Details

Time bar (total: 11.4s)

sample141.0ms

Algorithm
intervals
Results
65.0ms256×body80nan
54.0ms256×body80valid

simplify43.0ms

Calls
1 calls:
Slowest
43.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ PI 3/2)
1.0b
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
1.0b
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
0.9b
(/ (acos (/ (- g) h)) 3)

rewrite39.0ms

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
18.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
12.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
7.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

series206.0ms

Calls
4 calls:
Slowest
133.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
52.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
21.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify886.0ms

Calls
23 calls:
Slowest
87.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
84.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
65.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
62.0ms
(* 1/3 (acos (* -1 (/ g h))))
62.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune738.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

55.3b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(/ PI 3)
1.0b
(/ PI 3/2)

rewrite19.0ms

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
14.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
3.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3)
0.0ms
(/ PI 3/2)

series166.0ms

Calls
4 calls:
Slowest
166.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3)
0.0ms
(/ PI 3/2)

simplify917.0ms

Calls
10 calls:
Slowest
242.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
236.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
236.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
52.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
40.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune681.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

55.3b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(/ PI 3/2)
1.0b
(/ PI 3/2)
1.0b
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))

rewrite24.0ms

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
Calls
4 calls:
Slowest
14.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
9.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3/2)

series135.0ms

Calls
4 calls:
Slowest
134.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(/ PI 3/2)
0.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
0.0ms
(/ PI 3/2)

simplify220.0ms

Calls
6 calls:
Slowest
50.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
47.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
47.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
27.0ms
(* (cos (/ (acos (/ g h)) 3)) (cos (- (/ PI 3/2))))
25.0ms
(* (cos (/ (acos (/ g h)) 3)) (cos (- (/ PI 3/2))))

prune780.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

58.3b
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
1.6b
(cos (/ PI 3/2))
1.0b
(sin (/ PI 3/2))
1.0b
(/ PI 3/2)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×+-commutative clear-num sum-log frac-2neg flip3-+ frac-add cos-mult flip-+ div-inv sin-mult
Calls
4 calls:
Slowest
11.0ms
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
2.0ms
(cos (/ PI 3/2))
1.0ms
(sin (/ PI 3/2))
0.0ms
(/ PI 3/2)

series475.0ms

Calls
4 calls:
Slowest
475.0ms
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
0.0ms
(cos (/ PI 3/2))
0.0ms
(sin (/ PI 3/2))
0.0ms
(/ PI 3/2)

simplify647.0ms

Calls
9 calls:
Slowest
437.0ms
(+ (* (+ (cos (+ (/ (acos (/ g h)) 3) (/ PI 3/2))) (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))) 2) (* 2 (- (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) (cos (+ (/ (acos (/ g h)) 3) (/ PI 3/2))))))
60.0ms
(* (exp (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2)))) (exp (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2)))))
29.0ms
(+ (* (cos (* 2/3 PI)) (cos (* 1/3 (acos (/ g h))))) (* (sin (* 1/3 (acos (/ g h)))) (sin (* 2/3 PI))))
28.0ms
(+ (* (cos (* 2/3 PI)) (cos (* 1/3 (acos (/ g h))))) (* (sin (* 1/3 (acos (/ g h)))) (sin (* 2/3 PI))))
28.0ms
(+ (* (cos (* 2/3 PI)) (cos (* 1/3 (acos (/ g h))))) (* (sin (* 1/3 (acos (/ g h)))) (sin (* 2/3 PI))))

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes86.0ms

Accuracy

0% (0.0b remaining)

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

bsearch6.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.0s8000×body80valid
1.6s7987×body80nan