Details

sample107.0ms

Algorithm

intervals

Results

54.0ms	131×	body	1280	valid
14.0ms	57×	body	640	valid
11.0ms	256×	pre	80	true
3.0ms	19×	body	320	valid
2.0ms	45×	body	80	valid
0.0ms	4×	body	160	valid

simplify25.0ms

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: 15.1b

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))

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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
13.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series318.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(+ x (- (tan (+ y z)) (tan a)))
127.0ms	(- (tan (+ y z)) (tan a))
56.0ms	(tan (+ y z))

simplify97.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (89.0ms)

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

prune247.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

19.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
19.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(+ (tan y) (tan z))
6.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

421.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
379.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
102.0ms	(+ (tan y) (tan z))
105.0ms	(* (tan y) (tan z))

simplify87.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	676	4084
1	2087	3388
2	5001	3157

prune711.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	206	13	219
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	214	13	227

Merged error: 0.0b

Counts

227 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
44×	`tan-quot`
22×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
16×	`add-sqr-sqrt`
14×	`associate-r/` `associate-l/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `pow-sqr` `*-commutative` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

4 → 120

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
11.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (tan y) (tan z))
101.0ms	(* (tan y) (tan z))
101.0ms	(* (tan y) (tan z))
128.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	319	802
1	1443	681
2	5001	660

prune521.0ms

Filtered

132 candidates to 83 candidates (62.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Merged error: 0.0b

Counts

145 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`tan-quot` `pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`
1×	`frac-times` `associate-+r+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

3.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
5.0ms	(+ (tan y) (tan z))
1.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
6.0ms	(* (tan y) (tan z))

series880.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a))))
102.0ms	(+ (tan y) (tan z))
369.0ms	(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (tan a)))
103.0ms	(* (tan y) (tan z))

simplify83.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	318	751
1	968	707
2	3021	704
3	5001	702

prune340.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 0.0b

Counts

93 → 10

regimes304.0ms

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	34	24
1	34	24

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3816×	body	1280	valid
501.0ms	2058×	body	640	valid
321.0ms	8000×	pre	80	true
121.0ms	695×	body	320	valid
57.0ms	1165×	body	80	valid
31.0ms	266×	body	160	valid