Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	50×	body	1280	valid
6.0ms	142×	body	80	valid
4.0ms	39×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	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: 26.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub`

Counts

2 → 561

Calls

2 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
138.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify206.0ms

Algorithm

egg-herbie

Counts

567 → 567

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1161	18191
1	3350	13265
2	5002	13161

prune641.0ms

Filtered

567 candidates to 199 candidates (35.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	564	3	567
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	565	3	568

Merged error: 0.1b

Counts

568 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
27.2b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ 1 (+ x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series209.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(/ (+ x 1.0) (- x 1.0))
23.0ms	(/ 1 (+ x 1.0))
143.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	352	622
1	1229	566
2	5001	540

prune142.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Merged error: 0.1b

Counts

108 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

2707×	`*-un-lft-identity`
1732×	`times-frac`
1197×	`add-sqr-sqrt`
936×	`prod-diff`
815×	`add-cube-cbrt`
508×	`distribute-lft-out`
397×	`distribute-lft-out--`
186×	`sqrt-prod`
182×	`associate-/r/`
173×	`difference-of-squares`
91×	`div-inv`
79×	`swap-sqr`
55×	`flip3-+` `flip-+`
47×	`flip3--` `flip--`
36×	`fma-neg`
24×	`sqrt-div`
19×	`pow1` `associate-r` `associate-l`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 1238

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
71.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
39.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
331.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
138.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify407.0ms

Algorithm

egg-herbie

Counts

1250 → 1250

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	1303	37794
1	4264	27854
2	5001	27738

prune1.6s

Filtered

1250 candidates to 410 candidates (32.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1250	0	1250
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1250	3	1253

Merged error: 0.1b

Counts

1253 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.1b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.5b	(/ (- 1.0) (pow x 2))
7.4b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

448×	`times-frac`
372×	`add-sqr-sqrt`
346×	`*-un-lft-identity`
340×	`add-cube-cbrt`
252×	`prod-diff`
165×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
57×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
40×	`associate-r`
29×	`add-exp-log`
11×	`cube-prod` `add-cbrt-cube`
10×	`prod-exp` `associate-/l*`
9×	`div-exp` `unswap-sqr`
8×	`associate-/r*`
6×	`pow1` `div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u`
3×	`cube-mult` `rec-exp` `1-exp` `unpow3` `associate-l`
2×	`cbrt-undiv` `neg-sub0` `div-sub` `cbrt-unprod` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `distribute-frac-neg` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `associate--r+` `distribute-lft-out--`

Counts

4 → 561

Calls

4 calls:

14.0ms	(* 3.0 (/ 1 (pow x 3)))
1.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
10.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 3.0 (/ 1 (pow x 3)))
86.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
26.0ms	(/ (- 1.0) (pow x 2))
45.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify199.0ms

Algorithm

egg-herbie

Counts

573 → 573

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1314	12850
1	4714	6734
2	5001	6734

prune819.0ms

Filtered

573 candidates to 251 candidates (43.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	572	1	573
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	572	4	576

Merged error: 0b

Counts

576 → 4

regimes47.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 29.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	30
1	38	30
2	38	30

end0.0ms

sample657.0ms

Algorithm

intervals

Results

243.0ms	1766×	body	1280	valid
132.0ms	1237×	body	640	valid
116.0ms	4082×	body	80	valid
51.0ms	614×	body	320	valid
16.0ms	301×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6