Details

sample116.0ms

Algorithm

intervals

Results

58.0ms	138×	body	1280	valid
15.0ms	256×	pre	80	true
14.0ms	64×	body	640	valid
3.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid
1.0ms	25×	body	80	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

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: 15.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.9b	(tan (+ y z))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

13.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series332.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(+ x (- (tan (+ y z)) (tan a)))
133.0ms	(- (tan (+ y z)) (tan a))
59.0ms	(tan (+ y z))

simplify100.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune241.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 0.1b

Counts

82 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

19.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
9.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
19.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

397.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
247.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
444.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
107.0ms	(* (tan y) (tan z))

simplify91.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667

prune744.0ms

Filtered

239 candidates to 145 candidates (60.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	232	7	239
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	235	12	247

Merged error: 0.0b

Counts

247 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
0.2b	(/ (* (tan y) (sin z)) (cos z))
0.2b	(* (tan y) (sin z))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

13.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
24.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
7.0ms	(/ (* (tan y) (sin z)) (cos z))
6.0ms	(* (tan y) (sin z))

series899.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
457.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
112.0ms	(/ (* (tan y) (sin z)) (cos z))
75.0ms	(* (tan y) (sin z))

simplify97.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	694	4964
1	2578	4037
2	5001	3998

prune668.0ms

Filtered

248 candidates to 125 candidates (50.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	248	12	260

Merged error: 0.0b

Counts

260 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
0.2b	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
0.3b	(* (tan y) (tan z))
0.3b	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

495×	`times-frac`
414×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
305×	`add-cube-cbrt`
186×	`prod-diff`
62×	`fma-neg`
56×	`associate-/r/`
52×	`distribute-lft-out`
39×	`tan-quot`
23×	`associate-/r*` `div-inv`
19×	`add-exp-log`
17×	`flip3-+` `frac-add` `flip-+`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `clear-num` `flip--` `associate-/l/` `distribute-lft-out--`
1×	`frac-times` `sub-neg` `pow-flip` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 434

Calls

4 calls:

40.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
11.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
6.0ms	(* (tan y) (tan z))
9.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

437.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
243.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))
107.0ms	(* (tan y) (tan z))
308.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))

simplify161.0ms

Algorithm

egg-herbie

Counts

446 → 446

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1108	9686
1	4183	7247
2	5002	7188

prune824.0ms

Filtered

446 candidates to 183 candidates (41.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	446	0	446
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	446	12	458

Merged error: 0.0b

Counts

458 → 12

regimes660.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3907×	body	1280	valid
468.0ms	1991×	body	640	valid
330.0ms	8000×	pre	80	true
109.0ms	664×	body	320	valid
57.0ms	1159×	body	80	valid
31.0ms	279×	body	160	valid