Details

sample131.0ms

Algorithm

intervals

Results

56.0ms	256×	body	80	valid
51.0ms	280×	body	80	nan

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	28
4	28
3	27
2	24
1	21
0	14

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:

10.0ms	(/ (acos (/ (- g) h)) 3)
10.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
28.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
7.0ms	(/ PI 3/2)

series229.0ms

Counts

4 → 10

Calls

4 calls:

19.0ms	(/ (acos (/ (- g) h)) 3)
45.0ms	(+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2))
164.0ms	(cos (+ (/ (acos (/ (- g) h)) 3) (/ PI 3/2)))
0.0ms	(/ PI 3/2)

simplify1.5s

Counts

96 → 96

Iterations

Iter	Nodes
4	2790
3	1279
2	625
1	319
0	172

prune886.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ PI 3/2)
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
57.4b	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`times-frac`
12×	`add-cube-cbrt`
8×	`add-log-exp` `difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `insert-posit16` `distribute-lft-out--`
3×	`associate-/r` `sub-neg` `associate-/l`
2×	`associate--l-` `acos-asin` `cos-sum` `flip3--` `diff-log` `div-sub` `frac-sub` `flip--`
1×	`cos-diff` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 81

Calls

4 calls:

4.0ms	(/ PI 3/2)
11.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
11.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
16.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))

series235.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(/ PI 3/2)
44.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
44.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
147.0ms	(cos (- (/ (acos (/ g h)) 3) (/ PI 3/2)))

simplify2.7s

Counts

91 → 91

Iterations

Iter	Nodes
5	3848
4	1815
3	863
2	449
1	237
0	129

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ PI 3/2)
1.0b	(/ (/ PI 2) 3)
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
57.4b	(cos (- (/ (/ PI 2) 3) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
66×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
54×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16` `difference-of-squares`
3×	`cos-sum`
2×	`clear-num` `sub-neg` `frac-2neg` `div-sub` `distribute-lft-out--`
1×	`associate--l-` `acos-asin` `cos-diff` `asin-acos` `flip3--` `diff-log` `frac-sub` `associate-+l-` `flip--` `associate--r-` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

3.0ms	(/ PI 3/2)
7.0ms	(/ (/ PI 2) 3)
11.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
83.0ms	(cos (- (/ (/ PI 2) 3) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))

series209.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(/ PI 3/2)
0.0ms	(/ (/ PI 2) 3)
70.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
138.0ms	(cos (- (/ (/ PI 2) 3) (+ (/ (asin (/ g h)) 3) (/ PI 3/2))))

simplify1.5s

Counts

140 → 140

Iterations

Iter	Nodes
3	2716
2	1159
1	562
0	271

prune2.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize124.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ PI 3/2)
1.0b	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
57.4b	(cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))
60.8b	(log (exp (cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
15×	`times-frac`
14×	`add-cube-cbrt`
10×	`cos-sum`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `log-div` `sub-neg` `exp-diff`
4×	`log-prod` `associate--l+` `log-pow` `insert-posit16` `difference-of-squares`
3×	`exp-prod` `associate-/r` `div-sub` `associate-/l`
2×	`cos-diff` `asin-acos` `distribute-lft-out--` `associate--r-`
1×	`associate--l-` `acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `diff-log` `div-exp` `rem-log-exp` `exp-sum` `frac-sub` `div-inv` `flip--`

Counts

4 → 85

Calls

4 calls:

3.0ms	(/ PI 3/2)
11.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
112.0ms	(cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))
195.0ms	(log (exp (cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))))

series395.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(/ PI 3/2)
56.0ms	(- (/ (acos (/ g h)) 3) (/ PI 3/2))
143.0ms	(cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))
196.0ms	(log (exp (cos (- (- (/ PI 6) (/ PI 3/2)) (/ (asin (/ g h)) 3)))))

simplify1.1s

Counts

95 → 95

Iterations

Iter	Nodes
4	2246
3	1130
2	627
1	344
0	192

prune1.8s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify8.0ms

Iterations

Iter	Nodes
2	32
1	32
0	28

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.1s	8000×	body	80	valid
1.4s	8177×	body	80	nan