Details

sample317.0ms

Algorithm

intervals

Results

200.0ms	52×	body	640	valid
61.0ms	131×	body	1280	valid
18.0ms	256×	pre	80	true
5.0ms	28×	body	320	valid
2.0ms	36×	body	80	valid
1.0ms	9×	body	160	valid

simplify449.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 12.9b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
5.1b	(tan (+ y z))

rewrite20.0ms

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))
6.0ms	(tan (+ y z))

series108.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ x (- (tan (+ y z)) (tan a)))
42.0ms	(- (tan (+ y z)) (tan a))
25.0ms	(tan (+ y z))

simplify62.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5182	570

prune104.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 0.1b

Counts

52 → 8

localize16.0ms

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

rewrite37.0ms

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:

4.0ms	(+ (tan y) (tan z))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series293.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (tan y) (tan z))
128.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
120.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify40.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5564	1289

prune141.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

18.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
17.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
5.0ms	(* (tan y) (sin z))
6.0ms	(/ (* (tan y) (sin z)) (cos z))

series289.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
121.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
15.0ms	(* (tan y) (sin z))
25.0ms	(/ (* (tan y) (sin z)) (cos z))

simplify38.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5172	1496

prune133.0ms

Filtered

65 candidates to 86 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (sin z) (cos y))
20.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (sin z) (cos y))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
10.0ms	(/ (+ (* (sin y) (cos z)) (* (sin z) (cos y))) (* (cos y) (cos z)))
5.0ms	(* (tan y) (tan z))

series186.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin z) (cos y))
123.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (sin z) (cos y))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
32.0ms	(/ (+ (* (sin y) (cos z)) (* (sin z) (cos y))) (* (cos y) (cos z)))
22.0ms	(* (tan y) (tan z))

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4976	1602
1	4976	1602

prune94.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 0.0b

Counts

103 → 10

regimes665.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	30
1	29	30

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	3850×	body	1280	valid
534.0ms	8000×	pre	80	true
488.0ms	2031×	body	640	valid
120.0ms	723×	body	320	valid
56.0ms	1095×	body	80	valid
37.0ms	301×	body	160	valid

Details

sample317.0ms

simplify449.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series108.0ms

simplify62.0ms

prune104.0ms

localize16.0ms

rewrite37.0ms

series293.0ms

simplify40.0ms

prune141.0ms

localize23.0ms

rewrite47.0ms

series289.0ms

simplify38.0ms

prune133.0ms

localize29.0ms

rewrite41.0ms

series186.0ms

simplify47.0ms

prune94.0ms

regimes665.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.5s

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