Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	58×	body	1280	valid
6.0ms	41×	body	640	valid
3.0ms	136×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite108.0ms

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:

8.0ms	(/ (+ x 1.0) (- x 1.0))
42.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series173.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify194.0ms

Algorithm

egg-herbie

Counts

567 → 567

Iterations

Useful iterations: 2 (71.0ms)

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

prune685.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.1b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite418.0ms

Algorithm

rewrite-expression-head

Rules

2796×	`*-un-lft-identity`
2108×	`times-frac`
1668×	`add-sqr-sqrt`
1404×	`prod-diff`
1190×	`add-cube-cbrt`
940×	`exp-sum`
537×	`distribute-lft-out`
473×	`log-prod`
268×	`associate-/r/`
260×	`distribute-lft-out--`
233×	`difference-of-squares`
134×	`div-inv`
80×	`flip3-+` `flip-+`
56×	`flip3--` `flip--`
32×	`exp-prod`
18×	`fma-neg`
17×	`log-pow`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`sub-neg`
2×	`exp-diff` `diff-log` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `frac-sub`

Counts

4 → 1560

Calls

4 calls:

69.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
9.0ms	(/ (+ x 1.0) (- x 1.0))
84.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
45.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
39.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
339.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify501.0ms

Algorithm

egg-herbie

Counts

1572 → 1572

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1832	54596
1	4490	43049
2	5001	42969

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
2.2b	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite604.0ms

Algorithm

rewrite-expression-head

Rules

3694×	`*-un-lft-identity`
2792×	`times-frac`
2202×	`add-sqr-sqrt`
1872×	`prod-diff`
1578×	`add-cube-cbrt`
952×	`log-prod`
946×	`sqrt-prod`
940×	`exp-sum`
710×	`distribute-lft-out`
356×	`associate-/r/`
340×	`distribute-lft-out--`
304×	`difference-of-squares`
178×	`div-inv`
106×	`flip3-+` `flip-+`
74×	`flip3--` `flip--`
38×	`log-pow`
36×	`fma-neg`
34×	`sqrt-pow1`
32×	`exp-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 2040

Calls

4 calls:

109.0ms	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
101.0ms	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
48.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
48.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series918.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
324.0ms	(log (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
131.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
140.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify697.0ms

Algorithm

egg-herbie

Counts

2052 → 2052

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	2048	77172
1	4311	63986
2	5001	63882

prune4.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.2b	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
3.2b	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))

rewrite655.0ms

Algorithm

rewrite-expression-head

Rules

3696×	`*-un-lft-identity`
2792×	`times-frac`
2204×	`add-sqr-sqrt`
1898×	`sqrt-prod`
1872×	`prod-diff`
1580×	`add-cube-cbrt`
958×	`log-prod`
940×	`exp-sum`
710×	`distribute-lft-out`
356×	`associate-/r/`
340×	`distribute-lft-out--`
304×	`difference-of-squares`
178×	`div-inv`
106×	`flip3-+` `flip-+`
74×	`flip3--` `flip--`
72×	`sqrt-pow1`
42×	`log-pow`
36×	`fma-neg`
32×	`exp-prod`
10×	`pow1`
8×	`add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 2050

Calls

4 calls:

43.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
48.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
125.0ms	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
127.0ms	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
611.0ms	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))
419.0ms	(log (sqrt (sqrt (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))))

simplify702.0ms

Algorithm

egg-herbie

Counts

2062 → 2062

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	2349	79268
1	4612	66076
2	5001	66034

prune5.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes73.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.4b

bsearch91.0ms

Steps

Iters	Range		Point
9	1078.5849367128544	2491217878.346211	13264.4327344624
9	-66949431.36780037	-914.1439753575298	-12332.748446321157

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	21
1	42	21

end0.0ms

sample569.0ms

Algorithm

intervals

Results

197.0ms	1691×	body	1280	valid
109.0ms	4151×	body	80	valid
108.0ms	1225×	body	640	valid
43.0ms	607×	body	320	valid
15.0ms	326×	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