Details

Time bar (total: 5.9s)

sample44.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
14.0ms286×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01416
12116
22516
32816
42916
done2916

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (acos (/ (- g) h)) 3.0)
1.0b
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
1.0b
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(/ (* 2.0 PI) 3.0)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
12×times-frac
11×add-exp-log add-cbrt-cube
6×div-sub associate-/r* add-log-exp
4×pow1 associate-+r- div-inv associate-/l*
3×cbrt-undiv acos-neg acos-asin distribute-frac-neg div-exp
2×cos-diff frac-2neg clear-num
1×+-commutative cos-sum distribute-rgt-out flip3-+ frac-add prod-exp sum-log cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 76
Calls
4 calls:
2.0ms
(/ (acos (/ (- g) h)) 3.0)
11.0ms
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
21.0ms
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
3.0ms
(/ (* 2.0 PI) 3.0)

series144.0ms

Counts
4 → 10
Calls
4 calls:
10.0ms
(/ (acos (/ (- g) h)) 3.0)
35.0ms
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
98.0ms
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
0.0ms
(/ (* 2.0 PI) 3.0)

simplify1.1s

Counts
86 → 86
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
01591223
13281165
29251075
333721075
done50001075

prune216.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* 2.0 PI) 3.0)
1.0b
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
1.0b
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
58.2b
(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
19×times-frac
10×add-sqr-sqrt add-cube-cbrt distribute-rgt-out
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×div-inv
4×pow1
3×associate-/r*
2×cbrt-undiv +-commutative distribute-lft1-in flip3-+ div-exp frac-add sum-log flip-+ distribute-lft-out
1×frac-2neg sin-sum prod-exp clear-num cbrt-unprod associate-/l*
Counts
4 → 67
Calls
4 calls:
5.0ms
(/ (* 2.0 PI) 3.0)
11.0ms
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
11.0ms
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
20.0ms
(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/ (* 2.0 PI) 3.0)
0.0ms
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
0.0ms
(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
0.0ms
(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

simplify957.0ms

Counts
71 → 71
Iterations

Useful iterations: 3 (237.0ms)

IterNodesCost
0103943
1241900
2685820
32911804
done5000804

prune278.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
1.0b
(pow (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))) 3)
1.0b
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(/ (* 2.0 PI) 3.0)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-exp-log add-cbrt-cube
9×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×pow1
4×associate-+r- div-sub
3×unpow-prod-down pow-unpow times-frac cube-prod associate-/r* div-inv
2×cbrt-undiv acos-neg acos-asin cos-diff distribute-frac-neg div-exp
1×+-commutative cube-mult pow-to-exp cos-sum distribute-rgt-out pow-pow frac-2neg flip3-+ unpow3 frac-add pow-exp prod-exp clear-num sum-log cbrt-unprod flip-+ distribute-lft-out associate-/l* rem-cube-cbrt sqr-pow
Counts
4 → 70
Calls
4 calls:
11.0ms
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
2.0ms
(pow (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))) 3)
20.0ms
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
3.0ms
(/ (* 2.0 PI) 3.0)

series286.0ms

Counts
4 → 10
Calls
4 calls:
35.0ms
(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
153.0ms
(pow (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))) 3)
98.0ms
(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
0.0ms
(/ (* 2.0 PI) 3.0)

simplify2.2s

Counts
80 → 80
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
01471439
13421321
210181193
346921193
done50001193

prune206.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0))
1.0b
(cos (+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0)))
1.0b
(/ (* 2.0 PI) 3.0)
1.6b
(pow (/ (* 2.0 PI) 3.0) 3)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log add-cbrt-cube
13×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
9×times-frac
7×unpow-prod-down cube-prod
6×add-log-exp
5×pow1
4×cbrt-undiv associate-+r- div-sub div-exp
3×pow-unpow pow-exp associate-/r* div-inv rem-cube-cbrt
2×acos-neg cube-div acos-asin cos-diff distribute-frac-neg prod-exp cbrt-unprod
1×+-commutative cube-mult pow-to-exp cbrt-div cos-sum pow-pow frac-2neg flip3-+ unpow3 frac-add clear-num sum-log flip-+ distribute-lft-out associate-/l* sqr-pow
Counts
4 → 82
Calls
4 calls:
32.0ms
(+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0))
54.0ms
(cos (+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0)))
3.0ms
(/ (* 2.0 PI) 3.0)
4.0ms
(pow (/ (* 2.0 PI) 3.0) 3)

series137.0ms

Counts
4 → 8
Calls
4 calls:
34.0ms
(+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0))
103.0ms
(cos (+ (cbrt (pow (/ (* 2.0 PI) 3.0) 3)) (/ (acos (/ (- g) h)) 3.0)))
0.0ms
(/ (* 2.0 PI) 3.0)
0.0ms
(pow (/ (* 2.0 PI) 3.0) 3)

simplify37.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
01621354