Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	79×	body	1280	valid
7.0ms	57×	body	640	valid
4.0ms	169×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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)
3.6b	(- (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:

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

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
18.0ms	(- (exp x) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (32.0ms)

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

prune118.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	2	75

Merged error: 0.1b

Counts

75 → 2

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(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))

simplify28.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

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

prune28.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.1b

Counts

15 → 2

localize10.0ms

Local error

Found 4 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)
0.0b	(+ (exp x) 1.0)
3.5b	(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`
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:

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

series219.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (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)
8.0ms	(+ (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 (45.0ms)

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

prune336.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	165	3	168

Merged error: 0.1b

Counts

168 → 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)) x)
0.0b	(+ (exp x) 1.0)
3.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.5b	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

214×	`times-frac`
164×	`*-un-lft-identity`
106×	`add-sqr-sqrt` `add-cube-cbrt`
68×	`log-pow`
51×	`exp-prod`
34×	`associate-/l*`
29×	`distribute-lft-out`
21×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp` `associate-/r*`
2×	`fma-udef`
1×	`+-commutative` `frac-2neg` `rem-log-exp` `exp-sum` `clear-num` `sum-log` `associate-/l/`

Counts

4 → 201

Calls

4 calls:

13.0ms	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
4.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
2.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (/ (log (exp (fma (- 1.0) 1.0 (exp (+ x x))))) (+ (exp x) 1.0)) x)
8.0ms	(+ (exp x) 1.0)
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
41.0ms	(log (exp (fma (- 1.0) 1.0 (exp (+ x x)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	710	2903
1	2399	2725
2	5001	2724

prune421.0ms

Filtered

213 candidates to 142 candidates (66.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	213	3	216

Merged error: 0.0b

Counts

216 → 3

regimes21.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 21.5b

bsearch47.0ms

Steps

Iters	Range		Point
9	-0.0014803844373699059	-6.09662256770312e-09	-0.00014416421256948652

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	33
1	32	33

end0.0ms

sample1.0s

Algorithm

intervals

Results

440.0ms	2236×	body	1280	valid
212.0ms	1679×	body	640	valid
133.0ms	5474×	body	80	valid
69.0ms	817×	body	320	valid
24.0ms	417×	body	160	valid