Details

sample106.0ms

Algorithm

intervals

Results

52.0ms	131×	body	1280	valid
13.0ms	57×	body	640	valid
10.0ms	256×	pre	80	true
6.0ms	45×	body	80	valid
3.0ms	19×	body	320	valid
0.0ms	4×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 15.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.6b	(tan (+ y z))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`tan-quot`
4×	`tan-sum`
3×	`+-commutative` `frac-sub`
2×	`sub-neg` `associate-+r+`
1×	`associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+`

Counts

3 → 16

Calls

3 calls:

3.0ms	(+ x (- (tan (+ y z)) (tan a)))
5.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series294.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(+ x (- (tan (+ y z)) (tan a)))
117.0ms	(- (tan (+ y z)) (tan a))
55.0ms	(tan (+ y z))

simplify75.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	166	201
1	390	199
2	971	199
3	3324	198
4	5002	198

prune74.0ms

Filtered

25 candidates to 17 candidates (68.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	20	5	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	5	26

Merged error: 0.1b

Counts

26 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`tan-quot`
6×	`frac-sub`
3×	`flip3-+` `fma-neg` `flip-+` `associate-/l/`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `frac-add` `associate-/r/` `flip--`
1×	`frac-times` `associate-+r-` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `*-commutative` `div-inv`

Counts

4 → 27

Calls

4 calls:

9.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
5.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
4.0ms	(+ (tan y) (tan z))
4.0ms	(* (tan z) (tan y))

series936.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
355.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
94.0ms	(+ (tan y) (tan z))
95.0ms	(* (tan z) (tan y))

simplify97.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	340	549
1	1078	543
2	3992	529
3	5001	525

prune183.0ms

Filtered

39 candidates to 33 candidates (84.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	31	8	39
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	36	8	44

Merged error: 0.1b

Counts

44 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan y))
0.2b	(* (tan z) (tan y))
0.2b	(* (tan z) (tan y))
0.3b	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
8×	`*-commutative`
2×	`swap-sqr` `associate-r` `associate-l`
1×	`pow2`

Counts

4 → 35

Calls

4 calls:

4.0ms	(* (tan z) (tan y))
4.0ms	(* (tan z) (tan y))
4.0ms	(* (tan z) (tan y))
9.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan z) (tan y))
92.0ms	(* (tan z) (tan y))
92.0ms	(* (tan z) (tan y))
115.0ms	(* (* (tan z) (tan y)) (* (tan z) (tan y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	210	296
1	827	292
2	3374	291
3	5002	287

prune221.0ms

Filtered

47 candidates to 35 candidates (74.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	49	6	55

Merged error: 0.1b

Counts

55 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`tan-quot`
2×	`+-commutative` `flip3-+` `flip-+` `fma-udef`
1×	`frac-times` `associate-+r+` `associate-r/` `associate-l/` `frac-add` `*-commutative`

Counts

4 → 13

Calls

4 calls:

2.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan z) (tan y)))) (- (tan a))))
3.0ms	(+ (tan y) (tan z))
1.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan z) (tan y)))) (- (tan a)))
4.0ms	(* (tan z) (tan y))

series875.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan z) (tan y)))) (- (tan a))))
103.0ms	(+ (tan y) (tan z))
352.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan z) (tan y)))) (- (tan a)))
93.0ms	(* (tan z) (tan y))

simplify51.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	207	301
1	505	296
2	1516	295
3	5001	294

prune109.0ms

Filtered

25 candidates to 21 candidates (84.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	26	5	31

Merged error: 0.0b

Counts

31 → 5

regimes179.0ms

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	23	20
1	23	20

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	3816×	body	1280	valid
495.0ms	2058×	body	640	valid
326.0ms	8000×	pre	80	true
113.0ms	695×	body	320	valid
59.0ms	1165×	body	80	valid
31.0ms	266×	body	160	valid