Details

sample119.0ms

Algorithm

intervals

Results

40.0ms	47×	body	2560	valid
32.0ms	46×	body	640	valid
21.0ms	46×	body	1280	valid
8.0ms	37×	body	320	valid
5.0ms	64×	body	80	valid
2.0ms	16×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize10.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
14.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
26.0ms	(/ (- 1.0 (cos x)) (* x x))

series83.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
62.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts

64 → 64

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	116	808
1	301	681
2	1709	566
done	5001	553

prune328.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
110×	`add-sqr-sqrt` `*-un-lft-identity`
76×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 165

Calls

3 calls:

53.0ms	(/ (/ (- 1.0 (cos x)) x) x)
33.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (/ (- 1.0 (cos x)) x) x)
71.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify1.7s

Counts

174 → 174

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	259	2577
1	621	2361
2	2999	2187
done	5000	2152

prune645.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

48.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
15.0ms	(exp (log (- 1.0 (cos x))))
12.0ms	(log (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))

series201.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
30.0ms	(exp (log (- 1.0 (cos x))))
91.0ms	(log (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	201	1670
1	380	1307
2	1388	1170
done	5001	1129

prune952.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow E (log (- 1.0 (cos x)))) x)
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
36×	`times-frac`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`expm1-log1p-u` `pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `log1p-expm1-u` `pow-sub`
3×	`fma-neg` `associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 144

Calls

4 calls:

20.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
7.0ms	(pow E (log (- 1.0 (cos x))))
12.0ms	(log (- 1.0 (cos x)))
9.0ms	(- 1.0 (cos x))

series906.0ms

Counts

4 → 12

Calls

4 calls:

432.0ms	(/ (pow E (log (- 1.0 (cos x)))) x)
321.0ms	(pow E (log (- 1.0 (cos x))))
126.0ms	(log (- 1.0 (cos x)))
26.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

156 → 156

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	247	2271
1	539	2022
2	2218	1856
done	5001	1651

prune441.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes88.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.8b

bsearch109.0ms

Steps

Iters	Range		Point
11	9.093534403752284e-26	13730598.322931442	0.029815137429186504
8	-24.398001816905442	-0.001242952878385433	-0.034013493959747065

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	46
1	37	46
done	37	46

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.2s	1584×	body	2560	valid
698.0ms	1258×	body	1280	valid
424.0ms	458×	body	160	valid
362.0ms	1519×	body	640	valid
169.0ms	953×	body	320	valid
164.0ms	2228×	body	80	valid