Details

Time bar (total: 16.3s)

sample68.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
22.0ms197×body80nan

simplify66.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
66.0ms
(* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize34.0ms

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))
0.9b
(/ (acos (/ (- g) h)) 3)

rewrite54.0ms

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
21.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
14.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
10.0ms
(/ (acos (/ (- g) h)) 3)
7.0ms
(/ PI 3/2)

series205.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
144.0ms
(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
47.0ms
(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
13.0ms
(/ (acos (/ (- g) h)) 3)
0.0ms
(/ PI 3/2)

simplify2.0s

Counts
71 → 96
Calls
71 calls:
Slowest
243.0ms
(/ (* (* (acos (/ (- g) h)) (acos (/ (- g) h))) (acos (/ (- g) h))) (* (* 3 3) 3))
207.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
101.0ms
(* (cos (/ (/ PI 2) 3)) (cos (- (/ (asin (/ (- g) h)) 3) (/ PI 3/2))))
84.0ms
(+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI))
81.0ms
(cos (+ (* 1/3 (acos (* -1 (/ g h)))) (* 2/3 PI)))

prune823.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

56.3b
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
1.0b
(sin (/ PI 3))
1.0b
(/ PI 3)
1.0b
(/ PI 3/2)

rewrite60.0ms

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
38.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
7.0ms
(/ PI 3/2)
7.0ms
(/ PI 3)
6.0ms
(sin (/ PI 3))

series138.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
138.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
0.0ms
(sin (/ PI 3))
0.0ms
(/ PI 3)
0.0ms
(/ PI 3/2)

simplify1.8s

Counts
58 → 82
Calls
58 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)
236.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
235.0ms
(* (+ (* (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) 1/2) (* (sin (/ PI 3)) (sin (- (/ (acos (/ g h)) 3) (/ PI 3/2))))) 2)
220.0ms
(/ (* (* PI PI) PI) (* (* 3 3) 3))
209.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

56.3b
(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))))

rewrite63.0ms

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
32.0ms
(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))
16.0ms
(sin (* (sqrt (/ PI 3)) (sqrt (/ PI 3))))
7.0ms
(/ PI 3/2)
7.0ms
(/ PI 3/2)

series168.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
168.0ms
(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
273.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
240.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
52.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))
42.0ms
(cos (- (* 1/3 (acos (/ g h))) (* 2/3 PI)))
39.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize89.0ms

Local error

Found 4 expressions with local error:

59.6b
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
1.6b
(cos (/ PI 3/2))
1.0b
(sin (/ PI 3/2))
1.0b
(/ PI 3/2)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
4×pow1 insert-posit16
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-+ div-exp frac-add cos-mult flip-+ div-inv sin-mult
Counts
4 → 57
Calls
4 calls:
Slowest
23.0ms
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
4.0ms
(/ PI 3/2)
3.0ms
(cos (/ PI 3/2))
3.0ms
(sin (/ PI 3/2))

series424.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
423.0ms
(+ (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2))) (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2))))
0.0ms
(cos (/ PI 3/2))
0.0ms
(sin (/ PI 3/2))
0.0ms
(/ PI 3/2)

simplify1.2s

Counts
33 → 63
Calls
33 calls:
Slowest
354.0ms
(+ (* (+ (cos (+ (/ (acos (/ g h)) 3) (/ PI 3/2))) (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))) 2) (* 2 (- (cos (- (/ (acos (/ g h)) 3) (/ PI 3/2))) (cos (+ (/ (acos (/ g h)) 3) (/ PI 3/2))))))
252.0ms
(/ (* (* PI PI) PI) (* (* 3/2 3/2) 3/2))
239.0ms
(* (exp (* (cos (/ (acos (/ g h)) 3)) (cos (/ PI 3/2)))) (exp (* (sin (/ (acos (/ g h)) 3)) (sin (/ PI 3/2)))))
41.0ms
(/ (* (cbrt PI) (cbrt PI)) (* (cbrt 3/2) (cbrt 3/2)))
29.0ms
(+ (* (cos (* 2/3 PI)) (cos (* 1/3 (acos (/ g h))))) (* (sin (* 1/3 (acos (/ g h)))) (sin (* 2/3 PI))))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.0b remaining)

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

bsearch10.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.2s8000×body80valid
1.6s7818×body80nan