Details

sample169.0ms

Algorithm

intervals

Results

72.0ms	96×	body	1280	valid
34.0ms	56×	body	640	valid
31.0ms	24×	body	2560	valid
13.0ms	38×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	11×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize19.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
6.1b	(sin (+ x eps))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

74.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

series74.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify3.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (451.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune126.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-cos-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

30.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
33.0ms	(+ (+ x eps) x)
33.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
72.0ms	(cos (/ (+ (+ x eps) x) 2))

series226.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
31.0ms	(+ (+ x eps) x)
69.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
37.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	118	1100
1	292	1077
2	819	917
3	2476	893
done	5000	885

prune205.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (* 2 (sin (/ eps 2))) (cos (/ (+ (+ x eps) x) 2)))
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

33.0ms	(+ (+ x eps) x)
31.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (+ (+ x eps) x) 2)))
56.0ms	(cos (/ (+ (+ x eps) x) 2))

series119.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (+ x eps) x)
64.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.6s

Counts

49 → 49

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	93	691
1	240	673
2	749	561
3	2306	543
done	5000	537

prune118.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
15×	`associate-r`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`unpow-prod-down` `cube-prod`
8×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `associate-l` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

36.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
8.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
42.0ms	(cos (/ (+ (+ x eps) x) 2))

series170.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
25.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
54.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	121	1649
1	284	1375
2	911	1195
done	5000	1173

prune212.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

Details

sample169.0ms

simplify7.0ms

prune4.0ms

localize19.0ms

rewrite95.0ms

series74.0ms

simplify3.0s

prune126.0ms

localize32.0ms

rewrite171.0ms

series226.0ms

simplify2.2s

prune205.0ms

localize15.0ms

rewrite121.0ms

series119.0ms

simplify1.6s

prune118.0ms

localize18.0ms

rewrite91.0ms

series170.0ms

simplify1.0s

prune212.0ms

regimes109.0ms

bsearch1.0ms