Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	78×	body	1280	valid
7.0ms	54×	body	640	valid
4.0ms	192×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

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: 40.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.2b	(- (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-/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:

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

series59.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

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

prune113.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Merged error: 0.0b

Counts

75 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(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

prune26.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Merged error: 0.0b

Counts

16 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (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)) x)
4.4b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
95×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
16×	`distribute-lft-out`
10×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
7×	`associate-/r*`
6×	`div-inv`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 137

Calls

3 calls:

6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
9.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
3.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
101.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	513	1944
1	1881	1851
2	5001	1846

prune305.0ms

Filtered

146 candidates to 111 candidates (76.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	144	5	149

Merged error: 0.0b

Counts

149 → 5

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)
4.4b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.4b	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

rewrite38.0ms

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:

7.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
13.0ms	(/ (/ (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)))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0))
99.0ms	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
40.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (51.0ms)

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

prune453.0ms

Filtered

251 candidates to 161 candidates (64.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	252	4	256

Merged error: 0.0b

Counts

256 → 4

regimes25.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch34.0ms

Steps

Iters	Range		Point
10	-0.05202343663643454	-5.738045557766166e-18	-0.00012167591385668957

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample993.0ms

Algorithm

intervals

Results

427.0ms	2213×	body	1280	valid
205.0ms	1672×	body	640	valid
127.0ms	5409×	body	80	valid
69.0ms	839×	body	320	valid
26.0ms	437×	body	160	valid