Details

sample108.0ms

Algorithm

intervals

Results

51.0ms	256×	body	80	valid
39.0ms	226×	body	80	nan

simplify38.0ms

Calls

1 calls:

Slowest

38.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize40.0ms

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)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

15.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
6.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
4.0ms	(/ (acos (/ (- g) h)) 3)
0.0ms	(/ PI 3/2)

series144.0ms

Calls

4 calls:

Slowest

109.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
23.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
12.0ms	(/ (acos (/ (- g) h)) 3)
0.0ms	(/ PI 3/2)

simplify941.0ms

Calls

23 calls:

Slowest

106.0ms	(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
78.0ms	(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
71.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
66.0ms	(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
65.0ms	(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune699.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

57.5b	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b	(sin (/ PI 3))
1.0b	(/ PI 3)
1.0b	(/ PI 3/2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
2×	`cos-sum` `clear-num` `frac-2neg` `div-inv`
1×	`cos-diff` `sub-neg` `sin-PI/3`

Calls

4 calls:

Slowest

19.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
3.0ms	(sin (/ PI 3))
0.0ms	(/ PI 3)
0.0ms	(/ PI 3/2)

series81.0ms

Calls

4 calls:

Slowest

81.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms	(sin (/ PI 3))
0.0ms	(/ PI 3/2)
0.0ms	(/ PI 3)

simplify1.3s

Calls

10 calls:

Slowest

403.0ms	(* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2)))
246.0ms	(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
242.0ms	(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
213.0ms	(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
50.0ms	(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune692.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ PI 3/2) (/ PI 3/2))
1.0b	(/ PI 3/2)
1.0b	(/ PI 3/2)
1.0b	(/ PI 3/2)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`div-inv`
4×	`associate-r` `associate-l` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `pow-prod-up` `cbrt-unprod`

Calls

4 calls:

Slowest

7.0ms	(* (/ PI 3/2) (/ PI 3/2))
0.0ms	(/ PI 3/2)
0.0ms	(/ PI 3/2)
0.0ms	(/ PI 3/2)

series0.0ms

Calls

4 calls:

Slowest

0.0ms	(* (/ PI 3/2) (/ PI 3/2))
0.0ms	(/ PI 3/2)
0.0ms	(/ PI 3/2)
0.0ms	(/ PI 3/2)

simplify316.0ms

Calls

15 calls:

Slowest

169.0ms	(* (* (* (/ PI 3/2) (/ PI 3/2)) (/ PI 3/2)) (* (* (/ PI 3/2) (/ PI 3/2)) (/ PI 3/2)))
43.0ms	(+ (log (/ PI 3/2)) (log (/ PI 3/2)))
28.0ms	(* (/ PI 3/2) (/ PI 3/2))
10.0ms	(/ PI 3/2)
10.0ms	(* PI (/ PI 3/2))

prune798.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.6b	(cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2)))
1.0b	(/ PI 3/2)
1.0b	(/ PI 3/2)
1.0b	(/ (/ PI 2) 3)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`cos-sum`
1×	`cos-diff` `sub-neg` `associate-/l/`

Calls

4 calls:

Slowest

25.0ms	(cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2)))
6.0ms	(/ (/ PI 2) 3)
1.0ms	(/ PI 3/2)
0.0ms	(/ PI 3/2)

series87.0ms

Calls

4 calls:

Slowest

87.0ms	(cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2)))
0.0ms	(/ PI 3/2)
0.0ms	(/ (/ PI 2) 3)
0.0ms	(/ PI 3/2)

simplify641.0ms

Calls

11 calls:

Slowest

105.0ms	(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
101.0ms	(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
93.0ms	(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
84.0ms	(cos (- (* 1/3 (asin (* -1 (/ g h)))) (* 2/3 PI)))
78.0ms	(cos (- (* 1/3 (asin (* -1 (/ g h)))) (* 2/3 PI)))

prune765.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes330.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch12.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.7s	8052×	body	80	nan