Details

Time bar (total: 17.3s)

sample149.0ms

Algorithm
intervals
Results
71.0ms256×body80valid
55.0ms296×body80nan

simplify49.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
49.0ms
(* 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

localize41.0ms

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)))
1.0b
(/ (acos (/ (- g) h)) 3)

rewrite39.0ms

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
16.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
11.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
6.0ms
(/ PI 3/2)
5.0ms
(/ (acos (/ (- g) h)) 3)

series187.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
133.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
41.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
12.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify1.9s

Counts
71 → 96
Calls
71 calls:
Slowest
258.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
223.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
100.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
84.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
69.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

56.3b
(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))

rewrite80.0ms

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
39.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
23.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
15.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
3.0ms
(sin (/ PI 3))

series258.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
152.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
62.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
44.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms
(sin (/ PI 3))

simplify1.3s

Counts
44 → 72
Calls
44 calls:
Slowest
246.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
88.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
54.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
50.0ms
(- (sqrt (/ (acos (/ g h)) 3)) (/ (sqrt PI) (sqrt 3/2)))
46.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

60.3b
(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))

rewrite49.0ms

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
22.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
13.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
7.0ms
(/ PI 3/2)
6.0ms
(sin (/ PI 3))

series229.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
184.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
45.0ms
(- (/ (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
287.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
276.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
229.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
155.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))
137.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

60.3b
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
1.0b
(- (/ (acos (/ g h)) 3) (* (sqrt PI) (/ (sqrt PI) 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(sqrt PI)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-log-exp
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16
3×sqrt-prod
2×div-sub
1×associate--l- acos-asin cos-diff rem-sqrt-square sub-neg sin-PI/3 sqrt-pow1 flip3-- pow1/2 diff-log associate-*r/ frac-sub flip--
Counts
4 → 47
Calls
4 calls:
Slowest
17.0ms
(- (/ (acos (/ g h)) 3) (* (sqrt PI) (/ (sqrt PI) 3/2)))
7.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
5.0ms
(sin (/ PI 3))
1.0ms
(sqrt PI)

series225.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
171.0ms
(cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2))
54.0ms
(- (/ (acos (/ g h)) 3) (* (sqrt PI) (/ (sqrt PI) 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(sqrt PI)

simplify1.5s

Counts
18 → 55
Calls
18 calls:
Slowest
354.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (* (sqrt PI) (/ (sqrt PI) 3/2)))))) 2)
310.0ms
(* (+ (* (cos (/ (- (* (acos (/ g h)) 3/2) (* 3 PI)) 9/2)) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (* (sqrt PI) (/ (sqrt PI) 3/2)))))) 2)
215.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (* (sqrt PI) (/ (sqrt PI) 3/2))))
134.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))
107.0ms
(cos (* 2/9 (- (* 3/2 (acos (/ g h))) (* 3 PI))))

prune953.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes406.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s8043×body80nan
1.6s8000×body80valid