Details

sample86.0ms

Algorithm

intervals

Results

42.0ms	103×	body	1280	valid
16.0ms	68×	body	640	valid
14.0ms	17×	body	2560	valid
2.0ms	18×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	11×	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 (100.0%)

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: 37.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
2.4b	(tan (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`tan-quot`
4×	`add-sqr-sqrt` `tan-sum` `*-un-lft-identity` `add-log-exp`
3×	`frac-sub`
2×	`pow1` `add-exp-log` `+-commutative` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 27

Calls

2 calls:

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

series146.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	144	236
1	299	227
2	753	225
3	2459	224
4	5001	224

prune69.0ms

Filtered

33 candidates to 25 candidates (24.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 16.1b

Counts

34 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (tan x))
4.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
37×	`times-frac`
29×	`tan-quot`
26×	`difference-of-squares`
23×	`add-cube-cbrt`
19×	`frac-sub`
18×	`associate-/r*`
13×	`distribute-lft-out--` `unswap-sqr`
12×	`distribute-lft-out`
9×	`associate-l`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
6×	`pow1` `associate-/l/`
3×	`flip3-+` `associate-r` `frac-add` `flip-+`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 134

Calls

4 calls:

16.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan eps) (tan x))
27.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series789.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
96.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan eps) (tan x))
376.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify66.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	596	2006
1	2300	1933
2	5001	1933

prune306.0ms

Filtered

146 candidates to 96 candidates (34.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	131	15	146
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	138	15	153

Merged error: 15.9b

Counts

153 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan eps) (tan x))
0.2b	(* (tan eps) (tan x))
9.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`associate-l`
28×	`add-sqr-sqrt`
18×	`distribute-lft-out--`
17×	`associate-*l/`
14×	`tan-quot`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
7×	`unswap-sqr`
6×	`frac-sub` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3--` `flip--` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log`

Counts

4 → 98

Calls

4 calls:

7.0ms	(* (+ (tan x) (tan eps)) (cos x))
5.0ms	(* (tan eps) (tan x))
5.0ms	(* (tan eps) (tan x))
28.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (+ (tan x) (tan eps)) (cos x))
95.0ms	(* (tan eps) (tan x))
94.0ms	(* (tan eps) (tan x))
217.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	540	1221
1	2382	1169
2	5003	1169

prune340.0ms

Filtered

110 candidates to 76 candidates (30.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Merged error: 0.1b

Counts

125 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (pow (sin x) 2) (sin eps))
0.2b	(* (tan eps) (tan x))
0.2b	(pow (sin x) 2)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

254×	`add-sqr-sqrt`
240×	`times-frac`
178×	`associate-l`
126×	`add-cube-cbrt` `*-un-lft-identity`
108×	`associate-r`
78×	`unswap-sqr`
59×	`unpow-prod-down`
36×	`add-exp-log` `*-commutative`
29×	`unpow2` `sqr-pow`
20×	`add-cbrt-cube` `associate-/l*`
14×	`prod-exp`
12×	`associate-/r*`
9×	`pow1`
8×	`div-exp`
6×	`cbrt-unprod`
4×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp` `add-log-exp`
3×	`pow-unpow`
2×	`pow-prod-down`
1×	`frac-times` `pow-pow` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r/` `cos-mult` `div-inv`

Counts

4 → 362

Calls

4 calls:

19.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
7.0ms	(* (pow (sin x) 2) (sin eps))
5.0ms	(* (tan eps) (tan x))
2.0ms	(pow (sin x) 2)

series277.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps)))
53.0ms	(* (pow (sin x) 2) (sin eps))
93.0ms	(* (tan eps) (tan x))
19.0ms	(pow (sin x) 2)

simplify76.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1492	4669
1	5001	4380

prune1.2s

Filtered

374 candidates to 220 candidates (41.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	361	13	374
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	363	18	381

Merged error: 0.0b

Counts

381 → 18

regimes415.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	23
1	46	23
2	51	23
3	51	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3312×	body	1280	valid
525.0ms	610×	body	2560	valid
410.0ms	1852×	body	640	valid
104.0ms	753×	body	320	valid
47.0ms	1098×	body	80	valid
38.0ms	375×	body	160	valid