Details

sample425.0ms

Algorithm

halfpoints

Results

simplify209.0ms

Calls

1 calls:

Slowest

208.0ms

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.5b

localize119.0ms

Local error

Found 3 expressions with local error:

57.6b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(+ (exp x) (exp (- x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-log-exp`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`associate-l`
3×	`expm1-log1p-u` `fma-def` `fma-neg` `associate-r` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Calls

3 calls:

Slowest

19.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
11.0ms	(- (exp x) (exp (- x)))
5.0ms	(+ (exp x) (exp (- x)))

series161.0ms

Calls

3 calls:

Slowest

91.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
44.0ms	(- (exp x) (exp (- x)))
25.0ms	(+ (exp x) (exp (- x)))

simplify2.7s

Calls

47 calls:

Slowest

657.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
188.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
186.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
143.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
130.0ms	(+ (log (/ (- (exp x) (exp (- x))) 2)) (log (sin y)))

prune819.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

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)))
0.0b	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`associate-l`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `associate-r`
2×	`*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Calls

4 calls:

Slowest

6.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
5.0ms	(+ (exp x) (exp (- x)))
3.0ms	(* (fma 1/3 (* x x) 2) x)
0.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

series148.0ms

Calls

4 calls:

Slowest

64.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
34.0ms	(* (fma 1/3 (* x x) 2) x)
25.0ms	(+ (exp x) (exp (- x)))
24.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

simplify1.9s

Calls

28 calls:

Slowest

253.0ms	(* (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (sin y))
194.0ms	(* (* (* (/ (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)))
161.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
152.0ms	(+ (log (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2)) (log (sin y)))
123.0ms	(+ (* 1/120 (* (pow x 5) (sin y))) (* 1/6 (* (pow x 3) (sin y))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

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	(sqrt (fma 1/3 (* x x) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

11.0ms	(* (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)
1.0ms	(sqrt (fma 1/3 (* x x) 2))

series203.0ms

Calls

4 calls:

Slowest

75.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
58.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)
37.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
32.0ms	(sqrt (fma 1/3 (* x x) 2))

simplify5.5s

Calls

39 calls:

Slowest

702.0ms	(* (* (* (/ (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)))
561.0ms	(* (* (* (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)))
538.0ms	(- (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))) (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))))
439.0ms	(- (+ (sqrt 2) (* 1/6 (/ (pow x 2) (sqrt 2)))) (* 1/72 (/ (pow x 4) (pow (sqrt 2) 3))))
438.0ms	(- (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))) (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))))

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
0.4b	(* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))
0.4b	(* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x)
0.1b	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))) 2) (sin y))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod`
20×	`associate-l`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `associate-r`
10×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1/2` `pow-prod-down` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`pow-prod-up`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-*l/` `div-inv`

Calls

4 calls:

Slowest

50.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))
16.0ms	(* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x)
11.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
7.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))) 2) (sin y))

series634.0ms

Calls

4 calls:

Slowest

452.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))
79.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x))) 2) (sin y))
76.0ms	(* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) x)
27.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))

simplify5.1s

Calls

59 calls:

Slowest

477.0ms	(- (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))) (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))))
469.0ms	(- (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))) (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))))
447.0ms	(- (+ (sqrt 2) (* 1/6 (/ (pow x 2) (sqrt 2)))) (* 1/72 (/ (pow x 4) (pow (sqrt 2) 3))))
319.0ms	(- (+ (* 1/6 (/ (pow x 3) (sqrt 2))) (* (sqrt 2) x)) (* 1/72 (/ (pow x 5) (pow (sqrt 2) 3))))
271.0ms	(- (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))) (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))))

prune2.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch4.0ms

end0.0ms

sample11.9s

Algorithm

halfpoints

Results