Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	69×	body	1280	valid
8.0ms	72×	body	10240	exit
6.0ms	60×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	88×	body	80	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 41.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

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

series45.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify192.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (185.0ms)

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

prune126.0ms

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: 0.1b

Counts

74 → 3

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:

1.0ms

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

series44.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

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

simplify62.0ms

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

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: 0.1b

Counts

16 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite26.0ms

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:

9.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.0ms	(+ (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)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
61.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (52.0ms)

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

prune375.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	163	6	169

Merged error: 0.1b

Counts

169 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `distribute-lft-out`
2×	`associate-/r/`
1×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
39.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify68.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	227	703
1	585	654
2	2358	637
3	5002	628

prune232.0ms

Filtered

71 candidates to 61 candidates (85.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	71	6	77

Merged error: 0.1b

Counts

77 → 6

regimes36.0ms

Accuracy

99% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.0b

bsearch35.0ms

Steps

Iters	Range		Point
8	-0.002595282603730271	-2.587228857819641e-07	-0.001541657862432784

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	54
1	36	54

end0.0ms

sample1.1s

Algorithm

intervals

Results

383.0ms	2324×	body	1280	valid
273.0ms	2564×	body	10240	exit
172.0ms	1638×	body	640	valid
54.0ms	829×	body	320	valid
50.0ms	2804×	body	80	valid
17.0ms	406×	body	160	valid