Details

sample126.0ms

Algorithm

intervals

Results

57.0ms	132×	body	1280	valid
23.0ms	256×	pre	80	true
15.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	9×	body	160	valid

simplify30.0ms

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: 14.3b

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))
4.8b	(tan (+ y z))

rewrite26.0ms

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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
12.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series330.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(+ x (- (tan (+ y z)) (tan a)))
132.0ms	(- (tan (+ y z)) (tan a))
58.0ms	(tan (+ y z))

simplify111.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (100.0ms)

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

prune275.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	68	13	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	13	82

Merged error: 0.1b

Counts

82 → 13

localize18.0ms

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))

rewrite64.0ms

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:

6.0ms	(+ (tan y) (tan z))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (tan y) (tan z))
387.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
445.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
109.0ms	(* (tan y) (tan z))

simplify91.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5001	3265

prune668.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	209	10	219
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	215	17	232

Merged error: 0.1b

Counts

232 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
12×	`times-frac` `prod-diff`
11×	`add-log-exp`
10×	`tan-quot` `distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+` `associate-/l/`
2×	`flip3--` `diff-log` `frac-add` `sum-log` `associate-/r/` `frac-sub` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

9.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
9.0ms	(+ (tan y) (tan z))
16.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
6.0ms	(* (tan y) (tan z))

series788.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
99.0ms	(+ (tan y) (tan z))
364.0ms	(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
101.0ms	(* (tan y) (tan z))

simplify67.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	529	1617
1	1908	1421
2	5001	1403

prune396.0ms

Filtered

128 candidates to 92 candidates (71.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	5	11	16
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Merged error: 0.0b

Counts

145 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan z)) (cbrt (tan z)))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))
0.6b	(cbrt (tan z))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
2.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))
2.0ms	(cbrt (tan z))

series534.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (cbrt (tan z)) (cbrt (tan z)))
132.0ms	(cbrt (tan z))
125.0ms	(cbrt (tan z))
127.0ms	(cbrt (tan z))

simplify81.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	176	527
1	546	490
2	2172	458
3	5001	454

prune332.0ms

Filtered

99 candidates to 73 candidates (73.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	99	14	113

Merged error: 0.0b

Counts

113 → 14

regimes743.0ms

Accuracy

0% (0.2b 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	19	11
1	19	11

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3822×	body	1280	valid
548.0ms	8000×	pre	80	true
519.0ms	2067×	body	640	valid
119.0ms	697×	body	320	valid
62.0ms	1119×	body	80	valid
38.0ms	295×	body	160	valid