Details

sample613.0ms

Algorithm

halfpoints

Results

simplify198.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

198.0ms

(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: 44.2b

localize143.0ms

Local error

Found 4 expressions with local error:

58.0b	(- (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)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
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 → 103

Calls

4 calls:

Slowest

57.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
50.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
19.0ms	(+ (exp x) (exp (- x)))
11.0ms	(- (exp x) (exp (- x)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

89.0ms	(* (/ (- (exp x) (exp (- x))) 2) (sin y))
76.0ms	(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
63.0ms	(- (exp x) (exp (- x)))
43.0ms	(+ (exp x) (exp (- x)))

simplify5.4s

Counts

77 → 115

Calls

77 calls:

Slowest

868.0ms	(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
419.0ms	(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
249.0ms	(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
223.0ms	(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
217.0ms	(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize120.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 x)
0.1b	(* x (* 1/3 x))
0.1b	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
0.0b	(* (pow x 5) 1/60)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`associate-l`
21×	`add-exp-log`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
13×	`pow1`
10×	`times-frac` `associate-r`
9×	`prod-exp`
7×	`cbrt-unprod`
6×	`unswap-sqr`
5×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`sqr-pow`
1×	`pow-to-exp` `cbrt-undiv` `div-exp` `associate-*l/` `pow-exp` `div-inv`

Counts

4 → 97

Calls

4 calls:

Slowest

73.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
25.0ms	(* x (* 1/3 x))
15.0ms	(* (pow x 5) 1/60)
11.0ms	(* 1/3 x)

series247.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
54.0ms	(* (pow x 5) 1/60)
41.0ms	(* x (* 1/3 x))
16.0ms	(* 1/3 x)

simplify8.6s

Counts

72 → 109

Calls

72 calls:

Slowest

589.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)
561.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
537.0ms	(* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* 2 2) 2)) (* (* (sin y) (sin y)) (sin y)))
515.0ms	(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
503.0ms	(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) 1)

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize146.0ms

Local error

Found 4 expressions with local error:

32.9b	(log (exp (* x (* 1/3 x))))
0.3b	(* 1/3 x)
0.1b	(* x (* 1/3 x))
0.1b	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-l`
16×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
14×	`pow1`
10×	`times-frac`
7×	`associate-r`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-prod-down` `add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `log-pow` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `exp-prod` `exp-to-pow` `div-exp` `rem-log-exp` `associate-*l/` `div-inv`

Counts

4 → 86

Calls

4 calls:

Slowest

49.0ms	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))
27.0ms	(* x (* 1/3 x))
5.0ms	(* 1/3 x)
5.0ms	(log (exp (* x (* 1/3 x))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

146.0ms	(* (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2) (sin y))
42.0ms	(* x (* 1/3 x))
38.0ms	(log (exp (* x (* 1/3 x))))
15.0ms	(* 1/3 x)

simplify7.8s

Counts

59 → 98

Calls

59 calls:

Slowest

743.0ms	(+ (log (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2)) (log (sin y)))
695.0ms	(* (/ (* (* (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (* (* 2 2) 2)) (* (* (sin y) (sin y)) (sin y)))
334.0ms	(* (cbrt (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2)) (cbrt (/ (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)) 2)))
315.0ms	(/ (* (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60)))) 1)
314.0ms	(+ (- (log (+ (* x (+ (log (exp (* x (* 1/3 x)))) 2)) (* (pow x 5) 1/60))) (log 2)) (log (sin y)))

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
51×	`add-sqr-sqrt` `add-exp-log`
49×	`*-un-lft-identity` `add-cube-cbrt`
33×	`sqrt-prod`
31×	`add-cbrt-cube`
25×	`associate-l`
21×	`prod-exp`
13×	`pow1` `div-exp`
12×	`associate-/r*`
11×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/` `div-inv` `pow-flip`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

Slowest

93.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
80.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
11.0ms	(/ 1 (sqrt 2))
5.0ms	(* 1/3 x)

series422.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

254.0ms	(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
142.0ms	(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
25.0ms	(* 1/3 x)
0.0ms	(/ 1 (sqrt 2))

simplify25.4s

Counts

162 → 172

Calls

162 calls:

Slowest

1.4s	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
1.0s	(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
758.0ms	(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
640.0ms	(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))
628.0ms	(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))

prune3.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (0.7b remaining)

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

bsearch6.0ms

end0.0ms

sample11.7s

Algorithm

halfpoints

Results