Details

sample126.0ms

Algorithm

intervals

Results

60.0ms	123×	body	1280	valid
19.0ms	256×	pre	80	true
16.0ms	59×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	42×	body	80	valid
1.0ms	9×	body	160	valid

simplify27.0ms

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: 12.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.9b	(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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series330.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(+ x (- (tan (+ y z)) (tan a)))
130.0ms	(- (tan (+ y z)) (tan a))
62.0ms	(tan (+ y z))

simplify102.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (94.0ms)

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

prune227.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 0.1b

Counts

82 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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))
20.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
15.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series972.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan y) (tan z))
360.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
413.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
103.0ms	(* (tan y) (tan z))

simplify83.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	676	4084
1	2087	3388
2	5001	3271

prune617.0ms

Filtered

219 candidates to 132 candidates (60.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	218	10	228

Merged error: 0.0b

Counts

228 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 185

Calls

4 calls:

5.0ms	(/ (sin z) (cos z))
5.0ms	(/ (sin y) (cos y))
28.0ms	(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
6.0ms	(* (tan y) (tan z))

series547.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin z) (cos z))
20.0ms	(/ (sin y) (cos y))
405.0ms	(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (tan y) (tan z)))) (tan a))
101.0ms	(* (tan y) (tan z))

simplify80.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	658	3456
1	2136	2806
2	5001	2760

prune645.0ms

Filtered

197 candidates to 118 candidates (59.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	197	10	207

Merged error: 0.0b

Counts

207 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.7b	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
2.2b	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
54×	`prod-diff`
53×	`times-frac`
18×	`cbrt-prod` `fma-neg`
12×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
10×	`difference-of-squares`
8×	`associate-/r/`
7×	`tan-quot` `pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
6×	`cube-div` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `cbrt-div` `associate-r` `associate-l` `frac-sub`
2×	`cube-mult` `unpow3` `sqr-pow`
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` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 179

Calls

4 calls:

15.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
17.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
14.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

417.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
98.0ms	(* (tan y) (tan z))
639.0ms	(pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3)
406.0ms	(cbrt (pow (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	620	3625
1	2348	3053
2	5001	3023

prune470.0ms

Filtered

191 candidates to 103 candidates (53.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	191	10	201

Merged error: 0.0b

Counts

201 → 10

regimes618.0ms

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	25	15
1	25	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3928×	body	1280	valid
544.0ms	8000×	pre	80	true
499.0ms	1965×	body	640	valid
117.0ms	668×	body	320	valid
62.0ms	1150×	body	80	valid
35.0ms	289×	body	160	valid