Details

Time bar (total: 19.9s)

sample103.0ms

Algorithm
intervals
Results
46.0ms256×body80valid
38.0ms242×body80nan

simplify77.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
77.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize36.0ms

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)

rewrite64.0ms

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
32.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
17.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
9.0ms
(/ (acos (/ (- g) h)) 3)
3.0ms
(/ PI 3/2)

series205.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
136.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
52.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
17.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify2.2s

Counts
71 → 96
Calls
71 calls:
Slowest
255.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
179.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
95.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
94.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
91.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune935.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

56.6b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(/ PI 3)
1.0b
(/ PI 3/2)

rewrite49.0ms

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
Counts
4 → 76
Calls
4 calls:
Slowest
30.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
7.0ms
(/ PI 3/2)
6.0ms
(/ PI 3)
5.0ms
(sin (/ PI 3))

series170.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
170.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3)

simplify1.9s

Counts
58 → 82
Calls
58 calls:
Slowest
279.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
268.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
254.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
233.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
223.0ms
(/ (* (* PI PI) PI) (* (* 3 3) 3))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ PI 3/2)
1.0b
(+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2))
1.0b
(cos (+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2)))
0.0b
(/ (acos (/ (- g) h)) (sqrt 3))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
29×times-frac
27×add-sqr-sqrt add-cube-cbrt
12×sqrt-prod
10×div-sub
9×associate-/r*
8×add-cbrt-cube add-exp-log
6×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 → 98
Calls
4 calls:
Slowest
38.0ms
(cos (+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2)))
21.0ms
(+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2))
10.0ms
(/ (acos (/ (- g) h)) (sqrt 3))
3.0ms
(/ PI 3/2)

series469.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
275.0ms
(cos (+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2)))
125.0ms
(+ (/ (/ (acos (/ (- g) h)) (sqrt 3)) (sqrt 3)) (/ PI 3/2))
68.0ms
(/ (acos (/ (- g) h)) (sqrt 3))
0.0ms
(/ PI 3/2)

simplify3.5s

Counts
93 → 108
Calls
93 calls:
Slowest
285.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
254.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* (sqrt 3) (sqrt 3)) (sqrt 3)))
215.0ms
(cos (+ (/ (acos (* -1 (/ g h))) (pow (sqrt 3) 2)) (* 2/3 PI)))
200.0ms
(+ (/ (acos (* -1 (/ g h))) (pow (sqrt 3) 2)) (* 2/3 PI))
194.0ms
(cos (+ (/ (acos (* -1 (/ g h))) (pow (sqrt 3) 2)) (* 2/3 PI)))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
29×times-frac
28×add-sqr-sqrt add-cube-cbrt
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
6×add-log-exp
4×pow1 insert-posit16
3×cbrt-undiv clear-num frac-2neg div-exp div-inv
2×div-sub associate-+l- distribute-lft-out
1×acos-asin acos-neg +-commutative sum-log flip3-+ frac-add distribute-frac-neg flip-+
Counts
4 → 101
Calls
4 calls:
Slowest
11.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
8.0ms
(/ PI 3/2)
7.0ms
(/ PI 3/2)
7.0ms
(/ PI 3/2)

series40.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
40.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3/2)

simplify1.7s

Counts
83 → 107
Calls
83 calls:
Slowest
248.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
237.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
204.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
71.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
68.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes401.0ms

Accuracy

0% (0.0b remaining)

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

bsearch7.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.7s8000×body80valid
1.5s7811×body80nan