Details

sample477.0ms

Algorithm

halfpoints

Results

simplify197.0ms

Calls

1 calls:

Slowest

197.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.7b

localize86.0ms

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))) 2) (cos y))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`prod-diff`
8×	`associate-l`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r`
5×	`add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

3 calls:

Slowest

18.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
14.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
14.0ms	(- (exp x) (exp (- x)))

series207.0ms

Calls

3 calls:

Slowest

82.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
70.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
55.0ms	(- (exp x) (exp (- x)))

simplify4.0s

Calls

53 calls:

Slowest

717.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
333.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
249.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
218.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
179.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
0.0b	(* (fma 1/3 (* x x) 2) x)
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-l`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv`
1×	`fma-udef`

Calls

4 calls:

Slowest

18.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
8.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
4.0ms	(* (fma 1/3 (* x x) 2) x)
0.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

series529.0ms

Calls

4 calls:

Slowest

373.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
80.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
43.0ms	(* (fma 1/3 (* x x) 2) x)
33.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

simplify2.9s

Calls

34 calls:

Slowest

381.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
243.0ms	(* (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (sin y))
199.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
187.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
146.0ms	(* (* (* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2)) (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2)) (* (* (sin y) (sin y)) (sin y)))

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
0.4b	(* (sqrt (fma 1/3 (* x x) 2)) x)
0.1b	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-l`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`associate-r`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*l/` `div-inv`

Calls

4 calls:

Slowest

12.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
12.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
6.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
3.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)

series207.0ms

Calls

4 calls:

Slowest

59.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
51.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
49.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
47.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)

simplify4.7s

Calls

45 calls:

Slowest

581.0ms	(* (* (* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2)) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2)) (* (* (sin y) (sin y)) (sin y)))
430.0ms	(* (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))) (* (* (* (sqrt (fma 1/3 (* x x) 2)) x) (* (sqrt (fma 1/3 (* x x) 2)) x)) (* (sqrt (fma 1/3 (* x x) 2)) x)))
371.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
317.0ms	(- (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))))
290.0ms	(- (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))) (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))))

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fma 1/3 (* x x) 2)) x)
0.3b	(* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))
0.2b	(* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))
0.1b	(* (/ (fma 1/60 (pow x 5) (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) 2) (sin y))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `associate-l` `add-exp-log`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`cbrt-prod` `sqrt-prod`
5×	`associate-r`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-*l/` `div-inv`

Calls

4 calls:

Slowest

70.0ms	(* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))
20.0ms	(* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))
9.0ms	(* (/ (fma 1/60 (pow x 5) (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) 2) (sin y))
6.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)

series382.0ms

Calls

4 calls:

Slowest

206.0ms	(* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))
82.0ms	(* (/ (fma 1/60 (pow x 5) (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) 2) (sin y))
53.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)
41.0ms	(* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))

simplify7.2s

Calls

52 calls:

Slowest

526.0ms	(* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) (* (* (* (sqrt (fma 1/3 (* x x) 2)) x) (* (sqrt (fma 1/3 (* x x) 2)) x)) (* (sqrt (fma 1/3 (* x x) 2)) x))))
357.0ms	(- (+ (* 1/9 (* (pow x 3) (pow 4 1/3))) (* x (pow 4 1/3))) (* 1/324 (* (pow x 5) (pow 4 1/3))))
321.0ms	(* (fma 1/60 (pow x 5) (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) (sin y))
316.0ms	(* (* (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2)))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2))))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (cbrt (sqrt (fma 1/3 (* x x) 2))))) (* (* (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))) (* (cbrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))))
312.0ms	(- (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))))

prune2.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes282.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch9.0ms

end0.0ms

sample12.6s

Algorithm

halfpoints

Results