Details

sample107.0ms

Algorithm

intervals

Results

45.0ms	104×	body	1280	valid
16.0ms	256×	pre	80	true
15.0ms	64×	body	640	valid
5.0ms	34×	body	320	valid
2.0ms	37×	body	80	valid
2.0ms	17×	body	160	valid

simplify19.0ms

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

prune2.0ms

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: 11.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.4b	(tan (+ y z))

rewrite16.0ms

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))
4.0ms	(tan (+ y z))

series284.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(+ x (- (tan (+ y z)) (tan a)))
113.0ms	(- (tan (+ y z)) (tan a))
54.0ms	(tan (+ y z))

simplify40.0ms

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

prune157.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	10	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Merged error: 0.1b

Counts

52 → 10

localize15.0ms

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))
0.2b	(* (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))
13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series902.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan y) (tan z))
340.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
378.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
92.0ms	(* (tan y) (tan z))

simplify76.0ms

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

prune256.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	8	79
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 0.1b

Counts

89 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

7.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
17.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (+ (tan y) (tan z)) (cos a))
89.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))
463.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify75.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	587	1304
1	2701	1144
2	5003	1128

prune397.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1`
44×	`tan-quot`
27×	`associate-*l/`
26×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-*r/`
11×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow-pow` `flip3-+` `pow-plus` `div-exp` `frac-add` `pow-exp` `associate-/r/` `*-commutative` `flip-+` `rem-cube-cbrt`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `div-sub` `cube-prod` `swap-sqr` `clear-num` `associate-/r*` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
20.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
10.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
5.0ms	(pow (* (tan y) (tan z)) 3)

series885.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (tan y) (tan z))
539.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (pow (* (tan y) (tan z)) 3)) (cos a)))
111.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
122.0ms	(pow (* (tan y) (tan z)) 3)

simplify122.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	812	1495
1	4453	1335
2	5001	1331

prune509.0ms

Filtered

139 candidates to 88 candidates (63.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	139	10	149

Merged error: 0.0b

Counts

149 → 10

regimes441.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	36
1	47	36
2	47	36

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3868×	body	1280	valid
503.0ms	8000×	pre	80	true
457.0ms	1984×	body	640	valid
110.0ms	712×	body	320	valid
56.0ms	1151×	body	80	valid
34.0ms	285×	body	160	valid

Details

sample107.0ms

simplify19.0ms

prune2.0ms

localize10.0ms

rewrite16.0ms

series284.0ms

simplify40.0ms

prune157.0ms

localize15.0ms

rewrite35.0ms

series902.0ms

simplify76.0ms

prune256.0ms

localize19.0ms

rewrite37.0ms

series788.0ms

simplify75.0ms

prune397.0ms

localize30.0ms

rewrite45.0ms

series885.0ms

simplify122.0ms

prune509.0ms

regimes441.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling