Details

sample175.0ms

Algorithm

intervals

Results

105.0ms	131×	body	1280	valid
27.0ms	62×	body	640	valid
11.0ms	256×	pre	80	true
6.0ms	22×	body	320	valid
3.0ms	32×	body	80	valid
2.0ms	9×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.7b	(tan (+ y z))

rewrite22.0ms

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

series285.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(+ x (- (tan (+ y z)) (tan a)))
113.0ms	(- (tan (+ y z)) (tan a))
50.0ms	(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

prune150.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite114.0ms

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:

3.0ms	(+ (tan y) (tan z))
68.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
37.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series908.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan y) (tan z))
341.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
384.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
91.0ms	(* (tan y) (tan z))

simplify76.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (25.0ms)

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

prune309.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b	(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
0.2b	(* (tan y) (tan z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

3.0ms	(+ (tan y) (tan z))
10.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
19.0ms	(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
5.0ms	(* (tan y) (tan z))

series666.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan y) (tan z))
206.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
273.0ms	(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
96.0ms	(* (tan y) (tan z))

simplify104.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	383	942
1	1350	898
2	4359	898
3	5001	898

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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

rewrite45.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 96

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
11.0ms	(* (+ (tan y) (tan z)) (cos a))
21.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series790.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))
144.0ms	(* (+ (tan y) (tan z)) (cos a))
467.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	587	1304
1	2701	1144
2	5003	1128

prune442.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes341.0ms

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	26	20
1	26	20

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.2s	3906×	body	1280	valid
908.0ms	2019×	body	640	valid
343.0ms	8000×	pre	80	true
213.0ms	682×	body	320	valid
99.0ms	1094×	body	80	valid
65.0ms	299×	body	160	valid