Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	257×	pre	80	false

simplify53.0ms

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: 12.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* a a) (* b b))
0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
11.9b	(/ (- (* 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))))
8.0ms	(/ (- (* a a) (* b b)) (* a a))

series100.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(- (* a a) (* b b))
17.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
49.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify34.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (27.0ms)

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

prune139.0ms

Filtered

69 candidates to 53 candidates (76.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

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

rewrite39.0ms

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)
6.0ms	(/ (+ a b) a)
20.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series128.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
29.0ms	(/ (- a b) a)
26.0ms	(/ (+ a b) a)
58.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify69.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	505	991
1	2546	909
2	5002	905

prune277.0ms

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	2	0	2
Picked	1	0	1
Done	0	0	0
Total	164	2	166

Merged error: 0b

Counts

166 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

7.0ms	(/ (- a b) a)
6.0ms	(/ (+ a b) a)
1.0ms	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
17.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series241.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- a b) a)
21.0ms	(/ (+ a b) a)
127.0ms	(expm1 (log1p (* (/ (+ a b) a) (/ (- a b) a))))
62.0ms	(* (/ (+ a b) a) (/ (- 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	5001	840

prune344.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
0.0b	(/ (- a b) a)
0.0b	(* (+ a b) (/ (- a b) a))
0.2b	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
50×	`add-exp-log`
48×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-cube-cbrt` `associate-r` `add-cbrt-cube`
22×	`prod-exp`
12×	`pow1` `div-exp` `cbrt-unprod`
11×	`frac-times` `associate-*l/`
7×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares`
6×	`flip3-+` `flip-+`
5×	`associate-l` `associate-/l*`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-/r*` `sqrt-prod` `div-inv`
2×	`*-commutative` `associate-/l/` `unswap-sqr`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `clear-num` `un-div-inv` `flip--` `distribute-lft-out`

Counts

4 → 156

Calls

4 calls:

1.0ms	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
7.0ms	(/ (- a b) a)
12.0ms	(* (+ a b) (/ (- a b) a))
15.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

series169.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (fabs (* (* (+ a b) (/ (- a b) a)) (/ 1 a))))
30.0ms	(/ (- a b) a)
61.0ms	(* (+ a b) (/ (- a b) a))
62.0ms	(* (* (+ a b) (/ (- a b) a)) (/ 1 a))

simplify100.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	624	1129
1	3885	987
2	5002	972

prune287.0ms

Filtered

168 candidates to 112 candidates (66.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	2	170

Merged error: 0b

Counts

170 → 2

regimes25.0ms

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

sample754.0ms

Algorithm

intervals

Results

260.0ms	8000×	body	80	valid
136.0ms	8000×	pre	80	true
134.0ms	7853×	pre	80	false

Details

sample28.0ms

simplify53.0ms

prune2.0ms

localize11.0ms

rewrite14.0ms

series100.0ms

simplify34.0ms

prune139.0ms

localize9.0ms

rewrite39.0ms

series128.0ms

simplify69.0ms

prune277.0ms

localize13.0ms

rewrite35.0ms

series241.0ms

simplify70.0ms

prune344.0ms

localize10.0ms

rewrite40.0ms

series169.0ms

simplify100.0ms

prune287.0ms

regimes25.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample754.0ms

Profiling