Details

sample104.0ms

Algorithm

intervals

Results

51.0ms	122×	body	1280	valid
15.0ms	63×	body	640	valid
10.0ms	256×	pre	80	true
4.0ms	23×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	11×	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: 11.4b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.3b	(- (tan (+ y z)) (tan a))
2.3b	(tan (+ y z))

rewrite11.0ms

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))

series309.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(+ x (- (tan (+ y z)) (tan a)))
123.0ms	(- (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

prune77.0ms

Filtered

25 candidates to 17 candidates (68.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	18	7	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	7	26

Merged error: 0.1b

Counts

26 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

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:

5.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
3.0ms	(+ (tan y) (tan z))
4.0ms	(* (tan z) (tan y))
10.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))

series996.0ms

Counts

4 → 12

Calls

4 calls:

376.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
101.0ms	(+ (tan y) (tan z))
103.0ms	(* (tan z) (tan y))
416.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))

simplify99.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	340	549
1	1074	543
2	3987	529
3	5001	525

prune191.0ms

Filtered

39 candidates to 33 candidates (84.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	30	9	39
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	37	9	46

Merged error: 0.0b

Counts

46 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 25

Calls

4 calls:

4.0ms	(+ (tan y) (tan z))
5.0ms	(/ (* (sin z) (tan y)) (cos z))
4.0ms	(* (sin z) (tan y))
10.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (tan y)) (cos z)))) (tan a))

series726.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (tan y) (tan z))
112.0ms	(/ (* (sin z) (tan y)) (cos z))
87.0ms	(* (sin z) (tan y))
426.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (tan y)) (cos z)))) (tan a))

simplify92.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	312	459
1	980	453
2	3642	437
3	5001	432

prune212.0ms

Filtered

37 candidates to 32 candidates (86.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	36	10	46

Merged error: 0.0b

Counts

46 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin z) (tan y))
0.3b	(* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z)))
0.3b	(pow (/ (* (sin z) (tan y)) (cos z)) 3)
0.3b	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin z) (tan y)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z))) (* 1 (/ (* (sin z) (tan y)) (cos z))))) (- (tan a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

36×	`frac-times`
28×	`associate-/l*`
21×	`associate-*r/`
16×	`*-commutative`
15×	`tan-quot` `clear-num`
14×	`frac-2neg` `associate-/l/`
6×	`associate-*l/`
5×	`div-inv`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `unpow3` `swap-sqr` `associate-r` `associate-l` `un-div-inv` `fma-udef` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (sin z) (tan y))
12.0ms	(* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z)))
4.0ms	(pow (/ (* (sin z) (tan y)) (cos z)) 3)
1.0ms	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin z) (tan y)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z))) (* 1 (/ (* (sin z) (tan y)) (cos z))))) (- (tan a)))

series1.7s

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sin z) (tan y))
134.0ms	(* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z)))
153.0ms	(pow (/ (* (sin z) (tan y)) (cos z)) 3)
1.3s	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin z) (tan y)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (sin z) (tan y)) (cos z)) (/ (* (sin z) (tan y)) (cos z))) (* 1 (/ (* (sin z) (tan y)) (cos z))))) (- (tan a)))

simplify80.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	566	889
1	3069	863
2	5002	861

prune365.0ms

Filtered

73 candidates to 44 candidates (60.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	74	9	83

Merged error: 0.0b

Counts

83 → 9

regimes310.0ms

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	32	28
1	32	28

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3905×	body	1280	valid
467.0ms	2006×	body	640	valid
316.0ms	8000×	pre	80	true
103.0ms	641×	body	320	valid
56.0ms	1147×	body	80	valid
35.0ms	301×	body	160	valid