Details

sample94.0ms

Algorithm

intervals

Results

24.0ms	52×	body	1280	valid
23.0ms	59×	body	10240	exit
17.0ms	320×	body	80	valid
8.0ms	34×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 26.9b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.0b	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
10×	`add-cube-cbrt`
9×	`associate-l`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `times-frac` `associate-l/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

7.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
13.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
1.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
28.0ms	(* (+ 1.0 eps) x)
43.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
227.0ms	(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	462	738
1	1805	635
2	5002	628

prune333.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	7	97

Merged error: 4.5b

Counts

97 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
3.6b	(/ (pow x 3) eps)
3.8b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
13×	`add-exp-log`
12×	`cube-prod` `associate-/l*`
8×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqr-pow`
4×	`cube-mult` `unpow3` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `div-exp` `associate-l` `prod-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 106

Calls

3 calls:

6.0ms	(* 0.5 (pow x 2))
6.0ms	(/ (pow x 3) eps)
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

series94.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (pow x 2))
20.0ms	(/ (pow x 3) eps)
49.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5002	451

prune269.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 4.5b

Counts

122 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
3.8b	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

185×	`times-frac`
83×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
14×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`
13×	`associate-/r*`
12×	`div-exp`
10×	`div-inv`
9×	`add-cbrt-cube`
8×	`associate-/l*`
6×	`cbrt-prod`
4×	`pow1` `expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv`
2×	`pow-to-exp` `pow1/3` `prod-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef`

Counts

4 → 184

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
171.0ms	(cbrt x)
44.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
74.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify151.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	721	1771
1	4325	1200
2	5001	1159

prune570.0ms

Filtered

196 candidates to 136 candidates (69.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Merged error: 2.4b

Counts

206 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.6b	(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
13.6b	(log (exp (cbrt x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
3.0ms	(log (exp (cbrt x)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
179.0ms	(cbrt x)
72.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
175.0ms	(log (exp (cbrt x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	139	339
1	329	286
2	1862	275
3	5001	275

prune280.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 2.4b

Counts

76 → 8

regimes111.0ms

Accuracy

95.2% (0.8b remaining)

Error of 4.5b against oracle of 3.7b and baseline of 20.4b

bsearch153.0ms

Steps

Iters	Range		Point
10	1.5556181911831613e-38	6.800262453525831e-20	5.980611786382907e-20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	54	31
2	54	31

end0.0ms

sample2.8s

Algorithm

intervals

Results

749.0ms	1711×	body	1280	valid
746.0ms	1843×	body	10240	exit
547.0ms	9938×	body	80	valid
326.0ms	1274×	body	640	valid
105.0ms	636×	body	320	valid
39.0ms	324×	body	160	valid