Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
6.0ms	250×	pre	80	false
3.0ms	256×	pre	80	true

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 12.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
12.2b	(/ (- (* a a) (* b b)) (* a a))

rewrite15.0ms

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))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series101.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(- (* a a) (* b b))
18.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
52.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify32.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (25.0ms)

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

prune140.0ms

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)
0.0b	(/ (- a b) a)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite36.0ms

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))))
6.0ms	(/ (+ a b) a)
7.0ms	(/ (- a b) a)
17.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series130.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
21.0ms	(/ (+ a b) a)
30.0ms	(/ (- a b) a)
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify71.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	505	991
1	2546	909
2	5001	905

prune284.0ms

Filtered

163 candidates to 114 candidates (69.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0b

Counts

165 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
96×	`times-frac`
94×	`sqrt-prod`
62×	`add-cube-cbrt`
44×	`associate-r`
38×	`associate-l`
18×	`unswap-sqr`
14×	`distribute-lft-out--` `difference-of-squares`
12×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`sqrt-div`
6×	`pow-prod-down` `associate-/r*` `div-inv` `distribute-lft-out`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-times` `flip3--` `frac-2neg` `sqrt-unprod` `div-sub` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 218

Calls

4 calls:

21.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
23.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
7.0ms	(/ (- a b) a)
7.0ms	(/ (- a b) a)

series264.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
99.0ms	(* (sqrt (/ (+ a b) a)) (sqrt (/ (- a b) a)))
30.0ms	(/ (- a b) a)
35.0ms	(/ (- a b) a)

simplify60.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	1736
1	1269	1678
2	5001	1664

prune603.0ms

Filtered

230 candidates to 166 candidates (72.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	230	2	232

Merged error: 0b

Counts

232 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))))
0.0b	(log1p (/ (- (* a a) (* b b)) (* a a)))
0.0b	(expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))
12.2b	(/ (- (* a a) (* b b)) (* a a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(sqrt (fabs (expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))))
1.0ms	(log1p (/ (- (* a a) (* b b)) (* a a)))
1.0ms	(expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series259.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (fabs (expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))))
76.0ms	(log1p (/ (- (* a a) (* b b)) (* a a)))
112.0ms	(expm1 (log1p (/ (- (* a a) (* b b)) (* a a))))
52.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify162.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	251	589
1	979	509
2	4919	506
3	5001	506

prune174.0ms

Filtered

77 candidates to 61 candidates (79.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	77	2	79

Merged error: 0b

Counts

79 → 2

regimes64.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms

sample599.0ms

Algorithm

intervals

Results

187.0ms	8000×	body	80	valid
95.0ms	7937×	pre	80	false
93.0ms	8000×	pre	80	true