Details

sample520.0ms

Algorithm

halfpoints

Results

simplify166.0ms

Calls

1 calls:

Slowest

165.0ms

(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: 43.7b

localize113.0ms

Local error

Found 3 expressions with local error:

58.1b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite60.0ms

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

27.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
21.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
11.0ms	(- (exp x) (exp (- x)))

series188.0ms

Calls

3 calls:

Slowest

90.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
49.0ms	(- (exp x) (exp (- x)))
48.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify3.9s

Calls

53 calls:

Slowest

698.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
387.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
207.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
178.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
169.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune1.1s

Pruning

2 alts after pruning (2 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))

rewrite34.0ms

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

23.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
6.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
3.0ms	(* (fma 1/3 (* x x) 2) x)
0.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

series230.0ms

Calls

4 calls:

Slowest

95.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
70.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
33.0ms	(* (fma 1/3 (* x x) 2) x)
31.0ms	(fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x))

simplify3.3s

Calls

34 calls:

Slowest

447.0ms	(+ (log (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2)) (log (sin y)))
326.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
241.0ms	(* (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (sin y))
214.0ms	(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
179.0ms	(* (* (* (/ (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)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fma 1/3 (* x x) 2)) x)
0.4b	(* (sqrt (fma 1/3 (* x x) 2)) (* (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))

rewrite47.0ms

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

23.0ms	(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
13.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
7.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)
2.0ms	(sqrt (fma 1/3 (* x x) 2))

series212.0ms

Calls

4 calls:

Slowest

79.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
59.0ms	(* (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))
36.0ms	(sqrt (fma 1/3 (* x x) 2))

simplify5.0s

Calls

39 calls:

Slowest

636.0ms	(* (* (* (/ (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)))
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)))
438.0ms	(- (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))) (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))))
386.0ms	(- (+ (sqrt 2) (* 1/6 (/ (pow x 2) (sqrt 2)))) (* 1/72 (/ (pow x 4) (pow (sqrt 2) 3))))
339.0ms	(- (* 1/2 (/ 1 (* (pow x 3) (pow (sqrt 1/3) 3)))) (+ (* x (sqrt 1/3)) (/ 1 (* x (sqrt 1/3)))))

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

47.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))
11.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))
11.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) 2) (sin y))
5.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)

series420.0ms

Calls

4 calls:

Slowest

211.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x))
94.0ms	(* (/ (fma 1/60 (pow x 5) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) 2) (sin y))
62.0ms	(* (sqrt (fma 1/3 (* x x) 2)) x)
53.0ms	(* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))

simplify5.2s

Calls

53 calls:

Slowest

466.0ms	(* (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (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)))
324.0ms	(- (+ (* 1/8 (* (pow x 3) (pow 8 1/4))) (* x (pow 8 1/4))) (* 1/384 (* (pow x 5) (pow 8 1/4))))
323.0ms	(- (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))))
272.0ms	(- (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))) (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))))
269.0ms	(* (fma 1/60 (pow x 5) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (* (sqrt (fma 1/3 (* x x) 2)) x)))) (sin y))

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

0% (0.7b remaining)

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

bsearch5.0ms

end1.0ms

sample12.4s

Algorithm

halfpoints

Results