Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	63×	body	640	valid
4.0ms	138×	body	80	valid
3.0ms	38×	body	320	valid
1.0ms	17×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	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: 14.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
3.0b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
37.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series440.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ 1.0 (- x 1.0))
27.0ms	(/ 1.0 (+ x 1.0))
384.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify180.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1200	13350
1	3593	9620
2	5001	9568

prune612.0ms

Filtered

513 candidates to 209 candidates (40.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	510	3	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	511	3	514

Merged error: 0.5b

Counts

514 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
0.4b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
13.8b	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))
28.9b	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

37×	`times-frac`
36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
31×	`add-cube-cbrt`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
11×	`difference-of-squares`
8×	`associate-/r*`
6×	`pow1` `associate-/r/` `associate-/l*`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `div-inv`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate-r/` `pow-prod-down` `-commutative` `fma-udef` `distribute-lft-out`

Counts

4 → 124

Calls

4 calls:

5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
13.0ms	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))
1.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
52.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
47.0ms	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))
286.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))))

simplify87.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	445	1159
1	2507	1029
2	5001	991

prune339.0ms

Filtered

136 candidates to 114 candidates (83.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Merged error: 0.5b

Counts

139 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) (* 1.0 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.4b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
28.7b	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 1.0 (- x 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`times-frac`
23×	`add-cube-cbrt`
9×	`associate-/r*` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 101

Calls

4 calls:

4.0ms	(- (* x x) (* 1.0 1.0))
5.0ms	(/ 1.0 (- x 1.0))
6.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
1.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 1.0 (- x 1.0))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x x) (* 1.0 1.0))
35.0ms	(/ 1.0 (- x 1.0))
49.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
227.0ms	(fma (/ 1.0 (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ 1.0 (- x 1.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	415	747
1	1634	683
2	5002	668

prune224.0ms

Filtered

113 candidates to 92 candidates (81.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Merged error: 0.0b

Counts

116 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
0.1b	(/ (/ 2.0 x) x)
0.2b	(/ (- 2.0) (pow x 6))
0.3b	(/ 2.0 (pow x 4))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

9097×	`times-frac`
5884×	`add-sqr-sqrt`
5059×	`*-un-lft-identity`
4782×	`add-cube-cbrt`
3632×	`prod-diff`
3184×	`associate--l+`
1576×	`unpow-prod-down`
954×	`distribute-rgt-neg-in`
927×	`distribute-lft-neg-in`
578×	`sqr-pow`
364×	`div-inv`
316×	`difference-of-squares`
309×	`neg-mul-1`
85×	`distribute-lft-out--`
26×	`associate-/l*`
19×	`add-exp-log`
18×	`fma-neg`
17×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`div-exp` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`frac-2neg` `diff-log` `clear-num`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `flip--`
1×	`associate--l-` `neg-sub0` `div-sub` `distribute-frac-neg` `associate-/l/`

Counts

4 → 3903

Calls

4 calls:

427.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
6.0ms	(/ (/ 2.0 x) x)
6.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 2.0 (pow x 4))

series184.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
26.0ms	(/ (/ 2.0 x) x)
57.0ms	(/ (- 2.0) (pow x 6))
38.0ms	(/ 2.0 (pow x 4))

simplify798.0ms

Algorithm

egg-herbie

Counts

3915 → 3915

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	2625	95334
1	5001	81655

prune15.6s

Filtered

3915 candidates to 3244 candidates (82.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	3911	4	3915
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	3912	7	3919

Merged error: 0.0b

Counts

3919 → 7

regimes44.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 14.7b

bsearch114.0ms

Steps

Iters	Range		Point
10	6.398614580632226	3002406562115.273	283.6130444738584
11	-55383.34621353126	-7.66540900750845e-16	-232.32776769692475

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	32
1	53	32
2	53	32

end0.0ms

sample521.0ms

Algorithm

intervals

Results

185.0ms	1920×	body	640	valid
117.0ms	4132×	body	80	valid
96.0ms	1287×	body	320	valid
33.0ms	661×	body	160	valid