Details

sample927.0ms

Algorithm

intervals

Results

629.0ms	43×	body	2560	valid
94.0ms	82×	body	1280	valid
50.0ms	66×	body	640	valid
18.0ms	37×	body	320	valid
6.0ms	17×	body	160	valid
2.0ms	11×	body	80	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (tan x))
1.2b	(- x (sin x))

rewrite93.0ms

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:

68.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series242.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/ (- x (sin x)) (- x (tan x)))
69.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.3s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

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

prune431.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
13.9b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
13.9b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 144

Calls

4 calls:

17.0ms	(pow (sin x) 2)
7.0ms	(pow (cos x) 2)
38.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
19.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sin x) 2)
29.0ms	(pow (cos x) 2)
110.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))
111.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))

simplify903.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (315.0ms)

Iter	Nodes	Cost
0	185	2056
1	419	1851
2	1280	1658
done	5000	1658

prune596.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.2b	(* 9/40 (pow x 2))
14.3b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite35.0ms

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)
19.0ms	(* 9/40 (pow x 2))
14.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series226.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(fma 27/2800 (pow x 4) 1/2)
31.0ms	(* 9/40 (pow x 2))
54.0ms	(- (* 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

prune214.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 x)
0.1b	(* (* 9/40 x) x)
14.3b	(- (* (* 9/40 x) x) (fma 27/2800 (pow x 4) 1/2))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
13.0ms	(* 9/40 x)
38.0ms	(* (* 9/40 x) x)
38.0ms	(- (* (* 9/40 x) x) (fma 27/2800 (pow x 4) 1/2))

series223.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma 27/2800 (pow x 4) 1/2)
16.0ms	(* 9/40 x)
35.0ms	(* (* 9/40 x) x)
73.0ms	(- (* (* 9/40 x) x) (fma 27/2800 (pow x 4) 1/2))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	105	881
1	232	747
2	736	666
3	3052	613
done	5000	613

prune248.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes69.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.6b

bsearch215.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	2.401275434249347
9	-7465.585501010854	-0.008005822963963436	-0.030293763080502873

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	48	95
1	58	95
done	58	95

end0.0ms

sample13.8s

Algorithm

intervals

Results

7.1s	1659×	body	2560	valid
3.5s	2670×	body	1280	valid
2.1s	1927×	body	640	valid
527.0ms	942×	body	320	valid
165.0ms	422×	body	160	valid
62.0ms	380×	body	80	valid