Details

sample592.0ms

Algorithm

intervals

Results

198.0ms	46×	body	2560	valid
195.0ms	92×	body	1280	valid
49.0ms	63×	body	640	valid
15.0ms	29×	body	320	valid
5.0ms	11×	body	160	valid
3.0ms	15×	body	80	valid

simplify23.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite149.0ms

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:

54.0ms	(/ (- x (sin x)) (- x (tan x)))
18.0ms	(- x (tan x))
65.0ms	(- x (sin x))

series274.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- 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

prune396.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
0.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.7b	(- x (tan x))
0.7b	(- x (tan x))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

18.0ms	(/ (sin x) (- x (tan x)))
157.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
7.0ms	(- x (tan x))
7.0ms	(- x (tan x))

series551.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (sin x) (- x (tan x)))
299.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
81.0ms	(- x (tan x))
91.0ms	(- x (tan x))

simplify2.2s

Counts

600 → 600

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	617	35000
1	1353	31424
2	3023	23405
done	5001	20458

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 156

Calls

4 calls:

71.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
26.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
15.0ms	(- x (sin x))

series444.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
152.0ms	(/ (- x (sin x)) (- x (tan x)))
94.0ms	(- x (tan x))
62.0ms	(- x (sin x))

simplify1.6s

Counts

168 → 168

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	273	2551
1	544	2175
2	1422	1968
done	5000	1890

prune600.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
18.6b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite30.0ms

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:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
15.0ms	(* 9/40 (pow x 2))
11.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series203.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(fma 27/2800 (pow x 4) 1/2)
28.0ms	(* 9/40 (pow x 2))
58.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.6s

Counts

67 → 67

Iterations

Useful iterations: done (2.6s)

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

prune275.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes107.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch125.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.028662423939317287
9	-7.35943201301068	-4.403108084983288e-07	-0.029638169034640425

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	45
1	28	45
done	28	45

end0.0ms

sample14.2s

Algorithm

intervals

Results

6.1s	1601×	body	2560	valid
4.9s	2779×	body	1280	valid
1.7s	1836×	body	640	valid
634.0ms	474×	body	160	valid
422.0ms	963×	body	320	valid
58.0ms	347×	body	80	valid