Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	282×	pre	80	false
4.0ms	256×	pre	80	true

simplify54.0ms

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: 12.8b

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))))
12.4b	(/ (- (* 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:

30.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
54.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify34.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (28.0ms)

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

prune141.0ms

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

localize9.0ms

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)
0.1b	(* (/ (+ 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))))
5.0ms	(/ (+ a b) a)
6.0ms	(/ (- a b) a)
17.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series133.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
24.0ms	(/ (+ a b) a)
30.0ms	(/ (- a b) a)
62.0ms	(* (/ (+ a b) a) (/ (- 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

prune285.0ms

Filtered

163 candidates to 114 candidates (69.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	0	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	(/ (+ a b) a)
0.0b	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (- a b) a)
0.1b	(* (/ (+ a b) a) (/ (- 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))))
7.0ms	(/ (- a b) a)
19.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series240.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ a b) a)
125.0ms	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
29.0ms	(/ (- a b) a)
62.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (58.0ms)

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

prune340.0ms

Filtered

159 candidates to 114 candidates (71.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	159	2	161

Merged error: 0b

Counts

161 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

1.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
11.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
12.0ms	(* (+ a b) (/ (- a b) a))
7.0ms	(/ (- a b) a)

series169.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (/ (* (+ a b) (/ (- a b) a)) a)))
59.0ms	(/ (* (+ a b) (/ (- a b) a)) a)
59.0ms	(* (+ a b) (/ (- a b) a))
35.0ms	(/ (- a b) a)

simplify75.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	453	858
1	2492	775
2	5001	769

prune242.0ms

Filtered

142 candidates to 102 candidates (71.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	142	2	144

Merged error: 0b

Counts

144 → 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

sample782.0ms

Algorithm

intervals

Results

275.0ms	8000×	body	80	valid
141.0ms	8007×	pre	80	false
135.0ms	8000×	pre	80	true