Details

sample315.0ms

Algorithm

intervals

Results

205.0ms	68×	body	640	valid
57.0ms	127×	body	1280	valid
18.0ms	256×	pre	80	true
4.0ms	24×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	5×	body	160	valid

simplify22.0ms

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

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: 15.1b

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))
4.7b	(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))

series109.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(+ x (- (tan (+ y z)) (tan a)))
32.0ms	(- (tan (+ y z)) (tan a))
33.0ms	(tan (+ y z))

simplify38.0ms

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

prune99.0ms

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: 0.2b

Counts

52 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(+ 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))
0.3b	(* (tan y) (tan z))

rewrite35.0ms

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

series286.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan y) (tan z))
123.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
121.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(* (tan y) (tan z))

simplify74.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (24.0ms)

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

prune136.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 0.1b

Counts

87 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))
0.6b	(pow (+ (tan y) (tan z)) 3)
6.6b	(cbrt (pow (+ (tan y) (tan z)) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`add-cube-cbrt`
9×	`tan-quot` `unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp` `difference-of-squares`
5×	`times-frac`
4×	`distribute-lft-out`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l` `sqr-pow`
2×	`cube-mult` `flip3-+` `unpow3` `frac-add` `flip-+`
1×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow1/3` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

24.0ms	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
5.0ms	(pow (+ (tan y) (tan z)) 3)
5.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

series191.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
23.0ms	(* (tan y) (tan z))
30.0ms	(pow (+ (tan y) (tan z)) 3)
20.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	448	1027
1	1674	969
2	5002	949

prune156.0ms

Filtered

67 candidates to 107 candidates (-59.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Merged error: 0.1b

Counts

115 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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:

19.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
5.0ms	(/ (* (tan y) (sin z)) (cos z))
16.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
5.0ms	(* (tan y) (sin z))

series281.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
22.0ms	(/ (* (tan y) (sin z)) (cos z))
118.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
15.0ms	(* (tan y) (sin z))

simplify39.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	391	1035
1	1334	960
2	5002	951

prune80.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 0.1b

Counts

94 → 9

regimes432.0ms

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	22	13
1	22	13

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	3844×	body	1280	valid
520.0ms	8000×	pre	80	true
472.0ms	1981×	body	640	valid
121.0ms	728×	body	320	valid
57.0ms	1174×	body	80	valid
33.0ms	273×	body	160	valid

Details

sample315.0ms

simplify22.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series109.0ms

simplify38.0ms

prune99.0ms

localize19.0ms

rewrite35.0ms

series286.0ms

simplify74.0ms

prune136.0ms

localize19.0ms

rewrite42.0ms

series191.0ms

simplify51.0ms

prune156.0ms

localize21.0ms

rewrite48.0ms

series281.0ms

simplify39.0ms

prune80.0ms

regimes432.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling