Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	181×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	24×	body	640	valid
4.0ms	24×	body	1280	nan
3.0ms	24×	body	640	nan
3.0ms	88×	body	80	nan
2.0ms	13×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	14×	body	160	nan
1.0ms	8×	body	320	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

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: 18.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.6b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

16.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
8.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
16.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune304.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	3	121

Merged error: 0.1b

Counts

121 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.1b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
3.3b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`times-frac`
37×	`add-cube-cbrt`
28×	`difference-of-squares`
24×	`log-prod`
20×	`distribute-lft-out--`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
3×	`div-exp` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `rem-log-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `log-div` `diff-log` `log-pow` `associate--r-`

Counts

4 → 144

Calls

4 calls:

15.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
10.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
148.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	621	1546
1	1974	1467
2	5001	1448

prune331.0ms

Filtered

156 candidates to 118 candidates (75.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	155	4	159

Merged error: 0b

Counts

159 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0))))
0.0b	(+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0)))
0.4b	(* (* 1.0 (exp 1.0)) (- x y))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`add-cube-cbrt` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in`
3×	`log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `flip3--` `rem-log-exp` `associate-l` `sum-log` `log-pow` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 55

Calls

3 calls:

9.0ms	(log (+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0))))
10.0ms	(+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0)))
9.0ms	(* (* 1.0 (exp 1.0)) (- x y))

series367.0ms

Counts

3 → 9

Calls

3 calls:

180.0ms	(log (+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0))))
94.0ms	(+ (* (* 1.0 (exp 1.0)) (- x y)) (* 1.0 (exp 1.0)))
93.0ms	(* (* 1.0 (exp 1.0)) (- x y))

simplify48.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	326	591
1	1456	505
2	5001	464

prune115.0ms

Filtered

64 candidates to 43 candidates (67.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	64	4	68

Merged error: 0b

Counts

68 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x y) (- 1.0 y)) 3)
3.3b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
5.6b	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
10.6b	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

510×	`add-sqr-sqrt`
312×	`times-frac`
222×	`*-un-lft-identity`
212×	`difference-of-squares`
175×	`unpow-prod-down` `cube-prod`
105×	`log-prod`
102×	`add-cube-cbrt`
81×	`sqr-pow`
60×	`distribute-lft-out--`
33×	`associate-/l*`
12×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`difference-cubes` `associate-/r/`
6×	`pow1` `add-log-exp`
4×	`flip3--` `flip--` `div-inv`
3×	`pow-unpow` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `rem-log-exp` `pow-exp` `flip-+` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `log-div` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `log-pow`

Counts

4 → 392

Calls

4 calls:

10.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
45.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
74.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
74.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

series960.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
262.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
360.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0))))
273.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)) (* 1.0 1.0)))

simplify128.0ms

Algorithm

egg-herbie

Counts

404 → 404

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1359	10607
1	5002	10369

prune866.0ms

Filtered

404 candidates to 205 candidates (50.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	404	4	408

Merged error: 0b

Counts

408 → 4

regimes122.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

270.0ms	5641×	body	80	valid
189.0ms	819×	body	1280	valid
134.0ms	804×	body	640	valid
116.0ms	672×	body	1280	nan
103.0ms	751×	body	640	nan
94.0ms	2661×	body	80	nan
62.0ms	481×	body	320	valid
47.0ms	454×	body	320	nan
21.0ms	255×	body	160	valid
17.0ms	261×	body	160	nan