Details

sample113.0ms

Algorithm

intervals

Results

51.0ms	122×	body	1280	valid
17.0ms	54×	body	640	valid
17.0ms	256×	pre	80	true
4.0ms	23×	body	320	valid
2.0ms	48×	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

prune2.0ms

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: 13.4b

Counts

2 → 1

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))
4.6b	(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))

series282.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(+ x (- (tan (+ y z)) (tan a)))
112.0ms	(- (tan (+ y z)) (tan a))
53.0ms	(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

prune137.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize16.0ms

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`tan-quot`
6×	`pow1` `distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `sum-log` `associate-/r/` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

13.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
11.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

338.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
211.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
374.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
92.0ms	(* (tan y) (tan z))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	449	1261
1	1503	1213
2	5001	1205

prune319.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	9	102
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 0.1b

Counts

109 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`tan-quot`
13×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `frac-sub`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
3×	`associate-r` `associate-l` `frac-add` `sum-log`
2×	`+-commutative` `sub-neg` `associate-+r+` `diff-log` `associate-*r/` `distribute-lft-out`
1×	`associate-+r-` `flip3--` `pow-prod-down` `prod-exp` `un-div-inv` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

4.0ms	(+ (tan y) (tan z))
9.0ms	(+ x (- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a)))
12.0ms	(- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a))
5.0ms	(* (tan y) (tan z))

series887.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (tan y) (tan z))
336.0ms	(+ x (- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a)))
367.0ms	(- (* (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z))))) (tan a))
91.0ms	(* (tan y) (tan z))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	462	1037
1	1648	989
2	5002	973

prune273.0ms

Filtered

82 candidates to 65 candidates (79.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	82	12	94

Merged error: 0.1b

Counts

94 → 12

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)) (* (tan y) (tan z)))
0.3b	(pow (* (tan y) (tan z)) 3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
44×	`tan-quot`
23×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
14×	`associate-r/` `associate-l/`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative`
2×	`pow-pow` `pow-plus` `pow-exp` `rem-cube-cbrt` `unswap-sqr`
1×	`pow2` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
10.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
6.0ms	(pow (* (tan y) (tan z)) 3)

series424.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan y) (tan z))
92.0ms	(* (tan y) (tan z))
114.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
124.0ms	(pow (* (tan y) (tan z)) 3)

simplify77.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	433	671
1	2392	636
2	5001	632

prune408.0ms

Filtered

128 candidates to 77 candidates (60.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	129	11	140

Merged error: 0.1b

Counts

140 → 11

regimes610.0ms

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	35	27
1	40	27
2	40	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3888×	body	1280	valid
522.0ms	8000×	pre	80	true
476.0ms	1964×	body	640	valid
124.0ms	743×	body	320	valid
63.0ms	1152×	body	80	valid
29.0ms	253×	body	160	valid