Details

sample182.0ms

Algorithm

intervals

Results

100.0ms	137×	body	1280	valid
27.0ms	65×	body	640	valid
11.0ms	256×	pre	80	true
11.0ms	9×	body	160	valid
4.0ms	15×	body	320	valid
3.0ms	30×	body	80	valid

simplify25.0ms

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: 12.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.1b	(+ x (- (tan (+ y z)) (tan a)))
3.0b	(tan (+ y z))

rewrite48.0ms

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:

22.0ms	(- (tan (+ y z)) (tan a))
16.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(tan (+ y z))

series294.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(- (tan (+ y z)) (tan a))
125.0ms	(+ x (- (tan (+ y z)) (tan a)))
53.0ms	(tan (+ y z))

simplify101.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3057	507
3	5001	488

prune268.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite300.0ms

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:

28.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
145.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
97.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
367.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
391.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
98.0ms	(* (tan y) (tan z))

simplify86.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (56.0ms)

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

prune799.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite793.0ms

Algorithm

rewrite-expression-head

Rules

319×	`*-un-lft-identity`
235×	`add-sqr-sqrt`
180×	`prod-diff`
170×	`times-frac`
144×	`add-cube-cbrt`
92×	`associate-+r+`
58×	`difference-of-squares`
44×	`distribute-lft-out`
30×	`fma-neg` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r/`
11×	`add-log-exp`
8×	`flip3--` `flip--` `div-inv`
6×	`pow1`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `sum-log` `sin-mult`
1×	`tan-quot` `+-commutative` `associate-+r-` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `associate-/r` `cos-mult` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 296

Calls

4 calls:

440.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a)))
301.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a))
18.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
13.0ms	(* (sin y) (sin z))

series920.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a)))
400.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (sin z)) (* (cos z) (cos y))))) (tan a))
102.0ms	(/ (* (sin y) (sin z)) (* (cos z) (cos y)))
55.0ms	(* (sin y) (sin z))

simplify126.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	846	7884
1	3005	6646
2	5002	6457

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.8b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `cbrt-div` `pow1/3`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
0.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (tan a))
128.0ms	(cbrt (tan a))
134.0ms	(cbrt (tan a))
194.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (104.0ms)

Iter	Nodes	Cost
0	102	427
1	211	373
2	675	363
3	2633	349
4	5002	337

prune459.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes403.0ms

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	34	33
1	34	33

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	3888×	body	1280	valid
1.1s	2005×	body	640	valid
340.0ms	8000×	pre	80	true
186.0ms	664×	body	320	valid
109.0ms	1173×	body	80	valid
52.0ms	270×	body	160	valid