Algorithm

halfpoints

Results

simplify133.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

132.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize68.0ms

Local error

Found 3 expressions with local error:

58.5b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite95.0ms

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

40.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
37.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
15.0ms	(- (exp x) (exp (- x)))

series285.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

126.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
95.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
64.0ms	(- (exp x) (exp (- x)))

simplify4.2s

Counts

72 → 99

Calls

72 calls:

Slowest

708.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
340.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
241.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
201.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
192.0ms	(* (/ (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))) (* (* 2 2) 2)) (* (* (cos y) (cos y)) (cos y)))

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

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)

rewrite77.0ms

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

50.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
13.0ms	(* x (* 1/3 x))
8.0ms	(* (pow x 5) 1/60)
5.0ms	(* 1/3 x)

series225.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
80.0ms	(* (pow x 5) 1/60)
30.0ms	(* x (* 1/3 x))
15.0ms	(* 1/3 x)

simplify7.6s

Counts

72 → 109

Calls

72 calls:

Slowest

639.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
473.0ms	(* (/ (* (* (+ (* 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)))
463.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
441.0ms	(/ (* (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)
397.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize188.0ms

Local error

Found 4 expressions with local error:

28.0b	(log (exp (* x (* 1/3 x))))
0.3b	(* 1/3 x)
0.1b	(* x (* 1/3 x))
0.1b	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-l`
16×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
14×	`pow1`
10×	`times-frac`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-down` `add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `log-pow` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `exp-prod` `exp-to-pow` `div-exp` `rem-log-exp` `associate-*l/` `div-inv`

Counts

4 → 86

Calls

4 calls:

Slowest

78.0ms	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))
14.0ms	(* x (* 1/3 x))
5.0ms	(* 1/3 x)
4.0ms	(log (exp (* x (* 1/3 x))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))
50.0ms	(log (exp (* x (* 1/3 x))))
46.0ms	(* x (* 1/3 x))
29.0ms	(* 1/3 x)

simplify7.1s

Counts

59 → 98

Calls

59 calls:

Slowest

663.0ms	(* (/ (* (* (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (* (* 2 2) 2)) (* (* (sin y) (sin y)) (sin y)))
396.0ms	(+ (- (log (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (log 2)) (log (sin y)))
322.0ms	(/ (* (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)))) (* (cbrt 2) (cbrt 2)))
321.0ms	(* (* (* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2)) (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2)) (* (* (sin y) (sin y)) (sin y)))
317.0ms	(/ (* (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)))) (sqrt 2))

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize119.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt 2))
0.5b	(/ (+ (* 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)))

rewrite168.0ms

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

88.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
61.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
11.0ms	(* 1/3 x)
5.0ms	(/ 1 (sqrt 2))

series538.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

307.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
210.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
21.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify23.9s

Counts

162 → 172

Calls

162 calls:

Slowest

1.1s	(* (/ (* (* 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))))
875.0ms	(/ (* (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)
706.0ms	(* (/ (* (* 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))))
571.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))))

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.9b remaining)

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

bsearch5.0ms

end0.0ms

sample12.0s

Algorithm

halfpoints

Results