Details

sample496.0ms

Algorithm

halfpoints

Results

simplify606.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

606.0ms

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize95.0ms

Local error

Found 3 expressions with local error:

58.5b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite128.0ms

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--`

Counts

3 → 108

Calls

3 calls:

Slowest

57.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
55.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
14.0ms	(- (exp x) (exp (- x)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

123.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
85.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
55.0ms	(- (exp x) (exp (- x)))

simplify6.8s

Counts

92 → 117

Calls

92 calls:

Slowest

703.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
375.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
283.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
272.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
225.0ms	(* (/ (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))) (* (* 2 2) 2)) (* (* (cos y) (cos y)) (cos y)))

prune1.6s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize118.0ms

Local error

Found 2 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `associate-l`
25×	`*-un-lft-identity`
23×	`times-frac`
19×	`add-cube-cbrt`
12×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-r`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`distribute-lft-out`
2×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

2 → 73

Calls

2 calls:

Slowest

47.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
34.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))

series225.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

148.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
77.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify8.3s

Counts

59 → 79

Calls

59 calls:

Slowest

527.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
516.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
484.0ms	(* (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)))
464.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
448.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize136.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt 2))
0.5b	(/ (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)))
0.3b	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite103.0ms

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`

Counts

4 → 192

Calls

4 calls:

Slowest

54.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
24.0ms	(* (/ (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))

series710.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

304.0ms	(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
223.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
183.0ms	(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms	(/ 1 (sqrt 2))

simplify28.5s

Counts

187 → 202

Calls

187 calls:

Slowest

844.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))
744.0ms	(* (/ (* (* 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))))
667.0ms	(/ (* (* (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)))
559.0ms	(* (* (* (/ 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))))
536.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))

prune4.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize179.0ms

Local error

Found 3 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	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
68×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
16×	`associate-/r` `associate-l*`
15×	`add-cbrt-cube` `add-exp-log`
7×	`div-inv`
6×	`associate-/l*`
5×	`pow1` `cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative`

Counts

3 → 141

Calls

3 calls:

Slowest

66.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
14.0ms	(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
9.0ms	(/ 2 (sin y))

series210.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

119.0ms	(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
77.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
15.0ms	(/ 2 (sin y))

simplify23.2s

Counts

160 → 150

Calls

160 calls:

Slowest

526.0ms	(/ (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))
505.0ms	(/ (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ (sqrt 2) (cbrt (sin y))))
499.0ms	(/ (sqrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (sqrt (/ 2 (sin y))))
491.0ms	(/ (* (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))))) (/ 1 1))
480.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes207.0ms

Accuracy

0% (0.8b remaining)

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

bsearch8.0ms

end0.0ms

sample12.0s

Algorithm

halfpoints

Results