Details

sample381.0ms

Algorithm

intervals

Results

178.0ms	87×	body	1280	valid
76.0ms	57×	body	640	valid
69.0ms	86×	body	80	valid
17.0ms	19×	body	320	valid
4.0ms	7×	body	160	valid

simplify44.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

136.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
85.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms	(- 3.0 (sqrt 5.0))
17.0ms	(- (cos x) (cos y))

series364.0ms

Counts

4 → 10

Calls

4 calls:

169.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
119.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
76.0ms	(- (cos x) (cos y))

simplify63.0ms

Counts: 104 → 104

prune859.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b	(- (cos x) (cos y))

rewrite637.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
14×	`associate-*r/`
12×	`associate-r`
11×	`pow1`
10×	`add-cube-cbrt`
8×	`flip3--` `flip--`
7×	`associate-l`
6×	`add-log-exp`
5×	`sub-neg` `times-frac` `prod-exp` `cbrt-unprod` `difference-of-squares`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `associate-*l/` `sqrt-prod` `associate-/r/`
3×	`flip3-+` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `div-exp` `frac-add` `*-commutative` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/r*` `div-inv` `diff-cos`

Counts

4 → 106

Calls

4 calls:

94.0ms	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
154.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
373.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms	(- (cos x) (cos y))

series2.9s

Counts

4 → 12

Calls

4 calls:

2.5s	(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (+ (* 3.0 3.0) (- 5.0)) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
197.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
127.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
77.0ms	(- (cos x) (cos y))

simplify112.0ms

Counts: 118 → 118

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`sub-neg` `difference-of-squares`
4×	`flip3--` `sqrt-prod` `flip--` `distribute-lft-out--`
3×	`diff-log` `diff-cos`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `unswap-sqr`
1×	`times-frac` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

61.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms	(- (cos x) (cos y))
12.0ms	(- (cos x) (cos y))
13.0ms	(- (cos x) (cos y))

series343.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
70.0ms	(- (cos x) (cos y))
68.0ms	(- (cos x) (cos y))
69.0ms	(- (cos x) (cos y))

simplify84.0ms

Counts: 88 → 88

prune864.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

1.0b	(- 3.0 (sqrt 5.0))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))
1.7b	(- (cos x) (cos y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`diff-cos`
1×	`sqrt-prod`

Counts

4 → 60

Calls

4 calls:

18.0ms	(- 3.0 (sqrt 5.0))
12.0ms	(- (cos x) (cos y))
12.0ms	(- (cos x) (cos y))
12.0ms	(- (cos x) (cos y))

series196.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(- 3.0 (sqrt 5.0))
68.0ms	(- (cos x) (cos y))
68.0ms	(- (cos x) (cos y))
59.0ms	(- (cos x) (cos y))

simplify94.0ms

Counts: 70 → 70

prune649.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes340.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify68.0ms

end0.0ms

sample14.3s

Algorithm

intervals

Results

8.1s	2746×	body	1280	valid
3.4s	1824×	body	640	valid
1.2s	809×	body	320	valid
867.0ms	2278×	body	80	valid
237.0ms	343×	body	160	valid