Details

sample99.0ms

Algorithm

intervals

Results

27.0ms	58×	body	1280	valid
25.0ms	58×	body	10240	exit
17.0ms	295×	body	80	valid
8.0ms	33×	body	640	valid
4.0ms	25×	body	320	valid
0.0ms	4×	body	160	valid

simplify43.0ms

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

prune10.0ms

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: 27.9b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
2.9b	(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:

12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
7.0ms	(* (- 1.0 eps) x)
6.0ms	(* (+ 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)))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
33.0ms	(* (- 1.0 eps) x)
26.0ms	(* (+ 1.0 eps) x)
240.0ms	(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	5003	628

prune447.0ms

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: 3.9b

Counts

98 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
3.6b	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.1b	(/ (pow x 3) eps)

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:

5.0ms	(* 0.5 (pow x 2))
1.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.0ms	(/ (pow x 3) eps)

series96.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (pow x 2))
51.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms	(/ (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

prune238.0ms

Filtered

115 candidates to 66 candidates (57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Merged error: 3.9b

Counts

120 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.1b	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
3.6b	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

rewrite20.0ms

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))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt x)
172.0ms	(cbrt x)
49.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
78.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify153.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	721	1798
1	4325	1271
2	5003	1225

prune487.0ms

Filtered

196 candidates to 136 candidates (69.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	199	6	205

Merged error: 2.6b

Counts

205 → 6

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))))
11.5b	(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)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
180.0ms	(cbrt x)
72.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
176.0ms	(log (exp (cbrt x)))

simplify59.0ms

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

prune229.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Merged error: 2.6b

Counts

74 → 7

regimes127.0ms

Accuracy

96.1% (0.6b remaining)

Error of 4.2b against oracle of 3.6b and baseline of 20.0b

bsearch150.0ms

Steps

Iters	Range		Point
10	4.1340642299952195e-15	108.10498260228141	65.50693203954515

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	43
1	57	43
2	57	43

end0.0ms

sample3.1s

Algorithm

intervals

Results

878.0ms	1999×	body	10240	exit
773.0ms	1693×	body	1280	valid
596.0ms	10017×	body	80	valid
348.0ms	1279×	body	640	valid
118.0ms	644×	body	320	valid
36.0ms	294×	body	160	valid

Details

sample99.0ms

simplify43.0ms

prune10.0ms

localize17.0ms

rewrite29.0ms

series344.0ms

simplify50.0ms

prune447.0ms

localize10.0ms

rewrite16.0ms

series96.0ms

simplify61.0ms

prune238.0ms

localize14.0ms

rewrite20.0ms

series472.0ms

simplify153.0ms

prune487.0ms

localize17.0ms

rewrite7.0ms

series605.0ms

simplify59.0ms

prune229.0ms

regimes127.0ms

bsearch150.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling