Details

sample100.0ms

Algorithm

intervals

Results

49.0ms	124×	body	1280	valid
13.0ms	59×	body	640	valid
10.0ms	256×	pre	80	true
4.0ms	28×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	12×	body	160	valid

simplify20.0ms

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

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: 14.0b

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))
1.6b	(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:

11.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series295.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(+ x (- (tan (+ y z)) (tan a)))
118.0ms	(- (tan (+ y z)) (tan a))
51.0ms	(tan (+ y z))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

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

prune143.0ms

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

rewrite44.0ms

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:

19.0ms	(+ 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))

series898.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
93.0ms	(+ (tan y) (tan z))
378.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
93.0ms	(* (tan y) (tan z))

simplify80.0ms

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

prune263.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`tan-quot` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `-commutative` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `associate-l/` `clear-num` `associate-/r*` `associate-/r/` `cos-mult` `sin-cos-mult` `flip-+` `div-inv`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (cos y) (sin z))
5.0ms	(* (sin y) (cos z))
5.0ms	(* (tan y) (tan z))
10.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos y) (sin z))
42.0ms	(* (sin y) (cos z))
92.0ms	(* (tan y) (tan z))
144.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	425	757
1	1759	645
2	5001	645

prune375.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 0.0b

Counts

103 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.6b	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
1.7b	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))
14.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
14.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

362.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
88.0ms	(* (tan y) (tan z))
785.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
377.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	410	1748
1	1533	1668
2	5001	1660

prune273.0ms

Filtered

111 candidates to 68 candidates (61.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	111	8	119

Merged error: 0.0b

Counts

119 → 8

regimes445.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	3896×	body	1280	valid
433.0ms	1943×	body	640	valid
314.0ms	8000×	pre	80	true
108.0ms	712×	body	320	valid
53.0ms	1141×	body	80	valid
32.0ms	308×	body	160	valid