Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
4.0ms	249×	pre	80	false
4.0ms	256×	pre	80	true

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	48	7
2	110	7
3	284	7
4	1580	7
5	5001	7

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: 15.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
14.8b	(/ (- (* a a) (* b b)) (* a a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `times-frac` `associate-/l*`
3×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 60

Calls

3 calls:

4.0ms	(- (* a a) (* b b))
1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms	(/ (- (* a a) (* b b)) (* a a))

series101.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(- (* a a) (* b b))
20.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
50.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify33.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	241	458
1	1037	405
2	5001	401

prune146.0ms

Filtered

69 candidates to 53 candidates (76.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (+ a b) a)
0.1b	(* (/ (+ a b) a) (/ (- a b) a))
0.1b	(/ (- a b) a)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 151

Calls

4 calls:

1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
5.0ms	(/ (+ a b) a)
15.0ms	(* (/ (+ a b) a) (/ (- a b) a))
7.0ms	(/ (- a b) a)

series135.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
22.0ms	(/ (+ a b) a)
64.0ms	(* (/ (+ a b) a) (/ (- a b) a))
30.0ms	(/ (- a b) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	505	990
1	2546	909
2	5001	905

prune295.0ms

Filtered

163 candidates to 114 candidates (69.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	3	165

Merged error: 0b

Counts

165 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ a b) a)
0.0b	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
0.1b	(* (/ (+ a b) a) (/ (- a b) a))
0.1b	(/ (- a b) a)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
58×	`times-frac`
40×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `expm1-log1p` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+` `expm1-udef`

Counts

4 → 147

Calls

4 calls:

6.0ms	(/ (+ a b) a)
1.0ms	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))
10.0ms	(/ (- a b) a)

series244.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ a b) a)
127.0ms	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))
30.0ms	(/ (- a b) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	511	929
1	2554	843
2	5002	840

prune356.0ms

Filtered

159 candidates to 114 candidates (71.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	159	3	162

Merged error: 0b

Counts

162 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ a b) a) (* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a))))
0.1b	(/ (- a b) a)
0.1b	(/ (- a b) a)
0.1b	(* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
121×	`times-frac`
102×	`sqrt-prod`
76×	`add-cube-cbrt`
38×	`associate-l`
30×	`swap-sqr`
26×	`distribute-lft-out--`
24×	`pow1`
23×	`associate-r`
22×	`add-exp-log` `add-cbrt-cube`
20×	`difference-of-squares`
12×	`sqrt-div`
11×	`unswap-sqr`
10×	`associate-/l*`
8×	`sqrt-pow1` `pow1/2`
7×	`prod-exp` `cbrt-unprod` `div-inv`
6×	`frac-times` `associate-r/` `pow-prod-down` `associate-/r`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-sqr` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `div-sub` `clear-num` `*-commutative` `flip--`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 239

Calls

4 calls:

21.0ms	(* (/ (+ a b) a) (* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a))))
7.0ms	(/ (- a b) a)
7.0ms	(/ (- a b) a)
26.0ms	(* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ (+ a b) a) (* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a))))
30.0ms	(/ (- a b) a)
31.0ms	(/ (- a b) a)
45.0ms	(* (sqrt (/ (- a b) a)) (sqrt (/ (- a b) a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	543	1594
1	2993	1432
2	5002	1418

prune484.0ms

Filtered

251 candidates to 159 candidates (63.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	250	1	251
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	252	2	254

Merged error: 0b

Counts

254 → 2

regimes28.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample799.0ms

Algorithm

intervals

Results

268.0ms	8000×	body	80	valid
147.0ms	7995×	pre	80	false
142.0ms	8000×	pre	80	true