Details

sample117.0ms

Algorithm

intervals

Results

58.0ms	120×	body	1280	valid
16.0ms	60×	body	640	valid
11.0ms	256×	pre	80	true
5.0ms	32×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	7×	body	160	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: 13.1b

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))
3.2b	(tan (+ y z))

rewrite21.0ms

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))

series324.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(+ x (- (tan (+ y z)) (tan a)))
127.0ms	(- (tan (+ y z)) (tan a))
63.0ms	(tan (+ y z))

simplify104.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (96.0ms)

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

prune265.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*l/`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-sub`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3--` `flip--`
8×	`pow1` `associate-/l/`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
10.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

737.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
319.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
100.0ms	(* (tan y) (tan z))
102.0ms	(* (tan y) (tan z))

simplify108.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	688	1793
1	3313	1591
2	5001	1577

prune605.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
6.0ms	(pow (* (tan y) (tan z)) 3)

series447.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (tan y) (tan z))
103.0ms	(* (tan y) (tan z))
100.0ms	(* (tan y) (tan z))
141.0ms	(pow (* (tan y) (tan z)) 3)

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	251	512
1	1287	497
2	5001	496

prune683.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan y)) (cbrt (tan y)))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
2.0ms	(cbrt (tan y))
2.0ms	(cbrt (tan y))
2.0ms	(cbrt (tan y))

series572.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
133.0ms	(cbrt (tan y))
140.0ms	(cbrt (tan y))
135.0ms	(cbrt (tan y))

simplify81.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	176	527
1	546	490
2	2172	458
3	5001	454

prune667.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes644.0ms

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	46	44
1	50	44
2	50	44

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	3875×	body	1280	valid
500.0ms	2010×	body	640	valid
323.0ms	8000×	pre	80	true
122.0ms	683×	body	320	valid
59.0ms	1119×	body	80	valid
36.0ms	313×	body	160	valid