Details

sample181.0ms

Algorithm

intervals

Results

99.0ms	131×	body	1280	valid
32.0ms	59×	body	640	valid
12.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
3.0ms	30×	body	80	valid
3.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
5.1b	(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	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series301.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(+ x (- (tan (+ y z)) (tan a)))
120.0ms	(- (tan (+ y z)) (tan a))
57.0ms	(tan (+ y z))

simplify92.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (85.0ms)

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

prune255.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(- (/ (+ (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))

rewrite58.0ms

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))
16.0ms	(- (/ (+ (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))

series924.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan y) (tan z))
390.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
349.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
94.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (50.0ms)

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

prune737.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
1.0ms	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
6.0ms	(pow (* (tan y) (tan z)) 3)

series3.3s

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (tan y) (tan z))
103.0ms	(* (tan y) (tan z))
2.9s	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (* (tan y) (tan z)) 3))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
139.0ms	(pow (* (tan y) (tan z)) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	433	948
1	2169	882
2	5001	881

prune637.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (cbrt (pow (pow (* (tan y) (tan z)) 3) 3)))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
0.3b	(pow (pow (* (tan y) (tan z)) 3) 3)
0.3b	(pow (* (tan y) (tan z)) 3)
7.9b	(cbrt (pow (pow (* (tan y) (tan z)) 3) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
21×	`unpow-prod-down` `cube-prod`
15×	`cube-div`
12×	`tan-quot`
11×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-exp` `add-cbrt-cube`
7×	`pow1` `cube-mult` `unpow3` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-to-exp` `cbrt-div` `pow-pow` `associate-r/` `associate-l/` `rem-cube-cbrt`
2×	`prod-exp`
1×	`pow1/3` `pow-prod-down` `rem-cbrt-cube` `cbrt-unprod` `fma-udef`

Counts

4 → 114

Calls

4 calls:

1.0ms	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (cbrt (pow (pow (* (tan y) (tan z)) 3) 3)))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
7.0ms	(pow (pow (* (tan y) (tan z)) 3) 3)
6.0ms	(pow (* (tan y) (tan z)) 3)
7.0ms	(cbrt (pow (pow (* (tan y) (tan z)) 3) 3))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.0s	(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (cbrt (pow (pow (* (tan y) (tan z)) 3) 3)))) (fma (fma (tan y) (tan z) 1) (* (tan y) (tan z)) 1) (+ (- (tan a)) x))
186.0ms	(pow (pow (* (tan y) (tan z)) 3) 3)
135.0ms	(pow (* (tan y) (tan z)) 3)
150.0ms	(cbrt (pow (pow (* (tan y) (tan z)) 3) 3))

simplify100.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	570	1293
1	2843	1193
2	5001	1184

prune585.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes484.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	40	28
2	42	28
3	42	28

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.0s	3879×	body	1280	valid
925.0ms	2024×	body	640	valid
375.0ms	8000×	pre	80	true
211.0ms	683×	body	320	valid
108.0ms	1123×	body	80	valid
62.0ms	291×	body	160	valid