Details

analyze17.0s

Algorithm: search

sample120.0ms

Algorithm

intervals

Results

52.0ms	129×	body	1280	valid
30.0ms	256×	pre	80	true
14.0ms	55×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	9×	body	160	valid

simplify373.0ms

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: 13.5b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.5b	(tan (+ y z))

rewrite19.0ms

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))

series117.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ x (- (tan (+ y z)) (tan a)))
33.0ms	(- (tan (+ y z)) (tan a))
44.0ms	(tan (+ y z))

simplify39.0ms

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

prune103.0ms

Filtered

39 candidates to 51 candidates (-30.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	9	52

Merged error: 0.1b

Counts

52 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(+ x (- (/ (+ (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))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series290.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (tan y) (tan z))
121.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
126.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
22.0ms	(* (tan y) (tan z))

simplify83.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (25.0ms)

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

prune154.0ms

Filtered

59 candidates to 79 candidates (-33.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 0.1b

Counts

88 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
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) (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	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
17.0ms	(+ x (- (/ (+ (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))

series287.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
129.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
22.0ms	(/ (* (tan y) (sin z)) (cos z))
15.0ms	(* (tan y) (sin z))

simplify42.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (33.0ms)

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

prune133.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	86	11	97

Merged error: 0.1b

Counts

97 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `flip-+` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-times` `associate-+r-` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `cos-mult` `-commutative` `frac-sub` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

17.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
18.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))
10.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
129.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
21.0ms	(* (tan y) (tan z))
34.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	488	1545
1	1655	1422
2	5002	1407

prune97.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	90	11	101

Merged error: 0.1b

Counts

101 → 11

regimes620.0ms

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

analyze16.0s

Algorithm: search

sample3.4s

Algorithm

intervals

Results

1.9s	3903×	body	1280	valid
522.0ms	8000×	pre	80	true
449.0ms	1935×	body	640	valid
119.0ms	736×	body	320	valid
68.0ms	1135×	body	80	valid
32.0ms	291×	body	160	valid

Details

analyze17.0s

sample120.0ms

simplify373.0ms

prune6.0ms

localize13.0ms

rewrite19.0ms

series117.0ms

simplify39.0ms

prune103.0ms

localize16.0ms

rewrite37.0ms

series290.0ms

simplify83.0ms

prune154.0ms

localize21.0ms

rewrite48.0ms

series287.0ms

simplify42.0ms

prune133.0ms

localize31.0ms

rewrite52.0ms

series306.0ms

simplify50.0ms

prune97.0ms

regimes620.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze16.0s

sample3.4s

Profiling