Details

sample656.0ms

Algorithm

intervals

Results

327.0ms	52×	body	2560	valid
167.0ms	91×	body	1280	valid
55.0ms	38×	body	320	valid
35.0ms	46×	body	640	valid
7.0ms	20×	body	160	valid
2.0ms	9×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

40.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
59.0ms	(- x (sin x))

series275.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
81.0ms	(- x (tan x))
65.0ms	(- x (sin x))

simplify1.2s

Counts

119 → 119

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1343	1384
done	5000	1306

prune348.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.2b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
13.0ms	(* 9/40 (pow x 2))
12.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series257.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(fma 27/2800 (pow x 4) 1/2)
46.0ms	(* 9/40 (pow x 2))
94.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.7s

Counts

67 → 67

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	106	845
1	219	700
2	588	624
3	2787	573
done	5000	572

prune240.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
14.1b	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-l`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-r` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 37

Calls

2 calls:

25.0ms	(* (pow x 4) -27/2800)
1.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

series236.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (pow x 4) -27/2800)
161.0ms	(fma 9/40 (pow x 2) (* (pow x 4) -27/2800))

simplify2.4s

Counts

43 → 43

Iterations

Useful iterations: 3 (509.0ms)

Iter	Nodes	Cost
0	66	400
1	126	375
2	345	346
3	1266	343
done	5000	343

prune152.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.7b	(- x (tan x))
1.8b	(- x (sin x))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
214×	`add-sqr-sqrt` `*-un-lft-identity`
106×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`fma-neg` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 260

Calls

4 calls:

44.0ms	(/ (- x (tan x)) (- x (sin x)))
53.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
14.0ms	(- x (tan x))
16.0ms	(- x (sin x))

series384.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- x (tan x)) (- x (sin x)))
106.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
106.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify1.6s

Counts

272 → 272

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	374	5190
1	843	4436
2	2155	4000
done	5000	3846

prune602.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

Details

sample656.0ms

simplify30.0ms

prune8.0ms

localize23.0ms

rewrite115.0ms

series275.0ms

simplify1.2s

prune348.0ms

localize12.0ms

rewrite27.0ms

series257.0ms

simplify2.7s

prune240.0ms

localize22.0ms

rewrite28.0ms

series236.0ms

simplify2.4s

prune152.0ms

localize15.0ms

rewrite144.0ms

series384.0ms

simplify1.6s

prune602.0ms

regimes54.0ms

bsearch3.0ms