Details

Time bar (total: 18.0s)

sample118.0ms

Algorithm
intervals
Results
49.0ms256×body80valid
47.0ms256×body80nan

simplify69.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune9.0ms

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)

rewrite40.0ms

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
15.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
15.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
5.0ms
(/ (acos (/ (- g) h)) 3)
4.0ms
(/ PI 3/2)

series195.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
125.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
51.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
19.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify1.9s

Counts
71 → 96
Calls
71 calls:
Slowest
224.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
213.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
125.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
83.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
74.0ms
(/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (* (cbrt 3) (cbrt 3)))

prune927.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

57.4b
(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))

rewrite61.0ms

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
22.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
21.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
14.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
3.0ms
(sin (/ PI 3))

series267.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
168.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
51.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
48.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms
(sin (/ PI 3))

simplify1.5s

Counts
44 → 72
Calls
44 calls:
Slowest
267.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
75.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
59.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
53.0ms
(- (/ (sqrt (acos (/ g h))) (sqrt 3)) (/ (sqrt PI) (sqrt 3/2)))
49.0ms
(- (/ (sqrt (acos (/ g h))) (sqrt 3)) (/ (sqrt PI) (sqrt 3/2)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

61.5b
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
1.0b
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
1.0b
(/ PI 3/2)
1.0b
(sin (/ PI 3))

rewrite63.0ms

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×associate-/r* associate-/l*
2×div-sub distribute-lft-out--
1×associate--l- acos-asin cos-diff cbrt-undiv clear-num sub-neg sin-PI/3 frac-2neg flip3-- diff-log div-exp frac-sub div-inv flip--
Counts
4 → 67
Calls
4 calls:
Slowest
35.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
14.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
7.0ms
(/ PI 3/2)
5.0ms
(sin (/ PI 3))

series229.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
175.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
53.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms
(/ PI 3/2)
0.0ms
(sin (/ PI 3))

simplify2.0s

Counts
49 → 75
Calls
49 calls:
Slowest
329.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
277.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
213.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
140.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))
117.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize112.0ms

Local error

Found 4 expressions with local error:

57.4b
(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)

rewrite121.0ms

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))))
18.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
9.0ms
(/ PI 3/2)
5.0ms
(sin (/ PI 3))

series221.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
157.0ms
(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
65.0ms
(- (/ (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
318.0ms
(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
295.0ms
(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
204.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
139.0ms
(* (cos (/ PI 6)) (cos (- (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))
110.0ms
(* (cos (/ PI 6)) (cos (- (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s8000×body80valid
1.7s8226×body80nan