Details

sample41.0ms

Algorithm

intervals

Results

15.0ms	66×	body	1280	valid
9.0ms	53×	body	640	valid
4.0ms	39×	body	320	valid
3.0ms	88×	body	80	valid
3.0ms	92×	body	80	overflowed
1.0ms	10×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
4.0b	(- (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-/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:

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

series46.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify192.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (186.0ms)

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

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b	(fma 1/6 (pow x 3) x)
8.8b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-cbrt-cube`
4×	`add-exp-log`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

3.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series150.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
77.0ms	(fma 1/6 (pow x 3) x)
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify92.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414

prune171.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

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:

0.0ms

(fma 1/12 x (/ 1 x))

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(fma 1/12 x (/ 1 x))

simplify61.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	43
1	49	38
2	150	38
3	482	38
4	2338	38
5	5002	38

prune30.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.0b	(- 1 (/ 1.0 (exp x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

18.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
3.0ms	(/ 1.0 (exp x))
10.0ms	(- 1 (/ 1.0 (exp x)))

series104.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
38.0ms	(- 1 (/ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	552	1839
1	2298	1281
2	5001	1188

prune172.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

94.9% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 11.2b

bsearch25.0ms

Steps

Iters	Range		Point
8	-1.3862719480695398	-4.2961337728369966e-05	-0.0021727830323339213

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

556.0ms	2365×	body	1280	valid
256.0ms	1617×	body	640	valid
91.0ms	842×	body	320	valid
82.0ms	2779×	body	80	valid
79.0ms	2648×	body	80	overflowed
28.0ms	401×	body	160	valid