Details

sample179.0ms

Algorithm

intervals

Results

67.0ms	127×	body	1280	valid
29.0ms	256×	pre	80	true
24.0ms	67×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	29×	body	80	valid
1.0ms	7×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	9
1	70	9

prune6.0ms

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: 14.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
4.3b	(tan (+ y z))

rewrite23.0ms

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:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series120.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ x (- (tan (+ y z)) (tan a)))
38.0ms	(- (tan (+ y z)) (tan a))
35.0ms	(tan (+ y z))

simplify64.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4853	570
1	4853	570

prune94.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.1b

Counts

52 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:

6.0ms	(+ (tan y) (tan z))
14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
13.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series338.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (tan y) (tan z))
146.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
138.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
28.0ms	(* (tan y) (tan z))

simplify36.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5564	1289

prune178.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	70	14	84

Merged error: 0.1b

Counts

84 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

21.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a)))
20.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
6.0ms	(* (sin y) (sin z))
9.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a)))
135.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
11.0ms	(* (sin y) (sin z))
26.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4983	1680
1	4983	1680

prune153.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	88	13	101

Merged error: 0.1b

Counts

101 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos z) (sin z))
0.2b	(/ (cos y) (sin y))
0.3b	(* (/ (cos y) (sin y)) (/ (cos z) (sin z)))
0.7b	(/ 1 (* (/ (cos y) (sin y)) (/ (cos z) (sin z))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
48×	`add-sqr-sqrt`
43×	`times-frac`
38×	`add-cbrt-cube`
36×	`add-cube-cbrt` `*-un-lft-identity`
28×	`div-exp`
16×	`prod-exp`
15×	`cbrt-undiv`
13×	`associate-r` `associate-l`
9×	`pow1` `associate-/l*`
8×	`cbrt-unprod`
7×	`associate-/r*`
5×	`rec-exp` `1-exp` `div-inv`
4×	`add-log-exp` `unswap-sqr`
3×	`frac-2neg` `clear-num` `associate-/r/`
2×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/`
1×	`*-commutative` `inv-pow`

Counts

4 → 147

Calls

4 calls:

5.0ms	(/ (cos z) (sin z))
7.0ms	(/ (cos y) (sin y))
13.0ms	(* (/ (cos y) (sin y)) (/ (cos z) (sin z)))
11.0ms	(/ 1 (* (/ (cos y) (sin y)) (/ (cos z) (sin z))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (cos z) (sin z))
7.0ms	(/ (cos y) (sin y))
25.0ms	(* (/ (cos y) (sin y)) (/ (cos z) (sin z)))
25.0ms	(/ 1 (* (/ (cos y) (sin y)) (/ (cos z) (sin z))))

simplify55.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5123	1743

prune143.0ms

Filtered

107 candidates to 159 candidates (-48.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	159	13	172

Merged error: 0.1b

Counts

172 → 13

regimes931.0ms

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	25	26
1	25	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.7s	3963×	body	1280	valid
614.0ms	8000×	pre	80	true
522.0ms	2013×	body	640	valid
119.0ms	666×	body	320	valid
59.0ms	1056×	body	80	valid
38.0ms	302×	body	160	valid

Details

sample179.0ms

simplify11.0ms

prune6.0ms

localize12.0ms

rewrite23.0ms

series120.0ms

simplify64.0ms

prune94.0ms

localize17.0ms

rewrite41.0ms

series338.0ms

simplify36.0ms

prune178.0ms

localize26.0ms

rewrite61.0ms

series317.0ms

simplify51.0ms

prune153.0ms

localize27.0ms

rewrite42.0ms

series64.0ms

simplify55.0ms

prune143.0ms

regimes931.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.6s

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