Details

sample105.0ms

Algorithm

intervals

Results

47.0ms	116×	body	1280	valid
19.0ms	81×	body	640	valid
10.0ms	256×	pre	80	true
5.0ms	9×	body	160	valid
3.0ms	21×	body	320	valid
1.0ms	29×	body	80	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: 13.2b

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))
5.1b	(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:

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

series279.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ x (- (tan (+ y z)) (tan a)))
111.0ms	(- (tan (+ y z)) (tan a))
52.0ms	(tan (+ y z))

simplify80.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	208	371
1	479	360
2	1328	359
3	5002	359

prune149.0ms

Filtered

53 candidates to 39 candidates (73.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	47	6	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	6	54

Merged error: 0.1b

Counts

54 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

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:

22.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
4.0ms	(+ (tan y) (tan z))
30.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
5.0ms	(* (tan z) (tan y))

series890.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a)))
91.0ms	(+ (tan y) (tan z))
374.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan z) (tan y)))) (tan a))
90.0ms	(* (tan z) (tan y))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	578	1343
1	2009	1302
2	5001	1285

prune348.0ms

Filtered

97 candidates to 71 candidates (73.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	96	7	103

Merged error: 0.1b

Counts

103 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (* (tan z) (tan y)))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan z) (tan y)))))) (tan a))
0.3b	(* (tan z) (tan y))
2.5b	(log (exp (* (tan z) (tan y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

6.0ms	(exp (* (tan z) (tan y)))
26.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan z) (tan y)))))) (tan a))
5.0ms	(* (tan z) (tan y))
5.0ms	(log (exp (* (tan z) (tan y))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(exp (* (tan z) (tan y)))
380.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (log (exp (* (tan z) (tan y)))))) (tan a))
89.0ms	(* (tan z) (tan y))
91.0ms	(log (exp (* (tan z) (tan y))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	502	1253
1	1689	1183
2	5001	1163

prune441.0ms

Filtered

112 candidates to 80 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Merged error: 0.1b

Counts

119 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan z) (tan y)) 3)))) (tan a))
0.3b	(* (tan z) (tan y))
0.3b	(pow (* (tan z) (tan y)) 3)
27.6b	(cbrt (pow (* (tan z) (tan y)) 3))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
42×	`tan-quot` `cbrt-prod`
36×	`*-un-lft-identity`
28×	`unpow-prod-down` `cube-prod` `frac-sub`
22×	`add-cube-cbrt`
18×	`associate-/r*`
16×	`difference-of-squares`
15×	`associate-r` `associate-l`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `unswap-sqr`
6×	`cube-div` `add-log-exp`
5×	`*-commutative`
4×	`pow-unpow` `associate-/l*` `sqr-pow`
3×	`frac-times` `cbrt-div` `associate-r/` `associate-l/` `associate-/l/`
2×	`cube-mult` `pow-pow` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `times-frac` `pow1/3` `diff-log` `frac-add` `clear-num` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 154

Calls

4 calls:

44.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan z) (tan y)) 3)))) (tan a))
5.0ms	(* (tan z) (tan y))
7.0ms	(pow (* (tan z) (tan y)) 3)
8.0ms	(cbrt (pow (* (tan z) (tan y)) 3))

series685.0ms

Counts

4 → 12

Calls

4 calls:

380.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (cbrt (pow (* (tan z) (tan y)) 3)))) (tan a))
91.0ms	(* (tan z) (tan y))
122.0ms	(pow (* (tan z) (tan y)) 3)
92.0ms	(cbrt (pow (* (tan z) (tan y)) 3))

simplify105.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	813	1955
1	3659	1837
2	5001	1837

prune495.0ms

Filtered

166 candidates to 95 candidates (57.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	166	7	173

Merged error: 0.1b

Counts

173 → 7

regimes232.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	3927×	body	1280	valid
474.0ms	2004×	body	640	valid
310.0ms	8000×	pre	80	true
116.0ms	665×	body	320	valid
56.0ms	1105×	body	80	valid
33.0ms	299×	body	160	valid