Details

sample169.0ms

Algorithm

intervals

Results

96.0ms	131×	body	1280	valid
24.0ms	59×	body	640	valid
15.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
3.0ms	30×	body	80	valid
3.0ms	12×	body	160	valid

simplify18.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
5.1b	(tan (+ y z))

rewrite19.0ms

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:

8.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series290.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(+ x (- (tan (+ y z)) (tan a)))
115.0ms	(- (tan (+ y z)) (tan a))
56.0ms	(tan (+ y z))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (12.0ms)

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

prune144.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

3.0ms	(+ (tan y) (tan z))
41.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
72.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series911.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan y) (tan z))
385.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
339.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
94.0ms	(* (tan y) (tan z))

simplify82.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune293.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.7b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan z) (tan z))
5.0ms	(* (tan y) (tan y))
19.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan y) (tan z))
39.0ms	(* (tan z) (tan z))
32.0ms	(* (tan y) (tan y))
234.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify77.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	521	1251
1	2392	1138
2	5001	1094

prune537.0ms

Filtered

145 candidates to 98 candidates (67.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.0b	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
4.7b	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`tan-quot`
18×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`add-cube-cbrt`
10×	`times-frac` `associate-/r*`
6×	`swap-sqr` `associate-r` `associate-l` `associate-/r/` `associate-/l/`
4×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow2` `flip3--` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `pow-sqr` `-commutative` `pow-prod-up` `frac-sub` `flip--` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

5.0ms	(* (tan z) (tan z))
5.0ms	(* (tan y) (tan y))
9.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
10.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (tan z) (tan z))
37.0ms	(* (tan y) (tan y))
221.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
225.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

simplify80.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	464	881
1	2414	789
2	5001	780

prune424.0ms

Filtered

130 candidates to 84 candidates (64.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes254.0ms

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	24	23
1	24	23

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.0s	3879×	body	1280	valid
920.0ms	2024×	body	640	valid
338.0ms	8000×	pre	80	true
207.0ms	683×	body	320	valid
109.0ms	1123×	body	80	valid
64.0ms	291×	body	160	valid