Details

Time bar (total: 16.9s)

sample105.0ms

Algorithm
intervals
Results
53.0ms256×body80valid
35.0ms255×body80nan

simplify44.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
44.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

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)

rewrite37.0ms

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
17.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
10.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
5.0ms
(/ (acos (/ (- g) h)) 3)
4.0ms
(/ PI 3/2)

series230.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
156.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
58.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
16.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify1.9s

Counts
71 → 96
Calls
71 calls:
Slowest
230.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
214.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
83.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
79.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))
76.0ms
(/ (* (cbrt (acos (/ (- g) h))) (cbrt (acos (/ (- g) h)))) (* (cbrt 3) (cbrt 3)))

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

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)

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 sin-PI/3
Counts
4 → 76
Calls
4 calls:
Slowest
26.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
7.0ms
(/ PI 3/2)
7.0ms
(/ PI 3)
5.0ms
(sin (/ PI 3))

series152.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
152.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3/2)
0.0ms
(/ PI 3)

simplify1.8s

Counts
58 → 82
Calls
58 calls:
Slowest
270.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
259.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
258.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
222.0ms
(/ (* (* PI PI) PI) (* (* 3 3) 3))
187.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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
Counts
4 → 75
Calls
4 calls:
Slowest
17.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
10.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
8.0ms
(/ PI 3/2)
4.0ms
(/ PI 3/2)

series156.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
156.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(/ PI 3/2)
0.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
0.0ms
(/ PI 3/2)

simplify1.2s

Counts
54 → 81
Calls
54 calls:
Slowest
266.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
229.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
49.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
47.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
42.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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
Counts
4 → 75
Calls
4 calls:
Slowest
19.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
9.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
4.0ms
(/ PI 3/2)
3.0ms
(/ PI 3/2)

series186.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
186.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(/ PI 3/2)
0.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
0.0ms
(/ PI 3/2)

simplify1.1s

Counts
54 → 81
Calls
54 calls:
Slowest
258.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
232.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
57.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))
57.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))
42.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.2s8000×body80valid
1.6s7993×body80nan