Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 17.5b

localize9.0ms

Local error

Found 1 expressions with local error:

17.6b

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `flip3-+` `flip-+`
3×	`add-sqr-sqrt` `add-cube-cbrt` `flip3--` `-un-lft-identity` `times-frac` `associate-/r` `flip--`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

16.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	279	306
1	1480	261
2	5001	254

prune96.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
0.0b	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
0.0b	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
17.0b	(/ (fma x x (* y y)) (- x y))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

750×	`times-frac`
661×	`*-un-lft-identity`
449×	`add-sqr-sqrt`
315×	`add-cube-cbrt`
184×	`cbrt-prod`
178×	`unpow-prod-down` `cube-prod`
106×	`distribute-lft-out`
67×	`distribute-lft-out--` `difference-of-squares`
49×	`associate-/r/`
27×	`div-inv`
26×	`associate-/r*`
22×	`flip3--` `flip--`
17×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `flip3-+` `pow1/3` `rem-cbrt-cube` `flip-+`

Counts

4 → 565

Calls

4 calls:

32.0ms	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
16.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
28.0ms	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
5.0ms	(/ (fma x x (* y y)) (- x y))

series316.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
71.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
82.0ms	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
76.0ms	(/ (fma x x (* y y)) (- x y))

simplify113.0ms

Algorithm

egg-herbie

Counts

577 → 577

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1476	8064
1	5001	7838

prune928.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (fma x x (* y y)) (- x y)))
0.0b	(pow (* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y)))) 3)
0.2b	(* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y))))
17.0b	(/ (fma x x (* y y)) (- x y))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

252×	`times-frac`
187×	`add-sqr-sqrt`
177×	`*-un-lft-identity`
123×	`add-cube-cbrt`
68×	`associate-r`
56×	`add-exp-log`
30×	`add-cbrt-cube`
26×	`associate-/r*`
25×	`distribute-lft-out--` `difference-of-squares`
22×	`div-exp`
18×	`associate-/r/`
14×	`prod-exp`
10×	`pow1` `cbrt-undiv` `div-inv`
8×	`flip3--` `pow-exp` `flip--`
6×	`cube-div` `rec-exp` `1-exp` `cbrt-unprod` `associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-l` `associate-*l/` `flip-+` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow`
2×	`pow-pow` `frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `un-div-inv`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-flip` `unpow3` `cube-prod` `*-commutative` `distribute-lft-out` `inv-pow` `sqr-pow`

Counts

4 → 291

Calls

4 calls:

10.0ms	(/ 1 (/ (fma x x (* y y)) (- x y)))
17.0ms	(pow (* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y)))) 3)
42.0ms	(* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y))))
6.0ms	(/ (fma x x (* y y)) (- x y))

series282.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (/ (fma x x (* y y)) (- x y)))
83.0ms	(pow (* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y)))) 3)
74.0ms	(* (+ x y) (/ 1 (/ (fma x x (* y y)) (- x y))))
74.0ms	(/ (fma x x (* y y)) (- x y))

simplify54.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	873	2769
1	5001	2219

prune836.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (hypot x y) (/ (hypot x y) (- x y)))
0.0b	(pow (* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y))))) 3)
0.0b	(/ (hypot x y) (- x y))
0.2b	(* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y)))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-exp-log`
49×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
40×	`add-cbrt-cube`
34×	`times-frac` `prod-exp`
29×	`associate-r`
28×	`add-cube-cbrt`
20×	`div-exp`
14×	`cbrt-unprod`
11×	`pow1` `pow-exp`
10×	`cbrt-undiv`
7×	`associate-l` `distribute-lft-out--` `difference-of-squares`
6×	`cube-div` `rec-exp` `1-exp`
5×	`associate-/r*` `associate-/r/` `rem-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `div-inv` `associate-/l*` `unswap-sqr`
2×	`flip3--` `pow-pow` `un-div-inv` `*-commutative` `flip--`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `frac-2neg` `unpow3` `cube-prod` `clear-num` `distribute-lft-out` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

16.0ms	(* (hypot x y) (/ (hypot x y) (- x y)))
36.0ms	(pow (* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y))))) 3)
5.0ms	(/ (hypot x y) (- x y))
40.0ms	(* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y)))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (hypot x y) (/ (hypot x y) (- x y)))
103.0ms	(pow (* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y))))) 3)
91.0ms	(/ (hypot x y) (- x y))
94.0ms	(* (+ x y) (/ 1 (* (hypot x y) (/ (hypot x y) (- x y)))))

simplify99.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	613	1329
1	3217	1185
2	5001	1181

prune407.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

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	18	10
1	18	10

end0.0ms

sample473.0ms

Algorithm

intervals

Results

223.0ms	8000×	body	80	valid
110.0ms	8000×	pre	80	true