Details

sample117.0ms

Algorithm

intervals

Results

54.0ms	121×	body	1280	valid
17.0ms	68×	body	640	valid
17.0ms	256×	pre	80	true
6.0ms	16×	body	320	valid
2.0ms	44×	body	80	valid
1.0ms	7×	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: 13.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
1.9b	(tan (+ y z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `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 → 72

Calls

3 calls:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series272.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(+ x (- (tan (+ y z)) (tan a)))
109.0ms	(- (tan (+ y z)) (tan a))
51.0ms	(tan (+ y z))

simplify86.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune200.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Merged error: 0.0b

Counts

82 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
13.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series974.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
322.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
363.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
88.0ms	(* (tan y) (tan z))

simplify81.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667

prune604.0ms

Filtered

239 candidates to 145 candidates (60.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	237	8	245

Merged error: 0.0b

Counts

245 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 104

Calls

4 calls:

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

series766.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (+ (tan y) (tan z)) (cos a))
450.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
87.0ms	(* (tan y) (tan z))
89.0ms	(* (tan y) (tan z))

simplify77.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	607	1367
1	2828	1200
2	5002	1193

prune415.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	116	8	124

Merged error: 0.0b

Counts

124 → 8

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.8b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `cbrt-div` `pow1/3`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
1.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (tan a))
111.0ms	(cbrt (tan a))
110.0ms	(cbrt (tan a))
175.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (93.0ms)

Iter	Nodes	Cost
0	102	427
1	211	373
2	675	363
3	2633	349
4	5002	337

prune320.0ms

Filtered

64 candidates to 57 candidates (89.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 0.0b

Counts

72 → 8

regimes549.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3887×	body	1280	valid
524.0ms	8000×	pre	80	true
492.0ms	1994×	body	640	valid
118.0ms	709×	body	320	valid
60.0ms	1153×	body	80	valid
31.0ms	257×	body	160	valid