Details

sample166.0ms

Algorithm

intervals

Results

88.0ms	125×	body	1280	valid
33.0ms	65×	body	640	valid
9.0ms	256×	pre	80	true
5.0ms	20×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	10×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.5b	(tan (+ y z))

rewrite38.0ms

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:

14.0ms	(+ x (- (tan (+ y z)) (tan a)))
16.0ms	(- (tan (+ y z)) (tan a))
6.0ms	(tan (+ y z))

series304.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(+ x (- (tan (+ y z)) (tan a)))
120.0ms	(- (tan (+ y z)) (tan a))
54.0ms	(tan (+ y z))

simplify39.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

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

prune145.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

32.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
58.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
15.0ms	(* (tan y) (tan z))
18.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

313.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
506.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
97.0ms	(* (tan y) (tan z))
95.0ms	(* (tan y) (tan z))

simplify89.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (77.0ms)

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

prune496.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin y) (tan z)) (cos y))
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	(* (tan y) (tan z))
0.2b	(* (sin y) (tan z))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

14.0ms	(/ (* (sin y) (tan z)) (cos y))
66.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
15.0ms	(* (tan y) (tan z))
13.0ms	(* (sin y) (tan z))

series973.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(/ (* (sin y) (tan z)) (cos y))
501.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (cos a)))
95.0ms	(* (tan y) (tan z))
83.0ms	(* (sin y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	632	1392
1	3029	1208
2	5001	1208

prune504.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (log (exp (* (sin y) (tan z)))) (cos y))) (cos a)))
0.2b	(* (tan y) (tan z))
0.2b	(* (sin y) (tan z))
3.7b	(log (exp (* (sin y) (tan z))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `associate-*l/`
13×	`add-exp-log` `add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`tan-quot` `pow1`
8×	`associate-/l/`
6×	`associate-r` `associate-l` `frac-sub`
5×	`flip3--` `flip--` `add-log-exp`
3×	`log-prod` `times-frac` `prod-exp` `log-pow` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `frac-add` `associate-/r/` `-commutative` `flip-+` `unswap-sqr`
1×	`frac-times` `exp-prod` `exp-to-pow` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 86

Calls

4 calls:

72.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (log (exp (* (sin y) (tan z)))) (cos y))) (cos a)))
17.0ms	(* (tan y) (tan z))
13.0ms	(* (sin y) (tan z))
4.0ms	(log (exp (* (sin y) (tan z))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

499.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (/ (log (exp (* (sin y) (tan z)))) (cos y))) (cos a)))
96.0ms	(* (tan y) (tan z))
79.0ms	(* (sin y) (tan z))
80.0ms	(log (exp (* (sin y) (tan z))))

simplify71.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	583	1392
1	2619	1198
2	5001	1196

prune499.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes583.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	34	24

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.8s	3834×	body	1280	valid
878.0ms	2063×	body	640	valid
302.0ms	8000×	pre	80	true
191.0ms	677×	body	320	valid
106.0ms	1128×	body	80	valid
68.0ms	298×	body	160	valid