Details

Time bar (total: 16.1s)

sample123.0ms

Algorithm
intervals
Results
59.0ms256×body80valid
45.0ms249×body80nan

simplify40.0ms

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

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize21.0ms

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)

rewrite72.0ms

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-+
Calls
4 calls:
Slowest
32.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
25.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
9.0ms
(/ (acos (/ (- g) h)) 3)
4.0ms
(/ PI 3/2)

series216.0ms

Calls
4 calls:
Slowest
149.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
45.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
22.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify2.1s

Calls
71 calls:
Slowest
269.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
245.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
109.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
74.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
74.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))

prune900.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

56.8b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(/ PI 3)
1.0b
(/ PI 3/2)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
4×pow1 insert-posit16 add-log-exp
2×cbrt-undiv cos-sum clear-num frac-2neg div-exp div-inv
1×cos-diff sub-neg sin-PI/3
Calls
4 calls:
Slowest
35.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
7.0ms
(/ PI 3/2)
7.0ms
(/ PI 3)
5.0ms
(sin (/ PI 3))

series151.0ms

Calls
4 calls:
Slowest
151.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(/ PI 3)
0.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3/2)

simplify1.7s

Calls
58 calls:
Slowest
249.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
222.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
216.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
213.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
209.0ms
(/ (* (* PI PI) PI) (* (* 3 3) 3))

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

56.8b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(/ PI (* (cbrt 3/2) (cbrt 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(cbrt 3/2)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log
7×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
4×pow1 insert-posit16 add-log-exp
3×cbrt-prod times-frac associate-/l*
2×cbrt-undiv cos-sum div-exp
1×cos-diff clear-num associate-/r* sub-neg sin-PI/3 frac-2neg pow1/3 prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
18.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
13.0ms
(/ PI (* (cbrt 3/2) (cbrt 3/2)))
5.0ms
(sin (/ PI 3))
1.0ms
(cbrt 3/2)

series168.0ms

Calls
4 calls:
Slowest
167.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(/ PI (* (cbrt 3/2) (cbrt 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(cbrt 3/2)

simplify1.1s

Calls
26 calls:
Slowest
539.0ms
(/ (* (* PI PI) PI) (* (* (* (cbrt 3/2) (cbrt 3/2)) (* (cbrt 3/2) (cbrt 3/2))) (* (cbrt 3/2) (cbrt 3/2))))
120.0ms
(/ (* (* PI PI) PI) (* 3/2 3/2))
69.0ms
(- (log PI) (+ (log (cbrt 3/2)) (log (cbrt 3/2))))
56.0ms
(- (log PI) (log (* (cbrt 3/2) (cbrt 3/2))))
45.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

56.8b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(sin (/ (/ PI (sqrt 3)) (sqrt 3)))
1.0b
(/ PI 3/2)
1.0b
(/ PI 3/2)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
4×pow1 insert-posit16 add-log-exp
2×cbrt-undiv cos-sum clear-num frac-2neg div-exp div-inv
1×cos-diff sub-neg
Calls
4 calls:
Slowest
34.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
6.0ms
(sin (/ (/ PI (sqrt 3)) (sqrt 3)))
4.0ms
(/ PI 3/2)
3.0ms
(/ PI 3/2)

series127.0ms

Calls
4 calls:
Slowest
126.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(sin (/ (/ PI (sqrt 3)) (sqrt 3)))
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3/2)

simplify1.2s

Calls
57 calls:
Slowest
275.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
242.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
60.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))
46.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
43.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes350.0ms

Accuracy

0% (0.1b remaining)

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

bsearch10.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.8s7962×body80nan
1.7s8000×body80valid