Details

sample101.0ms

Algorithm

intervals

Results

47.0ms	116×	body	1280	valid
15.0ms	62×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	20×	body	320	valid
2.0ms	44×	body	80	valid
2.0ms	14×	body	160	valid

simplify19.0ms

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: 12.9b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
1.4b	(tan (+ y z))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series276.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(+ x (- (tan (+ y z)) (tan a)))
114.0ms	(- (tan (+ y z)) (tan a))
49.0ms	(tan (+ y z))

simplify40.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune145.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-sub`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`flip3-+` `frac-add` `flip-+`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 92

Calls

4 calls:

9.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series936.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
89.0ms	(* (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
462.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify90.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	655	1689
1	3093	1518
2	5001	1501

prune484.0ms

Filtered

104 candidates to 83 candidates (79.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Merged error: 0.1b

Counts

110 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
17×	`times-frac`
14×	`add-cube-cbrt`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`tan-quot` `distribute-lft-out--` `difference-of-squares`
3×	`associate-r` `associate-l` `associate-/r` `distribute-lft-out` `associate-/l`
2×	`sub-neg` `associate-+r+` `diff-log` `sum-log`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `quot-tan` `flip3--` `frac-2neg` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (sin a) (cos a))))
4.0ms	(/ (sin a) (cos a))
21.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (sin a) (cos a)))
5.0ms	(* (tan y) (tan z))

series798.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (sin a) (cos a))))
18.0ms	(/ (sin a) (cos a))
359.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (sin a) (cos a)))
89.0ms	(* (tan y) (tan z))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	411	1116
1	1181	1067
2	3506	1062
3	5001	1062

prune356.0ms

Filtered

98 candidates to 74 candidates (75.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
44×	`tan-quot`
27×	`associate-*l/`
26×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-*r/`
11×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow-pow` `flip3-+` `pow-plus` `div-exp` `frac-add` `pow-exp` `associate-/r/` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `div-sub` `cube-prod` `swap-sqr` `clear-num` `associate-/r*` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
21.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (cos a)))
10.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
6.0ms	(pow (* (tan y) (tan z)) 3)

series845.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan y) (tan z))
528.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (cos a)))
110.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
121.0ms	(pow (* (tan y) (tan z)) 3)

simplify119.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	818	1495
1	4461	1335
2	5002	1331

prune600.0ms

Filtered

139 candidates to 88 candidates (63.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Merged error: 0.0b

Counts

147 → 7

regimes409.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	36
1	48	36
2	48	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3821×	body	1280	valid
481.0ms	1964×	body	640	valid
318.0ms	8000×	pre	80	true
120.0ms	711×	body	320	valid
62.0ms	1209×	body	80	valid
34.0ms	295×	body	160	valid