Details

sample106.0ms

Algorithm

intervals

Results

51.0ms	131×	body	1280	valid
17.0ms	57×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	19×	body	320	valid
2.0ms	45×	body	80	valid
0.0ms	4×	body	160	valid

simplify20.0ms

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))

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)))
4.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series280.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(+ x (- (tan (+ y z)) (tan a)))
115.0ms	(- (tan (+ y z)) (tan a))
50.0ms	(tan (+ y z))

simplify68.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	156	202
1	359	202
2	859	201
3	2919	201
4	5001	201

prune70.0ms

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

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)))
3.0ms	(+ (tan y) (tan z))
4.0ms	(* (tan z) (tan y))

series885.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
332.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
94.0ms	(+ (tan y) (tan z))
91.0ms	(* (tan z) (tan y))

simplify90.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	321	548
1	1005	545
2	3675	533
3	5002	533

prune165.0ms

Filtered

36 candidates to 30 candidates (83.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	33	8	41

Merged error: 0.1b

Counts

41 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan z) (tan y))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.5b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

38×	`tan-quot`
11×	`associate-/l/`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-l/`
7×	`*-commutative`
4×	`associate-/l*` `difference-of-squares`
3×	`associate-/r/`
2×	`pow2` `flip3--` `flip--`
1×	`frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

4 → 36

Calls

4 calls:

3.0ms	(* (tan z) (tan y))
4.0ms	(* (tan z) (tan z))
4.0ms	(* (tan y) (tan y))
12.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (tan z) (tan y))
33.0ms	(* (tan z) (tan z))
30.0ms	(* (tan y) (tan y))
214.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify76.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	271	300
1	869	299
2	3028	292
3	5002	292

prune226.0ms

Filtered

48 candidates to 35 candidates (72.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	48	8	56

Merged error: 0.1b

Counts

56 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
3.1b	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))
5.6b	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`tan-quot`
6×	`associate-/r/` `associate-/l/`
4×	`frac-times` `associate-r/` `associate-l/` `-commutative` `associate-/l`
2×	`pow2` `flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv`

Counts

4 → 32

Calls

4 calls:

4.0ms	(* (tan z) (tan z))
4.0ms	(* (tan y) (tan y))
8.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))
8.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (tan z) (tan z))
31.0ms	(* (tan y) (tan y))
207.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))
219.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	232	277
1	711	277
2	2146	272
3	5002	271

prune168.0ms

Filtered

44 candidates to 32 candidates (72.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Merged error: 0.1b

Counts

52 → 8

regimes255.0ms

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	23
1	23	23

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3816×	body	1280	valid
513.0ms	2058×	body	640	valid
320.0ms	8000×	pre	80	true
116.0ms	695×	body	320	valid
57.0ms	1165×	body	80	valid
35.0ms	266×	body	160	valid