Details

sample85.0ms

Algorithm

intervals

Results

44.0ms	109×	body	1280	valid
13.0ms	14×	body	2560	valid
12.0ms	55×	body	640	valid
4.0ms	29×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	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: 37.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series139.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune112.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	35	12	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	12	48

Merged error: 14.2b

Counts

48 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
61×	`times-frac`
57×	`prod-diff`
21×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`tan-quot` `flip3--` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

9.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series751.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
103.0ms	(- 1 (* (tan x) (tan eps)))
88.0ms	(* (tan x) (tan eps))
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	566	2988
1	2124	2419
2	5002	2397

prune376.0ms

Filtered

183 candidates to 109 candidates (59.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	169	14	183
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	177	18	195

Merged error: 14.1b

Counts

195 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
27.5b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
233×	`add-sqr-sqrt`
161×	`times-frac`
138×	`prod-diff`
114×	`add-cube-cbrt`
98×	`difference-of-squares`
72×	`cbrt-prod`
46×	`fma-neg`
40×	`distribute-lft-out`
34×	`sqr-pow`
17×	`distribute-lft-out--`
13×	`tan-quot`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`cube-div` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow1/3` `diff-log` `*-commutative` `frac-sub` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 274

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(pow (* (tan x) (tan eps)) 3)
33.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
4.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series659.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (tan x) (tan eps))
120.0ms	(pow (* (tan x) (tan eps)) 3)
352.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
97.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify122.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	797	6024
1	3080	4621
2	5003	4586

prune521.0ms

Filtered

286 candidates to 128 candidates (44.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	283	3	286
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	288	16	304

Merged error: 14.1b

Counts

304 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
8.5b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
6.0ms	(* (tan x) (tan eps))
10.0ms	(* (tan x) (tan eps))
10.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (+ (tan x) (tan eps)) (cos x))
92.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
210.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	561	1030
1	2620	960
2	5001	955

prune340.0ms

Filtered

104 candidates to 82 candidates (78.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Merged error: 0.2b

Counts

120 → 9

regimes99.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	20
1	25	20

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3306×	body	1280	valid
552.0ms	634×	body	2560	valid
399.0ms	1833×	body	640	valid
114.0ms	759×	body	320	valid
50.0ms	1105×	body	80	valid
35.0ms	363×	body	160	valid