Details

Time bar (total: 22.5s)

sample129.0ms

Algorithm
intervals
Results
54.0ms256×body80valid
50.0ms251×body80nan

simplify73.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
73.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize45.0ms

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)

rewrite59.0ms

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
25.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
17.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
8.0ms
(/ PI 3/2)
7.0ms
(/ (acos (/ (- g) h)) 3)

series168.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
119.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
37.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
12.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify2.2s

Counts
71 → 96
Calls
71 calls:
Slowest
561.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
238.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
91.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
74.0ms
(/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (* (cbrt 3) (cbrt 3)))
71.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

56.8b
(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))

rewrite71.0ms

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
26.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
21.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
18.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
6.0ms
(sin (/ PI 3))

series247.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
162.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
46.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
39.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
0.0ms
(sin (/ PI 3))

simplify1.5s

Counts
44 → 72
Calls
44 calls:
Slowest
210.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
86.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
82.0ms
(/ (exp (/ (acos (/ g h)) 3)) (exp (/ PI 3/2)))
52.0ms
(- (/ (sqrt (acos (/ g h))) (sqrt 3)) (/ (sqrt PI) (sqrt 3/2)))
52.0ms
(- (/ (sqrt (acos (/ g h))) (sqrt 3)) (/ (sqrt PI) (sqrt 3/2)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

56.8b
(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)

rewrite126.0ms

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
105.0ms
(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
12.0ms
(- (/ (acos (/ g h)) 3) (/ PI 3/2))
5.0ms
(/ PI 3/2)
3.0ms
(sin (/ PI 3))

series207.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
142.0ms
(cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))
64.0ms
(- (/ (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
346.0ms
(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
332.0ms
(* (+ (* (cos (- (/ PI 6) (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
215.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
124.0ms
(* (cos (/ PI 6)) (cos (- (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))
97.0ms
(* (cos (- (/ PI 6) (/ (/ PI 2) 3))) (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize91.0ms

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)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
62×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/l*
13×add-cbrt-cube add-exp-log
9×associate-/r*
7×div-inv
5×cbrt-undiv div-exp
4×pow1 insert-posit16 add-log-exp
3×clear-num frac-2neg
2×cos-sum
1×cos-diff sub-neg associate-/l/
Counts
4 → 138
Calls
4 calls:
Slowest
19.0ms
(cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2)))
7.0ms
(/ (/ PI 2) 3)
4.0ms
(/ PI 3/2)
4.0ms
(/ PI 3/2)

series150.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
149.0ms
(cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2)))
0.0ms
(/ PI 3/2)
0.0ms
(/ (/ PI 2) 3)
0.0ms
(/ PI 3/2)

simplify4.7s

Counts
152 → 144
Calls
152 calls:
Slowest
296.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt 2) (cbrt 2))) (* (cbrt 3) (cbrt 3)))
231.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
226.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
178.0ms
(/ (* (* (/ PI 2) (/ PI 2)) (/ PI 2)) (* (* 3 3) 3))
170.0ms
(/ (/ (* (* PI PI) PI) (* (* 2 2) 2)) (* (* 3 3) 3))

prune2.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes390.0ms

Accuracy

0% (0.0b remaining)

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

bsearch9.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.2s7984×body80nan
1.8s8000×body80valid