Details

sample121.0ms

Algorithm

intervals

Results

54.0ms	125×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	65×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	8×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.4b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.8b	(tan (+ y z))

rewrite22.0ms

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:

8.0ms	(- (tan (+ y z)) (tan a))
8.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series340.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(- (tan (+ y z)) (tan a))
148.0ms	(+ x (- (tan (+ y z)) (tan a)))
57.0ms	(tan (+ y z))

simplify105.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3057	507
3	5001	488

prune244.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 0.1b

Counts

82 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
17.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
6.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (tan y) (tan z))
440.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
402.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
114.0ms	(* (tan y) (tan z))

simplify87.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	676	4084
1	2087	3388
2	5001	3151

prune694.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	208	11	219
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	215	12	227

Merged error: 0.0b

Counts

227 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

321×	`*-un-lft-identity`
237×	`add-sqr-sqrt`
180×	`prod-diff`
172×	`times-frac`
146×	`add-cube-cbrt`
92×	`associate-+r+`
58×	`difference-of-squares`
44×	`distribute-lft-out`
30×	`fma-neg` `distribute-lft-out--`
14×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`flip3--` `flip--` `div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`tan-quot` `fma-def` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-*l/` `prod-exp` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 295

Calls

4 calls:

28.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
6.0ms	(* (tan y) (sin z))
29.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
7.0ms	(/ (* (tan y) (sin z)) (cos z))

series1.1s

Counts

4 → 12

Calls

4 calls:

459.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
72.0ms	(* (tan y) (sin z))
406.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
117.0ms	(/ (* (tan y) (sin z)) (cos z))

simplify117.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	804	7012
1	2580	5836
2	5001	5650

prune860.0ms

Filtered

307 candidates to 150 candidates (48.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	305	2	307
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	307	12	319

Merged error: 0.0b

Counts

319 → 12

localize22.0ms

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)))

rewrite41.0ms

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:

8.0ms	(* (+ (tan y) (tan z)) (cos a))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (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)))

series900.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (+ (tan y) (tan z)) (cos a))
102.0ms	(* (tan y) (tan z))
99.0ms	(* (tan y) (tan z))
535.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	607	1365
1	2835	1198
2	5001	1191

prune450.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	116	12	128

Merged error: 0.0b

Counts

128 → 12

regimes450.0ms

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

sample3.3s

Algorithm

intervals

Results

1.7s	3900×	body	1280	valid
550.0ms	8000×	pre	80	true
504.0ms	2016×	body	640	valid
114.0ms	665×	body	320	valid
62.0ms	1150×	body	80	valid
32.0ms	269×	body	160	valid