Details

sample112.0ms

Algorithm

intervals

Results

61.0ms	128×	body	1280	valid
16.0ms	72×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	22×	body	320	valid
1.0ms	27×	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: 13.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.8b	(tan (+ y z))

rewrite16.0ms

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:

5.0ms	(+ x (- (tan (+ y z)) (tan a)))
6.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series271.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(+ x (- (tan (+ y z)) (tan a)))
113.0ms	(- (tan (+ y z)) (tan a))
46.0ms	(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

prune145.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.2b	(+ 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))
0.3b	(* (tan y) (tan z))

rewrite34.0ms

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	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series873.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (tan y) (tan z))
327.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
368.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
87.0ms	(* (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

prune278.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

10 alts after pruning (10 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))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite34.0ms

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:

7.0ms	(* (+ (tan y) (tan z)) (cos a))
14.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series792.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (+ (tan y) (tan z)) (cos a))
465.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
96.0ms	(* (tan y) (tan z))
90.0ms	(* (tan y) (tan z))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	587	1306
1	2694	1149
2	5001	1133

prune464.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

64×	`associate-*l/`
60×	`times-frac`
41×	`associate-/r/`
38×	`add-sqr-sqrt`
34×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
30×	`frac-sub`
28×	`tan-quot`
22×	`add-cbrt-cube`
21×	`flip3--` `flip--`
18×	`associate-/r*`
14×	`div-exp`
10×	`flip3-+` `frac-add` `flip-+`
9×	`pow1`
7×	`cbrt-undiv`
6×	`associate-r` `associate-l` `prod-exp` `div-inv`
4×	`cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 161

Calls

4 calls:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

450.0ms	(/ 1 (/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))))
88.0ms	(* (tan y) (tan z))
88.0ms	(* (tan y) (tan z))
534.0ms	(/ (* (- 1 (* (tan y) (tan z))) (cos a)) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))

simplify122.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	913	4624
1	4994	4130
2	5001	4130

prune600.0ms

Filtered

173 candidates to 107 candidates (61.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes287.0ms

Accuracy

0% (0.2b 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	30	23
1	30	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	3935×	body	1280	valid
433.0ms	1945×	body	640	valid
301.0ms	8000×	pre	80	true
103.0ms	695×	body	320	valid
51.0ms	1154×	body	80	valid
28.0ms	271×	body	160	valid