Details

sample62.0ms

Algorithm

intervals

Results

27.0ms	57×	body	2560	valid
10.0ms	37×	body	1280	valid
10.0ms	45×	body	640	valid
4.0ms	32×	body	320	valid
2.0ms	66×	body	80	valid
2.0ms	19×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (cos x))
16.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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:

4.0ms	(- 1.0 (cos x))
8.0ms	(/ (- 1.0 (cos x)) (* x x))

series69.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
51.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune129.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 0.2b

Counts

65 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1/2 (* 1/24 (pow x 2)))
0.2b	(* 1/24 (pow x 2))
12.3b	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

3.0ms	(- 1/2 (* 1/24 (pow x 2)))
5.0ms	(* 1/24 (pow x 2))
1.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series132.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(- 1/2 (* 1/24 (pow x 2)))
25.0ms	(* 1/24 (pow x 2))
47.0ms	(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify186.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	209	318
1	817	281
2	4271	278
3	5001	273

prune148.0ms

Filtered

68 candidates to 47 candidates (69.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	68	11	79

Merged error: 0.2b

Counts

79 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

181×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
156×	`times-frac`
104×	`sqrt-prod`
103×	`add-cube-cbrt`
40×	`swap-sqr`
28×	`associate-r` `associate-l`
24×	`distribute-lft-out--`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube` `difference-of-squares`
11×	`pow1`
9×	`unswap-sqr`
8×	`associate-/l*` `add-log-exp`
6×	`fma-neg`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 238

Calls

4 calls:

9.0ms	(/ (sqrt (- 1.0 (cos x))) x)
25.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
4.0ms	(- 1.0 (cos x))
5.0ms	(- 1.0 (cos x))

series182.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (sqrt (- 1.0 (cos x))) x)
49.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify104.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	729	2762
1	3588	2273
2	5002	2108

prune390.0ms

Filtered

250 candidates to 141 candidates (56.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	246	4	250
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	250	11	261

Merged error: 0.2b

Counts

261 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
2.2b	(- 1.0 (cos x))
2.2b	(- 1.0 (cos x))
2.3b	(log (exp (- 1.0 (cos x))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
72×	`times-frac`
63×	`add-cube-cbrt`
48×	`sqrt-prod`
40×	`associate-r`
28×	`associate-l`
27×	`prod-diff`
24×	`log-pow`
20×	`exp-prod`
16×	`add-exp-log` `add-cbrt-cube`
14×	`log-prod`
11×	`exp-sum`
10×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
8×	`add-log-exp`
6×	`fma-neg`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `flip--` `div-inv`
1×	`frac-times` `log-div` `exp-diff` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 186

Calls

4 calls:

31.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))
6.0ms	(log (exp (- 1.0 (cos x))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (log (exp (- 1.0 (cos x))))) x))
18.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	688	2088
1	2841	1468
2	5001	1375

prune373.0ms

Filtered

198 candidates to 121 candidates (61.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	198	11	209

Merged error: 0.1b

Counts

209 → 11

regimes103.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.6b

bsearch92.0ms

Steps

Iters	Range		Point
9	8.159003009805276e-07	0.06291072096871789	0.02982085320761324
9	-5.855776674212404	-7.74497267090904e-05	-0.03566864611298506

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

734.0ms	1543×	body	2560	valid
320.0ms	1260×	body	1280	valid
250.0ms	1534×	body	640	valid
121.0ms	898×	body	320	valid
79.0ms	2274×	body	80	valid
39.0ms	491×	body	160	valid