Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	87×	body	1280	valid
5.0ms	50×	body	640	valid
3.0ms	172×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	10×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

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: 41.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 68

Calls

2 calls:

8.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune148.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Merged error: 0.0b

Counts

75 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify25.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune37.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Merged error: 0.0b

Counts

17 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `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` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

5.0ms	(+ (exp x) 1.0)
10.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
101.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
62.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	531	2009
1	1917	1909
2	5001	1904

prune402.0ms

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	1	1	2
Picked	1	0	1
Done	0	1	1
Total	167	3	170

Merged error: 0.0b

Counts

170 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
0.0b	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
2.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.5b	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
195×	`*-un-lft-identity`
123×	`add-sqr-sqrt` `add-cube-cbrt`
88×	`log-pow`
66×	`exp-prod`
41×	`associate-/l*`
36×	`distribute-lft-out`
26×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log-prod` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`rem-log-exp` `exp-sum` `associate-/l/`

Counts

4 → 239

Calls

4 calls:

8.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
14.0ms	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
2.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
102.0ms	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
45.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	721	3618
1	2432	3370
2	5002	3361

prune540.0ms

Filtered

251 candidates to 162 candidates (64.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	250	4	254

Merged error: 0.0b

Counts

254 → 4

regimes26.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch27.0ms

Steps

Iters	Range		Point
9	-6.308761783247451	-1.485944467815708e-07	-0.00022688895910318228

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	13
1	20	13

end0.0ms

sample888.0ms

Algorithm

intervals

Results

402.0ms	2323×	body	1280	valid
177.0ms	1629×	body	640	valid
99.0ms	5547×	body	80	valid
54.0ms	788×	body	320	valid
19.0ms	434×	body	160	valid