Details

sample120.0ms

Algorithm

intervals

Results

59.0ms	131×	body	1280	valid
15.0ms	63×	body	640	valid
11.0ms	256×	pre	80	true
9.0ms	24×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	7×	body	160	valid

simplify26.0ms

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: 13.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.9b	(tan (+ y z))

rewrite18.0ms

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

series335.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms	(+ x (- (tan (+ y z)) (tan a)))
130.0ms	(- (tan (+ y z)) (tan a))
61.0ms	(tan (+ y z))

simplify52.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (18.0ms)

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

prune168.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(+ (tan y) (tan z))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

413.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
112.0ms	(+ (tan y) (tan z))
448.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
109.0ms	(* (tan y) (tan z))

simplify94.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (35.0ms)

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

prune304.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	74	12	86

Merged error: 0.0b

Counts

86 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
0.2b	(* (tan y) (tan z))
0.2b	(pow (* (tan y) (tan z)) 3)
29.3b	(cbrt (pow (* (tan y) (tan z)) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

26.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
6.0ms	(* (tan y) (tan z))
9.0ms	(pow (* (tan y) (tan z)) 3)
5.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

series820.0ms

Counts

4 → 12

Calls

4 calls:

445.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan y) (tan z)) 3)))) (tan a))
113.0ms	(* (tan y) (tan z))
148.0ms	(pow (* (tan y) (tan z)) 3)
114.0ms	(cbrt (pow (* (tan y) (tan z)) 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	377	783
1	1645	739
2	5001	738

prune344.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	94	12	106

Merged error: 0.0b

Counts

106 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
6.0ms	(* (sin y) (sin z))
21.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
14.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

series750.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (tan y) (tan z))
58.0ms	(* (sin y) (sin z))
467.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos y) (cos z))))) (tan a))
119.0ms	(/ (* (sin y) (sin z)) (* (cos y) (cos z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	432	913
1	1774	787
2	5001	787

prune317.0ms

Filtered

83 candidates to 60 candidates (72.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	84	11	95

Merged error: 0.0b

Counts

95 → 11

regimes660.0ms

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

sample3.1s

Algorithm

intervals

Results

1.7s	3916×	body	1280	valid
479.0ms	1949×	body	640	valid
347.0ms	8000×	pre	80	true
115.0ms	717×	body	320	valid
54.0ms	1116×	body	80	valid
33.0ms	302×	body	160	valid