Details

sample179.0ms

Algorithm

intervals

Results

101.0ms	121×	body	1280	valid
28.0ms	66×	body	640	valid
12.0ms	256×	pre	80	true
5.0ms	18×	body	320	valid
3.0ms	38×	body	80	valid
3.0ms	13×	body	160	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: 12.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
2.4b	(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:

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

series328.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (tan (+ y z)) (tan a))
136.0ms	(+ x (- (tan (+ y z)) (tan a)))
63.0ms	(tan (+ y z))

simplify98.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (91.0ms)

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

prune260.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

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:

51.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
3.0ms	(+ (tan y) (tan z))
81.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

436.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
105.0ms	(+ (tan y) (tan z))
389.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
105.0ms	(* (tan y) (tan z))

simplify89.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	676	4072
1	2087	3376
2	5002	3151

prune723.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
59.4b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite4.0ms

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:

1.0ms	(cbrt (tan a))
1.0ms	(cbrt (tan a))
1.0ms	(cbrt (tan a))
0.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (tan a))
137.0ms	(cbrt (tan a))
136.0ms	(cbrt (tan a))
218.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (105.0ms)

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

prune384.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite48.0ms

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:

12.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series916.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (+ (tan y) (tan z)) (cos a))
104.0ms	(* (tan y) (tan z))
105.0ms	(* (tan y) (tan z))
541.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify82.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (70.0ms)

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

prune539.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes271.0ms

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	27	29
1	27	29

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.0s	3877×	body	1280	valid
877.0ms	1986×	body	640	valid
368.0ms	8000×	pre	80	true
217.0ms	711×	body	320	valid
122.0ms	1150×	body	80	valid
57.0ms	276×	body	160	valid