Details

sample116.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	valid
43.0ms	219×	body	80	nan

simplify82.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

82.0ms

(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ PI 3/2)
1.0b	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
1.0b	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
1.0b	(/ (acos (/ (- g) h)) 3)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r` `div-sub` `associate-/l` `add-log-exp`
4×	`pow1` `associate-+l-` `insert-posit16`
3×	`acos-asin` `acos-neg` `distribute-frac-neg`
2×	`cos-diff` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `distribute-lft-out`
1×	`+-commutative` `cos-sum` `sum-log` `flip3-+` `frac-add` `flip-+`

Counts

4 → 86

Calls

4 calls:

Slowest

25.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
21.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
5.0ms	(/ (acos (/ (- g) h)) 3)
4.0ms	(/ PI 3/2)

series183.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

134.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
37.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
12.0ms	(/ (acos (/ (- g) h)) 3)
0.0ms	(/ PI 3/2)

simplify2.0s

Counts

71 → 96

Calls

71 calls:

Slowest

203.0ms	(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
202.0ms	(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
97.0ms	(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
80.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
76.0ms	(/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (* (cbrt 3) (cbrt 3)))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

57.3b	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
1.0b	(sin (/ PI 3))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp` `difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `distribute-lft-out--`
3×	`sub-neg`
2×	`associate--l-` `acos-asin` `cos-sum` `flip3--` `diff-log` `div-sub` `frac-sub` `flip--`
1×	`cos-diff` `sin-PI/3`

Counts

4 → 62

Calls

4 calls:

Slowest

24.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
21.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
13.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
5.0ms	(sin (/ PI 3))

series285.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

180.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
55.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
49.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms	(sin (/ PI 3))

simplify1.4s

Counts

44 → 72

Calls

44 calls:

Slowest

253.0ms	(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
87.0ms	(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
85.0ms	(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
46.0ms	(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
46.0ms	(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

57.3b	(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
1.0b	(sin (/ PI 3))
1.0b	(/ PI 3/2)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `insert-posit16` `difference-of-squares`
3×	`cos-sum` `associate-/r` `associate-/l`
2×	`sub-neg` `div-sub` `distribute-lft-out--`
1×	`associate--l-` `acos-asin` `cos-diff` `cbrt-undiv` `asin-acos` `clear-num` `sin-PI/3` `frac-2neg` `flip3--` `diff-log` `div-exp` `frac-sub` `associate-+l-` `div-inv` `flip--` `associate--r-`

Counts

4 → 70

Calls

4 calls:

Slowest

86.0ms	(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
25.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
8.0ms	(/ PI 3/2)
6.0ms	(sin (/ PI 3))

series235.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

177.0ms	(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
58.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms	(sin (/ PI 3))
0.0ms	(/ PI 3/2)

simplify2.1s

Counts

52 → 78

Calls

52 calls:

Slowest

315.0ms	(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
296.0ms	(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
191.0ms	(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
137.0ms	(* (cos (/ PI 6)) (cos (- (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))
103.0ms	(* (cos (/ PI 6)) (cos (- (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2))
1.0b	(+ (* (acos (/ (- g) h)) 3/2) (* 3 PI))
0.0b	(* (acos (/ (- g) h)) 3/2)
0.0b	(/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `associate-r` `associate-l` `associate-/l`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

Slowest

49.0ms	(/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2)
15.0ms	(+ (* (acos (/ (- g) h)) 3/2) (* 3 PI))
11.0ms	(cos (/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2))
11.0ms	(* (acos (/ (- g) h)) 3/2)

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

177.0ms	(cos (/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2))
55.0ms	(/ (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) 9/2)
42.0ms	(+ (* (acos (/ (- g) h)) 3/2) (* 3 PI))
15.0ms	(* (acos (/ (- g) h)) 3/2)

simplify2.9s

Counts

48 → 81

Calls

48 calls:

Slowest

449.0ms	(- (* (* (acos (/ (- g) h)) 3/2) (* (acos (/ (- g) h)) 3/2)) (* (* 3 PI) (* 3 PI)))
268.0ms	(* (exp (* (acos (/ (- g) h)) 3/2)) (exp (* 3 PI)))
204.0ms	(+ (pow (* (acos (/ (- g) h)) 3/2) 3) (pow (* 3 PI) 3))
191.0ms	(/ (* (* (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI)) (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI))) (+ (* (acos (/ (- g) h)) 3/2) (* 3 PI))) (* (* 9/2 9/2) 9/2))
157.0ms	(* (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3/2 3/2) 3/2))

prune845.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes185.0ms

Accuracy

0% (0.0b remaining)

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

bsearch10.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	7794×	body	80	nan
1.9s	8000×	body	80	valid