Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	67×	body	1280	valid
6.0ms	56×	body	640	valid
4.0ms	90×	body	80	overflowed
2.0ms	28×	body	320	valid
2.0ms	84×	body	80	valid
1.0ms	21×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

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: 42.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
6.2b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series40.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify191.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (184.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune127.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0.0b

Counts

74 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
48.0ms	(fma 1/12 x (/ 1 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116

prune57.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0.0b

Counts

37 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
6.1b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
17×	`distribute-lft-out`
11×	`associate-/r/` `add-cbrt-cube`
9×	`add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 154

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
10.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
81.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
67.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	508	2170
1	2199	2059
2	5001	2056

prune375.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	166	3	169

Merged error: 0.0b

Counts

169 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (log (exp (- (exp x) 1.0))))
0.0b	(exp (- (exp x) 1.0))
6.1b	(log (exp (- (exp x) 1.0)))
6.2b	(- (exp x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
30×	`exp-prod` `log-pow`
27×	`times-frac` `prod-diff`
22×	`exp-sum`
14×	`log-prod`
9×	`pow1` `associate-/r*` `add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-/l*`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 140

Calls

4 calls:

8.0ms	(/ (exp x) (log (exp (- (exp x) 1.0))))
6.0ms	(exp (- (exp x) 1.0))
10.0ms	(log (exp (- (exp x) 1.0)))
5.0ms	(- (exp x) 1.0)

series96.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (exp x) (log (exp (- (exp x) 1.0))))
40.0ms	(exp (- (exp x) 1.0))
14.0ms	(log (exp (- (exp x) 1.0)))
15.0ms	(- (exp x) 1.0)

simplify205.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	330	1170
1	950	900
2	4926	781
3	5001	781

prune216.0ms

Filtered

152 candidates to 94 candidates (61.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Merged error: 0.0b

Counts

155 → 3

regimes38.0ms

Accuracy

97.8% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 22.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample940.0ms

Algorithm

intervals

Results

416.0ms	2194×	body	1280	valid
186.0ms	1582×	body	640	valid
63.0ms	2995×	body	80	valid
62.0ms	796×	body	320	valid
52.0ms	2585×	body	80	overflowed
24.0ms	436×	body	160	valid