Details

sample86.0ms

Algorithm

intervals

Results

30.0ms	58×	body	1280	valid
20.0ms	295×	body	80	valid
10.0ms	33×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	58×	body	80	overflowed
1.0ms	4×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (44.0ms)

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

localize22.0ms

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)))))

rewrite27.0ms

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))))
6.0ms	(* (- 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)))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
29.0ms	(* (- 1.0 eps) x)
27.0ms	(* (+ 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

prune304.0ms

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

localize11.0ms

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:

6.0ms	(* 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)

series102.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 0.5 (pow x 2))
55.0ms	(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms	(/ (pow x 3) eps)

simplify63.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

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

prune243.0ms

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))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
186.0ms	(cbrt x)
54.0ms	(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
79.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify162.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (137.0ms)

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

prune501.0ms

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)))

series777.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(cbrt x)
185.0ms	(cbrt x)
80.0ms	(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
183.0ms	(log (exp (cbrt x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (14.0ms)

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

prune240.0ms

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

regimes130.0ms

Accuracy

96.1% (0.6b remaining)

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

bsearch172.0ms

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

sample2.6s

Algorithm

intervals

Results

859.0ms	1693×	body	1280	valid
697.0ms	10017×	body	80	valid
402.0ms	1279×	body	640	valid
136.0ms	644×	body	320	valid
135.0ms	1999×	body	80	overflowed
41.0ms	294×	body	160	valid