Details

sample113.0ms

Algorithm

intervals

Results

56.0ms	131×	body	1280	valid
14.0ms	63×	body	640	valid
11.0ms	256×	pre	80	true
4.0ms	24×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	7×	body	160	valid

simplify22.0ms

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: 13.5b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.9b	(tan (+ y z))

rewrite23.0ms

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:

10.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series294.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(+ x (- (tan (+ y z)) (tan a)))
116.0ms	(- (tan (+ y z)) (tan a))
51.0ms	(tan (+ y z))

simplify93.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (86.0ms)

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

prune220.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

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:

18.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(+ (tan y) (tan z))
18.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series940.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
93.0ms	(+ (tan y) (tan z))
396.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
99.0ms	(* (tan y) (tan z))

simplify79.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (51.0ms)

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

prune613.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	214	5	219
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	217	10	227

Merged error: 0.0b

Counts

227 → 10

localize24.0ms

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×	`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))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series825.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (+ (tan y) (tan z)) (cos a))
94.0ms	(* (tan y) (tan z))
95.0ms	(* (tan y) (tan z))
487.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify80.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	607	1367
1	2835	1200
2	5001	1193

prune444.0ms

Filtered

116 candidates to 91 candidates (78.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.6b	(pow (+ (tan y) (tan z)) 3)
5.7b	(cbrt (pow (+ (tan y) (tan z)) 3))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

247×	`*-un-lft-identity`
209×	`times-frac`
207×	`add-sqr-sqrt`
189×	`add-cube-cbrt`
186×	`cbrt-prod`
171×	`prod-diff`
57×	`unpow-prod-down` `fma-neg` `cube-prod`
28×	`distribute-lft-out`
15×	`sqr-pow`
14×	`cube-mult` `unpow3`
9×	`tan-quot`
8×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cube-div` `add-log-exp` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l`
2×	`flip3-+` `frac-add` `flip-+`
1×	`frac-times` `pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `prod-exp` `*-commutative` `frac-sub` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 331

Calls

4 calls:

31.0ms	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
6.0ms	(pow (+ (tan y) (tan z)) 3)
6.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

series704.0ms

Counts

4 → 12

Calls

4 calls:

393.0ms	(- (/ (cbrt (pow (+ (tan y) (tan z)) 3)) (- 1 (* (tan y) (tan z)))) (tan a))
95.0ms	(* (tan y) (tan z))
119.0ms	(pow (+ (tan y) (tan z)) 3)
96.0ms	(cbrt (pow (+ (tan y) (tan z)) 3))

simplify130.0ms

Algorithm

egg-herbie

Counts

343 → 343

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	898	7361
1	2977	5432
2	5001	5393

prune600.0ms

Filtered

343 candidates to 132 candidates (38.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	342	1	343
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	343	10	353

Merged error: 0.0b

Counts

353 → 10

regimes631.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3916×	body	1280	valid
453.0ms	1949×	body	640	valid
329.0ms	8000×	pre	80	true
115.0ms	717×	body	320	valid
53.0ms	1116×	body	80	valid
33.0ms	302×	body	160	valid