Details

sample173.0ms

Algorithm

intervals

Results

96.0ms	131×	body	1280	valid
31.0ms	59×	body	640	valid
10.0ms	256×	pre	80	true
7.0ms	24×	body	320	valid
3.0ms	12×	body	160	valid
3.0ms	30×	body	80	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `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 → 42

Calls

3 calls:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series292.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(+ x (- (tan (+ y z)) (tan a)))
115.0ms	(- (tan (+ y z)) (tan a))
56.0ms	(tan (+ y z))

simplify45.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune154.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

4.0ms	(+ (tan y) (tan z))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
17.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series916.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan y) (tan z))
386.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
342.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
95.0ms	(* (tan y) (tan z))

simplify89.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune290.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.7b	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`tan-quot`
35×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow1` `times-frac`
12×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l/` `difference-of-squares`
10×	`frac-sub`
9×	`frac-times` `associate-r/` `associate-r` `associate-l` `associate-l/`
6×	`swap-sqr`
5×	`associate-/r*` `distribute-lft-out--`
4×	`associate-/l*` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 133

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan z) (tan z))
5.0ms	(* (tan y) (tan y))
14.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan y) (tan z))
32.0ms	(* (tan z) (tan z))
36.0ms	(* (tan y) (tan y))
224.0ms	(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))

simplify83.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	521	1251
1	2392	1138
2	5001	1094

prune533.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan z) (tan z))
0.3b	(* (tan y) (tan y))
4.0b	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
4.7b	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`tan-quot`
18×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`add-cube-cbrt`
10×	`times-frac` `associate-/r*`
6×	`swap-sqr` `associate-r` `associate-l` `associate-/r/` `associate-/l/`
4×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow2` `flip3--` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `pow-sqr` `-commutative` `pow-prod-up` `frac-sub` `flip--` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

5.0ms	(* (tan z) (tan z))
5.0ms	(* (tan y) (tan y))
11.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
11.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (tan z) (tan z))
32.0ms	(* (tan y) (tan y))
216.0ms	(/ (* (tan y) (tan y)) (- (tan y) (tan z)))
215.0ms	(/ (* (tan z) (tan z)) (- (tan y) (tan z)))

simplify91.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	464	881
1	2414	789
2	5001	780

prune436.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes269.0ms

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	24	23
1	24	23

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.0s	3879×	body	1280	valid
894.0ms	2024×	body	640	valid
325.0ms	8000×	pre	80	true
215.0ms	683×	body	320	valid
106.0ms	1123×	body	80	valid
59.0ms	291×	body	160	valid