Details

sample422.0ms

Algorithm

halfpoints

Results

simplify200.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

200.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.0b

localize100.0ms

Local error

Found 3 expressions with local error:

57.4b	(- (exp x) (exp (- x)))
0.1b	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite133.0ms

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

54.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
54.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
21.0ms	(- (exp x) (exp (- x)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

145.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
86.0ms	(- (exp x) (exp (- x)))
73.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify7.1s

Counts

92 → 117

Calls

92 calls:

Slowest

762.0ms	(* (* (* (/ (- (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)))
348.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
273.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
246.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize92.0ms

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	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b	(fma 1/3 (* x x) 2)
0.0b	(* x (fma 1/3 (* x x) 2))

rewrite83.0ms

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`

Counts

4 → 107

Calls

4 calls:

Slowest

63.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
12.0ms	(* (/ (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)

series787.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

482.0ms	(* x (fma 1/3 (* x x) 2))
128.0ms	(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
104.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
74.0ms	(fma 1/3 (* x x) 2)

simplify10.1s

Counts

77 → 119

Calls

77 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)))
534.0ms	(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
487.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
463.0ms	(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
460.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize134.0ms

Local error

Found 4 expressions with local error:

0.4b	(* x (sqrt (fma 1/3 (* x x) 2)))
0.4b	(* (* x (sqrt (fma 1/3 (* x x) 2))) (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	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
33×	`associate-l`
32×	`*-un-lft-identity`
26×	`add-cube-cbrt`
23×	`times-frac`
21×	`add-cbrt-cube` `add-exp-log`
18×	`associate-r`
15×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`sqrt-prod`
6×	`pow-prod-down` `unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 122

Calls

4 calls:

Slowest

49.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
20.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
20.0ms	(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
18.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

168.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))
113.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
107.0ms	(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
73.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify9.3s

Counts

92 → 134

Calls

92 calls:

Slowest

559.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
467.0ms	(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
338.0ms	(* (* (* x x) x) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
254.0ms	(+ (* 1/120 (* (pow x 5) (sin y))) (* 1/6 (* (pow x 3) (sin y))))
253.0ms	(/ (* (cbrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (cbrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))))) 1)

prune2.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize140.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt 2))
0.5b	(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))
0.4b	(* x (sqrt (fma 1/3 (* x x) 2)))
0.4b	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
36×	`times-frac`
31×	`sqrt-prod`
17×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`pow1`
12×	`associate-/r` `associate-r*`
6×	`associate-/l*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `pow-flip`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `*-commutative` `div-inv` `unswap-sqr`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 139

Calls

4 calls:

Slowest

29.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
7.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))
5.0ms	(/ 1 (sqrt 2))
5.0ms	(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))

series465.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

175.0ms	(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))
155.0ms	(* x (sqrt (fma 1/3 (* x x) 2)))
135.0ms	(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
0.0ms	(/ 1 (sqrt 2))

simplify10.5s

Counts

133 → 149

Calls

133 calls:

Slowest

652.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (sqrt (sqrt 2)))
561.0ms	(/ (* (* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt 2) (sqrt 2)) (sqrt 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))))
235.0ms	(- (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))) (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))))
233.0ms	(/ (sqrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) 1)

prune3.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes249.0ms

Accuracy

0% (0.7b remaining)

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

bsearch7.0ms

end0.0ms

sample11.8s

Algorithm

halfpoints

Results