Details

sample577.0ms

Algorithm

halfpoints

Results

simplify167.0ms

Calls

1 calls:

Slowest

167.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize83.0ms

Local error

Found 3 expressions with local error:

58.4b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Calls

3 calls:

Slowest

54.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
47.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
23.0ms	(- (exp x) (exp (- x)))

series252.0ms

Calls

3 calls:

Slowest

113.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
95.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
44.0ms	(- (exp x) (exp (- x)))

simplify7.4s

Calls

92 calls:

Slowest

803.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
484.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
320.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
283.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
277.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize133.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`associate-l`
29×	`*-un-lft-identity`
23×	`times-frac` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-r`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative` `fma-udef` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in`

Calls

4 calls:

Slowest

53.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
20.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
11.0ms	(* x (fma 1/3 (* x x) 2))
0.0ms	(fma 1/3 (* x x) 2)

series409.0ms

Calls

4 calls:

Slowest

146.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
121.0ms	(* x (fma 1/3 (* x x) 2))
76.0ms	(fma 1/3 (* x x) 2)
66.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify10.4s

Calls

77 calls:

Slowest

761.0ms	(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
506.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
500.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
474.0ms	(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))
453.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize177.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt 2))
0.4b	(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.3b	(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
0.2b	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Calls

4 calls:

Slowest

56.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
14.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
10.0ms	(/ 1 (sqrt 2))
9.0ms	(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))

series703.0ms

Calls

4 calls:

Slowest

269.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
253.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
181.0ms	(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms	(/ 1 (sqrt 2))

simplify29.1s

Calls

187 calls:

Slowest

753.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
649.0ms	(/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
645.0ms	(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
594.0ms	(/ (* (cbrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (cbrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
533.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

prune4.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize157.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
0.1b	(/ 2 (sin y))
0.0b	(* x (fma 1/3 (* x x) 2))
0.0b	(fma 1/3 (* x x) 2)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `fma-udef`
2×	`clear-num` `frac-2neg`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Calls

4 calls:

Slowest

7.0ms	(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
6.0ms	(* x (fma 1/3 (* x x) 2))
5.0ms	(/ 2 (sin y))
0.0ms	(fma 1/3 (* x x) 2)

series422.0ms

Calls

4 calls:

Slowest

168.0ms	(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
147.0ms	(* x (fma 1/3 (* x x) 2))
79.0ms	(fma 1/3 (* x x) 2)
27.0ms	(/ 2 (sin y))

simplify23.5s

Calls

147 calls:

Slowest

782.0ms	(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
618.0ms	(/ (sqrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (cbrt (sin y))))
517.0ms	(* (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))))
510.0ms	(/ (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))
483.0ms	(/ (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))

prune2.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes152.0ms

Accuracy

0% (0.9b remaining)

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

bsearch4.0ms

end0.0ms

sample12.3s

Algorithm

halfpoints

Results