Details

sample112.0ms

Algorithm

intervals

Results

52.0ms	120×	body	1280	valid
21.0ms	67×	body	640	valid
11.0ms	256×	pre	80	true
4.0ms	25×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	12×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (100.0%)

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: 12.6b

Counts

2 → 1

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))
2.6b	(tan (+ y z))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`tan-quot` `add-sqr-sqrt`
4×	`tan-sum`
3×	`pow1` `add-exp-log` `+-commutative` `add-cube-cbrt` `frac-sub` `add-cbrt-cube`
2×	`sub-neg` `associate-+r+` `diff-log` `sum-log` `distribute-lft-out` `distribute-lft-out--`
1×	`associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 44

Calls

3 calls:

6.0ms	(+ x (- (tan (+ y z)) (tan a)))
7.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series299.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(+ x (- (tan (+ y z)) (tan a)))
118.0ms	(- (tan (+ y z)) (tan a))
56.0ms	(tan (+ y z))

simplify44.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	205	371
1	473	360
2	1325	359
3	5002	359

prune124.0ms

Filtered

53 candidates to 39 candidates (26.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	43	10	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	10	54

Merged error: 0.1b

Counts

54 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

27×	`tan-quot`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
19×	`frac-sub`
13×	`add-log-exp`
9×	`associate-/r*`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `difference-of-squares`
4×	`associate-l` `distribute-lft-out` `associate-/l*` `distribute-lft-out--`
3×	`flip3-+` `associate-r` `sum-log` `flip-+` `associate-/l/` `unswap-sqr`
2×	`+-commutative` `sub-neg` `associate-+r+` `diff-log` `frac-add`
1×	`frac-times` `associate-+r-` `flip3--` `frac-2neg` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
29.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
29.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
5.0ms	(* (tan z) (tan y))

series973.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+ (tan y) (tan z))
368.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
408.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
97.0ms	(* (tan z) (tan y))

simplify66.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	570	1343
1	1974	1302
2	5001	1285

prune281.0ms

Filtered

97 candidates to 71 candidates (26.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.1b

Counts

107 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
0.2b	(* (tan z) (tan y))
0.6b	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
2.5b	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`tan-quot` `*-un-lft-identity`
19×	`frac-sub`
12×	`exp-prod`
11×	`add-cube-cbrt`
10×	`difference-of-squares`
9×	`associate-/r*` `add-log-exp`
7×	`pow1` `add-exp-log` `log-pow`
6×	`add-cbrt-cube`
5×	`log-prod` `distribute-lft-out--`
4×	`associate-l` `exp-sum` `associate-/l*`
3×	`sub-neg` `times-frac` `associate-r` `associate-/l/` `unswap-sqr`
2×	`exp-diff` `diff-log` `rem-log-exp` `rem-exp-log`
1×	`frac-times` `log-div` `flip3--` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

33.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
6.0ms	(* (tan z) (tan y))
32.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
25.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

series1.4s

Counts

4 → 12

Calls

4 calls:

422.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
101.0ms	(* (tan z) (tan y))
460.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
413.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

simplify64.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	521	1560
1	1767	1472
2	5001	1455

prune338.0ms

Filtered

107 candidates to 76 candidates (29.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	106	10	116

Merged error: 0.1b

Counts

116 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
0.2b	(* (tan z) (tan y))
2.4b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`tan-quot`
24×	`add-sqr-sqrt`
19×	`frac-sub`
17×	`add-log-exp`
9×	`add-cube-cbrt` `associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`exp-prod` `distribute-lft-out` `distribute-lft-out--`
4×	`associate-+r+` `associate-l` `exp-sum` `sum-log` `associate-/l*`
3×	`sub-neg` `diff-log` `associate-r` `rem-exp-log` `associate-/l/` `unswap-sqr`
2×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`
1×	`frac-times` `flip3--` `frac-2neg` `times-frac` `exp-diff` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 92

Calls

4 calls:

26.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
34.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
6.0ms	(* (tan z) (tan y))
29.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

series1.6s

Counts

4 → 12

Calls

4 calls:

362.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
632.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
101.0ms	(* (tan z) (tan y))
458.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))))

simplify69.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	569	1536
1	1964	1478
2	5002	1461

prune294.0ms

Filtered

104 candidates to 73 candidates (29.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	106	8	114

Merged error: 0.1b

Counts

114 → 8

regimes253.0ms

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	24	33
1	24	33

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	3927×	body	1280	valid
481.0ms	2030×	body	640	valid
320.0ms	8000×	pre	80	true
104.0ms	656×	body	320	valid
50.0ms	1085×	body	80	valid
33.0ms	302×	body	160	valid