Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	59×	body	1280	valid
3.0ms	38×	body	640	valid
3.0ms	131×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	9×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 29.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub`

Counts

2 → 561

Calls

2 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
48.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (+ x 1.0) (- x 1.0))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify204.0ms

Algorithm

egg-herbie

Counts

567 → 567

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1161	18191
1	3350	13265
2	5002	13161

prune680.0ms

Filtered

567 candidates to 199 candidates (35.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	562	5	567
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	563	5	568

Merged error: 0.1b

Counts

568 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
18.6b	(- (* (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
26×	`prod-diff`
25×	`add-sqr-sqrt`
20×	`times-frac`
17×	`add-cube-cbrt`
9×	`cbrt-prod`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`pow1/3`
2×	`flip3--` `associate-*r/` `associate-/r/` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `frac-sub` `div-inv`

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
25.0ms	(- (* (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
179.0ms	(cbrt x)
179.0ms	(cbrt x)
151.0ms	(- (* (cbrt x) (* (cbrt x) (/ (cbrt x) (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	546	1354
1	2067	936
2	5001	824

prune188.0ms

Filtered

93 candidates to 63 candidates (67.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Merged error: 0.1b

Counts

98 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
0.0b	(* (+ x 1.0) (+ x 1.0))
17.9b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
44×	`associate-*r/`
43×	`add-cube-cbrt`
37×	`prod-diff`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
24×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate--l+`
20×	`frac-times` `flip3--` `flip--`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 198

Calls

4 calls:

8.0ms	(* x (- x 1.0))
17.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
9.0ms	(* (+ x 1.0) (+ x 1.0))
11.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* x (- x 1.0))
56.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
16.0ms	(* (+ x 1.0) (+ x 1.0))
44.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	906	2204
1	5002	1888

prune407.0ms

Filtered

210 candidates to 139 candidates (66.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	210	5	215

Merged error: 0.1b

Counts

215 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 3.0 x) 1.0)
15.1b	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`difference-of-squares`
10×	`associate-/l*`
5×	`neg-mul-1`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `flip3--` `fma-def` `frac-2neg` `div-sub` `distribute-frac-neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 88

Calls

2 calls:

4.0ms	(+ (* 3.0 x) 1.0)
10.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* 3.0 x) 1.0)
54.0ms	(/ (- (+ (* 3.0 x) 1.0)) (- (* x x) (* 1.0 1.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	410	971
1	1643	910
2	5001	900

prune170.0ms

Filtered

94 candidates to 76 candidates (80.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	93	6	99

Merged error: 0.0b

Counts

99 → 6

regimes21.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	14	6
2	14	6

end0.0ms

sample545.0ms

Algorithm

intervals

Results

182.0ms	1705×	body	1280	valid
108.0ms	1231×	body	640	valid
99.0ms	4133×	body	80	valid
42.0ms	625×	body	320	valid
14.0ms	306×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6