Details

sample384.0ms

Algorithm

halfpoints

Results

simplify227.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

227.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize114.0ms

Local error

Found 3 expressions with local error:

58.0b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite101.0ms

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

42.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
41.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
17.0ms	(- (exp x) (exp (- x)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

102.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
74.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
55.0ms	(- (exp x) (exp (- x)))

simplify5.1s

Counts

72 → 99

Calls

72 calls:

Slowest

987.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
313.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
301.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
239.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
229.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize153.0ms

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)

rewrite96.0ms

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

62.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
13.0ms	(* x (* 1/3 x))
11.0ms	(* 1/3 x)
8.0ms	(* (pow x 5) 1/60)

series238.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

110.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
83.0ms	(* (pow x 5) 1/60)
29.0ms	(* x (* 1/3 x))
16.0ms	(* 1/3 x)

simplify9.0s

Counts

72 → 109

Calls

72 calls:

Slowest

593.0ms	(+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))
579.0ms	(/ (* (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))
503.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
501.0ms	(/ (* (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)
497.0ms	(* (/ (* (* (+ (* 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

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize138.0ms

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)))

rewrite229.0ms

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

115.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
87.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
11.0ms	(* 1/3 x)
11.0ms	(/ 1 (sqrt 2))

series457.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

239.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
194.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
24.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify23.6s

Counts

162 → 172

Calls

162 calls:

Slowest

1.0s	(* (* (* (/ 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))))
961.0ms	(* (/ (* (* 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))))
688.0ms	(* (/ (* (* 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))))
568.0ms	(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (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))))
565.0ms	(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))

prune4.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

606×	`sqrt-prod`
594×	`times-frac`
331×	`add-sqr-sqrt`
329×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
24×	`associate-/r*`
21×	`add-exp-log`
20×	`pow1` `sqrt-pow1`
15×	`add-cbrt-cube`
14×	`pow-flip`
13×	`div-inv`
10×	`pow1/2` `pow-div`
9×	`div-exp`
5×	`cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l` `associate-/l/`
2×	`rec-exp` `1-exp` `inv-pow`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 468

Calls

4 calls:

Slowest

84.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
18.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms	(* 1/3 x)
6.0ms	(/ 1 (sqrt (sqrt 2)))

series195.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

175.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
20.0ms	(* 1/3 x)
0.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms	(/ 1 (sqrt (sqrt 2)))

simplify36.6s

Counts

756 → 476

Calls

756 calls:

Slowest

647.0ms	(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
608.0ms	(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))
593.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
570.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
568.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (sqrt 2)))

prune11.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch5.0ms

end0.0ms

sample11.8s

Algorithm

halfpoints

Results