Details

sample120.0ms

Algorithm

intervals

Results

59.0ms	121×	body	1280	valid
17.0ms	256×	pre	80	true
17.0ms	68×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	44×	body	80	valid
1.0ms	7×	body	160	valid

simplify18.0ms

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: 13.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
1.9b	(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:

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

series270.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(+ x (- (tan (+ y z)) (tan a)))
107.0ms	(- (tan (+ y z)) (tan a))
50.0ms	(tan (+ y z))

simplify37.0ms

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

prune138.0ms

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: 0.0b

Counts

52 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

8.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
12.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))

series1.2s

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
515.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
360.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
86.0ms	(* (tan y) (tan z))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	449	1259
1	1503	1211
2	5001	1204

prune307.0ms

Filtered

102 candidates to 75 candidates (73.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
0.2b	(exp (* (tan y) (tan z)))
0.2b	(* (tan y) (tan z))
3.1b	(log (exp (* (tan y) (tan z))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`exp-prod` `exp-to-pow` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `times-frac` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

17.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
4.0ms	(exp (* (tan y) (tan z)))
5.0ms	(* (tan y) (tan z))
2.0ms	(log (exp (* (tan y) (tan z))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

365.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan y) (tan z)))))) (tan a))
122.0ms	(exp (* (tan y) (tan z)))
86.0ms	(* (tan y) (tan z))
100.0ms	(log (exp (* (tan y) (tan z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	261	684
1	705	622
2	1821	612
3	5002	612

prune270.0ms

Filtered

73 candidates to 55 candidates (75.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 0.0b

Counts

83 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
0.3b	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
0.3b	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

26.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
8.0ms	(* (tan y) (tan z))
8.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
10.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))

series933.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(- (/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))
89.0ms	(* (tan y) (tan z))
260.0ms	(/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z)))
211.0ms	(/ 1 (/ (- 1 (* (tan y) (tan z))) (+ (tan y) (tan z))))

simplify80.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	699	2789
1	3019	2504
2	5002	2478

prune368.0ms

Filtered

190 candidates to 108 candidates (56.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	190	10	200

Merged error: 0.0b

Counts

200 → 10

regimes523.0ms

Accuracy

0% (0.1b 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	21	13
1	21	13

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3887×	body	1280	valid
542.0ms	8000×	pre	80	true
497.0ms	1994×	body	640	valid
119.0ms	709×	body	320	valid
63.0ms	1153×	body	80	valid
30.0ms	257×	body	160	valid