Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	185×	body	80	valid
5.0ms	29×	body	640	valid
4.0ms	17×	body	1280	valid
3.0ms	23×	body	640	nan
3.0ms	92×	body	80	nan
3.0ms	15×	body	1280	nan
2.0ms	16×	body	320	nan
1.0ms	12×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	body	160	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: 17.9b

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))
4.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite54.0ms

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:

15.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
7.0ms	(/ (- x y) (- 1.0 y))
15.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
12.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (33.0ms)

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

prune274.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
5.9b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.7b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
16×	`add-cube-cbrt`
14×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `distribute-lft-out--`
5×	`associate-l` `difference-of-squares`
4×	`log-div` `prod-exp`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `log-pow` `cbrt-unprod` `associate--r-`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 96

Calls

4 calls:

5.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
13.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
37.0ms	(* (- x y) (/ 1 (- 1.0 y)))
85.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
55.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	516	863
1	2086	789
2	5003	762

prune203.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.1b

Counts

114 → 4

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))))
4.0b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite61.0ms

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)))))
8.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
42.0ms	(/ (- x y) (- 1.0 y))
125.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify55.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (39.0ms)

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

prune351.0ms

Filtered

156 candidates to 118 candidates (75.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	155	5	160

Merged error: 0.1b

Counts

160 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
1.9b	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
4.0b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`log-prod`
12×	`exp-prod`
10×	`log-pow`
8×	`pow1` `add-cube-cbrt` `exp-sum` `add-log-exp`
7×	`log-div`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `associate--r-`
4×	`flip3--` `add-cbrt-cube` `flip--`
3×	`sub-neg`
2×	`times-frac` `exp-diff` `diff-log` `rem-log-exp` `rem-exp-log`
1×	`div-sub`

Counts

4 → 76

Calls

4 calls:

5.0ms	(log (exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
5.0ms	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(log (exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
146.0ms	(exp (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify103.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	371	829
1	1113	749
2	4146	726
3	5003	725

prune185.0ms

Filtered

88 candidates to 67 candidates (76.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	88	5	93

Merged error: 0.1b

Counts

93 → 5

regimes199.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.3b

bsearch123.0ms

Steps

Iters	Range		Point
9	2622764.913020247	58586406052719.45	12727887057.006495
7	-591489333.2348301	-16040781.538086794	-152389660.09060627

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

270.0ms	5692×	body	80	valid
186.0ms	779×	body	1280	valid
134.0ms	808×	body	640	valid
124.0ms	715×	body	1280	nan
99.0ms	727×	body	640	nan
86.0ms	2567×	body	80	nan
56.0ms	466×	body	320	valid
46.0ms	441×	body	320	nan
21.0ms	255×	body	160	valid
15.0ms	225×	body	160	nan