Details

sample305.0ms

Algorithm

intervals

Results

52.0ms	115×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	64×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	35×	body	80	valid
0.0ms	4×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 12.4b

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))
3.7b	(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)))
33.0ms	(- (tan (+ y z)) (tan a))
32.0ms	(tan (+ y z))

simplify37.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (11.0ms)

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

prune90.0ms

Filtered

51 candidates to 39 candidates (23.5%)

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	(- 1 (* (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))
0.3b	(* (tan y) (tan z))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(- 1 (* (tan y) (tan z)))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
14.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series297.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- 1 (* (tan y) (tan z)))
129.0ms	(+ 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))

simplify85.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	356	871
1	1108	831
2	3700	824
3	5001	824

prune141.0ms

Filtered

78 candidates to 57 candidates (26.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.1b	(- (/ (+ (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) (sin 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))
6.0ms	(/ (* (tan y) (sin z)) (cos z))
5.0ms	(* (tan y) (sin z))

series285.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
119.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
22.0ms	(/ (* (tan y) (sin z)) (cos z))
17.0ms	(* (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

prune131.0ms

Filtered

86 candidates to 62 candidates (27.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.1b

Counts

96 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- 1 (* (tan y) (tan z))) 3))
0.1b	(- (/ (+ (tan y) (tan z)) (cbrt (pow (- 1 (* (tan y) (tan z))) 3))) (tan a))
0.2b	(pow (- 1 (* (tan y) (tan z))) 3)
0.3b	(* (tan y) (tan z))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

3.0ms	(cbrt (pow (- 1 (* (tan y) (tan z))) 3))
28.0ms	(- (/ (+ (tan y) (tan z)) (cbrt (pow (- 1 (* (tan y) (tan z))) 3))) (tan a))
4.0ms	(pow (- 1 (* (tan y) (tan z))) 3)
5.0ms	(* (tan y) (tan z))

series204.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt (pow (- 1 (* (tan y) (tan z))) 3))
121.0ms	(- (/ (+ (tan y) (tan z)) (cbrt (pow (- 1 (* (tan y) (tan z))) 3))) (tan a))
38.0ms	(pow (- 1 (* (tan y) (tan z))) 3)
21.0ms	(* (tan y) (tan z))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	402	1065
1	1536	998
2	5002	979

prune112.0ms

Filtered

101 candidates to 64 candidates (36.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	101	10	111

Merged error: 0.1b

Counts

111 → 10

regimes856.0ms

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

1.7s	3893×	body	1280	valid
527.0ms	8000×	pre	80	true
484.0ms	1948×	body	640	valid
124.0ms	738×	body	320	valid
56.0ms	1125×	body	80	valid
34.0ms	296×	body	160	valid

Details

sample305.0ms

simplify22.0ms

prune6.0ms

localize13.0ms

rewrite20.0ms

series109.0ms

simplify37.0ms

prune90.0ms

localize16.0ms

rewrite36.0ms

series297.0ms

simplify85.0ms

prune141.0ms

localize21.0ms

rewrite47.0ms

series285.0ms

simplify39.0ms

prune131.0ms

localize18.0ms

rewrite44.0ms

series204.0ms

simplify49.0ms

prune112.0ms

regimes856.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling