Details

sample144.0ms

Algorithm

intervals

Results

73.0ms	138×	body	1280	valid
20.0ms	256×	pre	80	true
19.0ms	64×	body	640	valid
4.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid
2.0ms	25×	body	80	valid

simplify28.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

9.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series327.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ x (- (tan (+ y z)) (tan a)))
129.0ms	(- (tan (+ y z)) (tan a))
58.0ms	(tan (+ y z))

simplify102.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (95.0ms)

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

prune253.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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)) (- 1 (* (tan y) (tan z))))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.3b	(* (tan y) (tan z))

rewrite165.0ms

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:

83.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
53.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

395.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
240.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
447.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
110.0ms	(* (tan y) (tan z))

simplify91.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (59.0ms)

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

prune804.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
90×	`prod-diff`
44×	`difference-of-squares`
31×	`distribute-lft-out`
30×	`fma-neg`
22×	`distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`pow1` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`tan-quot` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 236

Calls

4 calls:

20.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
102.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
5.0ms	(/ (* (tan y) (sin z)) (cos z))
5.0ms	(* (tan y) (sin z))

series893.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))
450.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
113.0ms	(/ (* (tan y) (sin z)) (cos z))
83.0ms	(* (tan y) (sin z))

simplify103.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	694	4972
1	2578	4045
2	5001	4005

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan y) (sin z)) (cos z))
0.2b	(* (tan y) (sin z))
0.2b	(/ 1 (/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z))))
0.3b	(/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

221×	`*-un-lft-identity`
216×	`times-frac`
161×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
42×	`difference-of-squares`
38×	`associate-/r*`
31×	`distribute-lft-out`
24×	`add-exp-log`
21×	`distribute-lft-out--`
18×	`add-cbrt-cube`
16×	`associate-/r/`
12×	`tan-quot`
10×	`div-exp` `associate-/l*`
7×	`pow1` `div-inv`
6×	`cbrt-undiv`
5×	`flip3-+` `frac-add` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num` `associate-/l/`
2×	`rec-exp` `1-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`flip3--` `pow-flip` `div-sub` `pow-prod-down` `*-commutative` `flip--` `inv-pow` `unswap-sqr`

Counts

4 → 249

Calls

4 calls:

5.0ms	(/ (* (tan y) (sin z)) (cos z))
5.0ms	(* (tan y) (sin z))
22.0ms	(/ 1 (/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z))))
24.0ms	(/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z)))

series721.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (* (tan y) (sin z)) (cos z))
79.0ms	(* (tan y) (sin z))
233.0ms	(/ 1 (/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z))))
299.0ms	(/ (- 1 (/ (* (tan y) (sin z)) (cos z))) (+ (tan y) (tan z)))

simplify106.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	836	4238
1	3919	3910
2	5001	3745

prune747.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes292.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	3907×	body	1280	valid
607.0ms	8000×	pre	80	true
586.0ms	1991×	body	640	valid
136.0ms	664×	body	320	valid
76.0ms	1159×	body	80	valid
43.0ms	279×	body	160	valid