Details

sample136.0ms

Algorithm

intervals

Results

67.0ms	49×	body	2560	valid
34.0ms	85×	body	1280	valid
13.0ms	60×	body	640	valid
4.0ms	27×	body	320	valid
3.0ms	1×	body	5120	valid
2.0ms	21×	body	160	valid
1.0ms	13×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
26.0ms	(- 1.0 (cos x))

simplify35.0ms

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460
done	5002	460

prune177.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 1.0 (cos x))

rewrite48.0ms

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:

20.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
7.0ms	(exp (log (- 1.0 (cos x))))
9.0ms	(log (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series155.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
19.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify38.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	354	1019
1	1045	861
2	5001	817
done	5001	817

prune283.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b	(- 1.0 (cos x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

21.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
26.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms	(- 1.0 (cos x))

series141.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms	(- 1.0 (cos x))

simplify40.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871
done	5002	871

prune357.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 1.0 (cos x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
13×	`times-frac` `associate-r` `exp-sum`
10×	`add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
8×	`pow1` `log-div` `associate-l`
6×	`exp-diff` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `exp-prod` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg`
2×	`frac-times` `div-exp` `associate-*l/` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 117

Calls

4 calls:

46.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
7.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series155.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
19.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify51.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	446	893
1	1626	727
2	5001	711
done	5001	711

prune277.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes158.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19
done	28	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	1584×	body	2560	valid
1.4s	2834×	body	1280	valid
422.0ms	1868×	body	640	valid
141.0ms	893×	body	320	valid
50.0ms	468×	body	160	valid
34.0ms	7×	body	5120	valid
22.0ms	346×	body	80	valid