Details

sample485.0ms

Algorithm

halfpoints

Results

simplify193.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

193.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.2b

localize116.0ms

Local error

Found 4 expressions with local error:

56.9b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b	(+ (exp x) (exp (- x)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

Slowest

62.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
52.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
26.0ms	(- (exp x) (exp (- x)))
10.0ms	(+ (exp x) (exp (- x)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
101.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
66.0ms	(- (exp x) (exp (- x)))
43.0ms	(+ (exp x) (exp (- x)))

simplify7.4s

Counts

99 → 138

Calls

99 calls:

Slowest

805.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
443.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
281.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
272.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
272.0ms	(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize107.0ms

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-prod-down` `*-commutative`
1×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 80

Calls

4 calls:

Slowest

19.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
6.0ms	(* x (fma 1/3 (* x x) 2))
0.0ms	(fma 1/3 (* x x) 2)
0.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

162.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
139.0ms	(* x (fma 1/3 (* x x) 2))
102.0ms	(fma 1/3 (* x x) 2)
100.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

simplify8.7s

Counts

49 → 92

Calls

49 calls:

Slowest

732.0ms	(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
530.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
455.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
455.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
453.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
21×	`add-sqr-sqrt`
20×	`pow1`
17×	`-un-lft-identity` `associate-l*`
15×	`add-cube-cbrt`
11×	`prod-exp` `cbrt-unprod`
10×	`times-frac` `pow-prod-down`
7×	`associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `div-exp` `associate-*l/` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

Slowest

42.0ms	(* (* 1/3 (* x x)) x)
23.0ms	(* 1/3 (* x x))
12.0ms	(* (/ (fma 1/60 (pow x 5) (+ (* (* 1/3 (* x x)) x) (* 2 x))) 2) (sin y))
10.0ms	(+ (exp x) (exp (- x)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(* (/ (fma 1/60 (pow x 5) (+ (* (* 1/3 (* x x)) x) (* 2 x))) 2) (sin y))
69.0ms	(* (* 1/3 (* x x)) x)
54.0ms	(* 1/3 (* x x))
26.0ms	(+ (exp x) (exp (- x)))

simplify10.7s

Counts

62 → 111

Calls

62 calls:

Slowest

874.0ms	(* (* (* (* 1/3 1/3) 1/3) (* (* (* x x) x) (* (* x x) x))) (* (* x x) x))
635.0ms	(* (* (* 1/3 1/3) 1/3) (* (* (* x x) x) (* (* x x) x)))
548.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (+ (* (* 1/3 (* x x)) x) (* 2 x))) 2)) (sqrt (sin y)))
539.0ms	(* (* (* (* 1/3 (* x x)) (* 1/3 (* x x))) (* 1/3 (* x x))) (* (* x x) x))
503.0ms	(/ (sqrt (fma 1/60 (pow x 5) (+ (* (* 1/3 (* x x)) x) (* 2 x)))) (* (cbrt 2) (cbrt 2)))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
13×	`pow1`
10×	`times-frac`
7×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
1×	`cbrt-undiv` `div-exp` `associate-*l/` `fma-udef` `div-inv`

Counts

4 → 95

Calls

4 calls:

Slowest

51.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
12.0ms	(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
9.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))
0.0ms	(fma 1/3 (* x x) 2)

series515.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))
141.0ms	(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
121.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
76.0ms	(fma 1/3 (* x x) 2)

simplify7.0s

Counts

64 → 107

Calls

64 calls:

Slowest

475.0ms	(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
311.0ms	(* (* (* x x) x) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
310.0ms	(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))
262.0ms	(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
243.0ms	(+ (- (log (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (log 2)) (log (sin y)))

prune2.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch9.0ms

end0.0ms

sample12.5s

Algorithm

halfpoints

Results