Details

sample99.0ms

Algorithm

intervals

Results

28.0ms	53×	body	1280	valid
25.0ms	341×	body	80	valid
15.0ms	45×	body	640	valid
9.0ms	75×	body	80	overflowed
2.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid

simplify39.0ms

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

prune9.0ms

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: 27.2b

Counts

2 → 2

localize17.0ms

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))))
3.6b	(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)))))

rewrite26.0ms

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:

6.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
11.0ms	(/ (+ 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)))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (- 1.0 eps) x)
28.0ms	(* (+ 1.0 eps) x)
50.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
235.0ms	(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)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

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

prune307.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 5.7b

Counts

98 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
3.8b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.2b	(/ (pow x 3) eps)

rewrite14.0ms

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:

5.0ms	(* 0.5 (pow x 2))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms	(/ (pow x 3) eps)

series102.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(* 0.5 (pow x 2))
47.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
25.0ms	(/ (pow x 3) eps)

simplify61.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	305	506
1	1561	465
2	5001	451

prune383.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	107	13	120

Merged error: 5.7b

Counts

120 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.9b	(/ (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))))

rewrite23.0ms

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)
12.0ms	(/ (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))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
182.0ms	(cbrt x)
47.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
76.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify159.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (140.0ms)

Iter	Nodes	Cost
0	721	1771
1	4325	1200
2	5001	1152

prune499.0ms

Filtered

196 candidates to 135 candidates (68.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Merged error: 4.2b

Counts

209 → 11

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 (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
10.7b	(log (exp (cbrt x)))

rewrite7.0ms

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

series609.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt x)
176.0ms	(cbrt x)
76.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
174.0ms	(log (exp (cbrt x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

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

prune240.0ms

Filtered

68 candidates to 58 candidates (85.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	70	9	79

Merged error: 4.2b

Counts

79 → 9

regimes122.0ms

Accuracy

95.9% (0.7b remaining)

Error of 4.2b against oracle of 3.6b and baseline of 19.8b

bsearch2.0ms

Steps

Iters	Range		Point
0	6.262145176279688e-07	6.47571746699048e-07	6.368931321635083e-07

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	52
1	59	52
2	59	52

end0.0ms

sample2.7s

Algorithm

intervals

Results

919.0ms	1729×	body	1280	valid
753.0ms	10160×	body	80	valid
426.0ms	1288×	body	640	valid
146.0ms	1986×	body	80	overflowed
139.0ms	618×	body	320	valid
50.0ms	336×	body	160	valid

Details

sample99.0ms

simplify39.0ms

prune9.0ms

localize17.0ms

rewrite26.0ms

series343.0ms

simplify56.0ms

prune307.0ms

localize10.0ms

rewrite14.0ms

series102.0ms

simplify61.0ms

prune383.0ms

localize27.0ms

rewrite23.0ms

series484.0ms

simplify159.0ms

prune499.0ms

localize17.0ms

rewrite7.0ms

series609.0ms

simplify60.0ms

prune240.0ms

regimes122.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling