Details

sample111.0ms

Algorithm

intervals

Results

52.0ms	131×	body	1280	valid
17.0ms	256×	pre	80	true
15.0ms	61×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.3b

Counts

2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.3b	(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:

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

series290.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(+ x (- (tan (+ y z)) (tan a)))
118.0ms	(- (tan (+ y z)) (tan a))
49.0ms	(tan (+ y z))

simplify43.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (14.0ms)

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

prune160.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	9	52

Merged error: 0.1b

Counts

52 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
4.0ms	(+ (tan y) (tan z))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series927.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
94.0ms	(+ (tan y) (tan z))
389.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
92.0ms	(* (tan y) (tan z))

simplify83.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (28.0ms)

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

prune274.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 0.0b

Counts

88 → 11

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))
0.2b	(* (tan y) (tan z))
0.2b	(* (+ (tan y) (tan z)) (cos a))

rewrite37.0ms

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:

15.0ms	(/ (- (* (+ (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))
7.0ms	(* (+ (tan y) (tan z)) (cos a))

series824.0ms

Counts

4 → 12

Calls

4 calls:

482.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
93.0ms	(* (tan y) (tan z))
94.0ms	(* (tan y) (tan z))
154.0ms	(* (+ (tan y) (tan z)) (cos a))

simplify75.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	587	1304
1	2696	1144
2	5002	1128

prune435.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 0.0b

Counts

119 → 10

localize26.0ms

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))
0.3b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
42×	`tan-quot`
22×	`add-exp-log` `add-cbrt-cube`
20×	`pow-prod-down`
19×	`frac-times`
16×	`add-sqr-sqrt` `associate-*l/`
13×	`associate-*r/`
12×	`*-un-lft-identity`
11×	`associate-l` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `associate-r`
4×	`pow-sqr` `*-commutative` `pow-prod-up` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-plus`
1×	`pow2` `flip3-+` `swap-sqr` `frac-add` `flip-+` `distribute-lft-out`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
8.0ms	(* (+ (tan y) (tan z)) (cos a))
11.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
151.0ms	(* (+ (tan y) (tan z)) (cos a))
115.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	426	797
1	1969	687
2	5002	681

prune401.0ms

Filtered

125 candidates to 75 candidates (60.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	124	11	135

Merged error: 0.0b

Counts

135 → 11

regimes710.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	29
1	32	29

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3926×	body	1280	valid
524.0ms	8000×	pre	80	true
485.0ms	1971×	body	640	valid
118.0ms	713×	body	320	valid
59.0ms	1120×	body	80	valid
35.0ms	270×	body	160	valid

Details

sample111.0ms

simplify19.0ms

prune3.0ms

localize16.0ms

rewrite17.0ms

series290.0ms

simplify43.0ms

prune160.0ms

localize19.0ms

rewrite36.0ms

series927.0ms

simplify83.0ms

prune274.0ms

localize21.0ms

rewrite37.0ms

series824.0ms

simplify75.0ms

prune435.0ms

localize26.0ms

rewrite37.0ms

series451.0ms

simplify57.0ms

prune401.0ms

regimes710.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.2s

Profiling