Details

sample162.0ms

Algorithm

intervals

Results

91.0ms	120×	body	1280	valid
26.0ms	60×	body	640	valid
10.0ms	256×	pre	80	true
9.0ms	32×	body	320	valid
3.0ms	37×	body	80	valid
1.0ms	7×	body	160	valid

simplify19.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize17.0ms

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))

rewrite20.0ms

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:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(tan (+ y z))

series287.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(+ x (- (tan (+ y z)) (tan a)))
118.0ms	(- (tan (+ y z)) (tan a))
51.0ms	(tan (+ y z))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (12.0ms)

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

prune152.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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))

rewrite46.0ms

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×	`flip3-+` `frac-add` `flip-+`
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` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 92

Calls

4 calls:

22.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series967.0ms

Counts

4 → 12

Calls

4 calls:

483.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
297.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
93.0ms	(* (tan y) (tan z))
94.0ms	(* (tan y) (tan z))

simplify83.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	655	1681
1	3086	1507
2	5001	1490

prune488.0ms

Filtered

104 candidates to 83 candidates (79.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

27×	`associate-*l/`
14×	`add-sqr-sqrt`
13×	`tan-quot` `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×	`flip3-+` `frac-add` `flip-+`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 90

Calls

4 calls:

25.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
4.0ms	(* (sin y) (tan z))
11.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms	(* (tan y) (tan z))

series950.0ms

Counts

4 → 12

Calls

4 calls:

485.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
79.0ms	(* (sin y) (tan z))
292.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
93.0ms	(* (tan y) (tan z))

simplify95.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	742	1769
1	3531	1588
2	5001	1587

prune554.0ms

Filtered

102 candidates to 80 candidates (78.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r` `associate-l`
7×	`prod-exp` `cbrt-unprod`
6×	`tan-quot`
5×	`associate-*l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`frac-times` `frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (sin y) (tan z))
4.0ms	(* (sin y) (tan z))
12.0ms	(/ (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
5.0ms	(* (tan y) (tan z))

series463.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (sin y) (tan z))
79.0ms	(* (sin y) (tan z))
215.0ms	(/ (* (- 1 (* (tan y) (tan z))) (sin a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
93.0ms	(* (tan y) (tan z))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	419	915
1	2111	717
2	5001	717

prune418.0ms

Filtered

96 candidates to 67 candidates (69.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes550.0ms

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	32	22
1	32	22

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.9s	3876×	body	1280	valid
906.0ms	2012×	body	640	valid
309.0ms	8000×	pre	80	true
204.0ms	682×	body	320	valid
116.0ms	1118×	body	80	valid
64.0ms	312×	body	160	valid