Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	52	6
2	117	6
3	240	6
4	478	6
5	947	6
6	1844	6
7	5001	6

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
20.3b	(/ (fma x x (* y y)) (+ x y))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
160×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`flip3--` `div-sub` `flip--`

Counts

2 → 168

Calls

2 calls:

31.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
12.0ms	(/ (fma x x (* y y)) (+ x y))

series128.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
63.0ms	(/ (fma x x (* y y)) (+ x y))

simplify75.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	640	2000
1	2737	1832
2	5001	1825

prune336.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
30×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r`
8×	`associate-/l*`
7×	`distribute-lft-out`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `associate-/r*` `associate-/r/`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`flip3--` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

3 → 107

Calls

3 calls:

28.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
12.0ms	(/ (hypot x y) (+ x y))
33.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
83.0ms	(/ (hypot x y) (+ x y))
81.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))

simplify48.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	372	831
1	1709	716
2	5001	709

prune220.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))
0.0b	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`add-sqr-sqrt` `times-frac`
32×	`add-cube-cbrt`
26×	`cbrt-prod`
21×	`add-exp-log` `add-cbrt-cube`
20×	`unpow-prod-down` `cube-prod`
18×	`associate-r`
8×	`associate-/r/`
7×	`pow1` `distribute-lft-out`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-exp` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `rem-cube-cbrt` `difference-of-squares`
3×	`pow-unpow` `associate-l` `associate-/l*`
2×	`cube-div` `cube-mult` `flip3-+` `unpow3` `flip-+` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `pow-prod-down` `clear-num` `*-commutative` `rem-cbrt-cube`

Counts

4 → 158

Calls

4 calls:

12.0ms	(cbrt (pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3))
14.0ms	(/ (hypot x y) (+ x y))
29.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
24.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)

series353.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3))
80.0ms	(/ (hypot x y) (+ x y))
83.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
95.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)

simplify64.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	1380
1	2281	1289
2	5001	1277

prune338.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b	(/ (hypot x y) (+ x y))
0.0b	(* (hypot x y) (/ (hypot x y) (+ x y)))
1.5b	(log1p (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
30×	`times-frac`
24×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r`
8×	`associate-/l*`
7×	`distribute-lft-out`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`expm1-log1p-u` `associate-/r*` `associate-/r/`
4×	`prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `div-inv`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`log1p-udef` `flip3--` `div-sub` `log1p-expm1` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 118

Calls

4 calls:

31.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
12.0ms	(/ (hypot x y) (+ x y))
29.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
1.0ms	(log1p (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
80.0ms	(/ (hypot x y) (+ x y))
80.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
143.0ms	(log1p (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	399	954
1	1769	821
2	5002	813

prune310.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.1b 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	16	10
1	16	10

end0.0ms

sample512.0ms

Algorithm

intervals

Results

217.0ms	8000×	body	80	valid
106.0ms	8000×	pre	80	true