Details

sample82.0ms

Algorithm

intervals

Results

26.0ms	53×	body	1280	valid
20.0ms	309×	body	80	valid
9.0ms	31×	body	640	valid
4.0ms	58×	body	80	overflowed
4.0ms	20×	body	320	valid
2.0ms	12×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	47	16
1	124	16
2	365	16
3	1376	16
4	5001	15

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 26.3b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(exp (- (* (- 1.0 eps) x)))
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
12×	`add-sqr-sqrt` `exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
3.0ms	(exp (- (* (+ 1.0 eps) x)))
4.0ms	(exp (- (* (- 1.0 eps) x)))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (- 1.0 eps) x)
26.0ms	(exp (- (* (+ 1.0 eps) x)))
27.0ms	(exp (- (* (- 1.0 eps) x)))
197.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify145.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	1290	3714
1	4701	3419
2	5001	3397

prune393.0ms

Filtered

171 candidates to 92 candidates (53.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Merged error: 0.3b

Counts

173 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- 2.0 (* 1.0 (pow x 2)))
7.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef`

Counts

2 → 30

Calls

2 calls:

3.0ms	(- 2.0 (* 1.0 (pow x 2)))
1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series101.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- 2.0 (* 1.0 (pow x 2)))
44.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify69.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	126	221
1	412	193
2	2139	191
3	5001	171

prune92.0ms

Filtered

36 candidates to 27 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Merged error: 0.3b

Counts

39 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

7.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
12.7b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
12.7b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
12.7b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
154.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
147.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
153.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	190	752
1	639	693
2	2777	627
3	5001	621

prune241.0ms

Filtered

61 candidates to 58 candidates (95.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	60	5	65

Merged error: 0.3b

Counts

65 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

7.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
7.8b	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
12.7b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
12.7b	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`

Counts

4 → 46

Calls

4 calls:

1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
1.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
45.0ms	(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))
156.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))
150.0ms	(cbrt (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	190	620
1	639	566
2	2777	522
3	5001	514

prune258.0ms

Filtered

58 candidates to 54 candidates (93.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	58	5	63

Merged error: 0.2b

Counts

63 → 5

regimes132.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.3b

bsearch148.0ms

Steps

Iters	Range		Point
9	3.220789993380391	25340457.240933813	173.79350790004767

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	57
1	57	57
2	57	57

end0.0ms

sample2.6s

Algorithm

intervals

Results

887.0ms	1763×	body	1280	valid
704.0ms	10034×	body	80	valid
400.0ms	1284×	body	640	valid
131.0ms	626×	body	320	valid
127.0ms	1874×	body	80	overflowed
41.0ms	303×	body	160	valid