Details

sample21.0ms

Algorithm

intervals

Results

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

simplify71.0ms

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: 19.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
19.1b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series90.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* x x) (* y y))
63.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify47.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	322	380
1	1875	324
2	5001	308

prune128.0ms

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	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
0.0b	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
0.0b	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
18.7b	(/ (fma x x (* y y)) (- x y))

rewrite108.0ms

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:

11.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
27.0ms	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
20.0ms	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
6.0ms	(/ (fma x x (* y y)) (- x y))

series302.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
85.0ms	(cbrt (pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3))
81.0ms	(pow (/ (+ x y) (/ (fma x x (* y y)) (- x y))) 3)
67.0ms	(/ (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

prune879.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y)))))
0.0b	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
0.3b	(expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y))))
18.7b	(/ (fma x x (* y y)) (- x y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
163×	`*-un-lft-identity`
119×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
26×	`associate-/r*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--`
5×	`log1p-expm1-u`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`log1p-udef` `expm1-log1p` `flip3-+` `log1p-expm1` `flip-+` `expm1-udef`

Counts

4 → 189

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y)))))
12.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
1.0ms	(expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y))))
6.0ms	(/ (fma x x (* y y)) (- x y))

series348.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(log1p (expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y)))))
68.0ms	(/ (+ x y) (/ (fma x x (* y y)) (- x y)))
97.0ms	(expm1 (/ (+ x y) (/ (fma x x (* y y)) (- x y))))
71.0ms	(/ (fma x x (* y y)) (- x y))

simplify76.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	544	2160
1	2422	1956
2	5001	1945

prune455.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

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) (/ (hypot x y) (- x y)))
0.0b	(/ (hypot x y) (- x y))
0.3b	(expm1 (/ (+ x y) (* (hypot x y) (/ (hypot x y) (- x y)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (+ x y) (* (hypot x y) (/ (hypot x y) (- x y))))
10.0ms	(* (hypot x y) (/ (hypot x y) (- x y)))
6.0ms	(/ (hypot x y) (- x y))
1.0ms	(expm1 (/ (+ x y) (* (hypot x y) (/ (hypot x y) (- x y)))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ x y) (* (hypot x y) (/ (hypot x y) (- x y))))
90.0ms	(* (hypot x y) (/ (hypot x y) (- x y)))
89.0ms	(/ (hypot x y) (- x y))
123.0ms	(expm1 (/ (+ x y) (* (hypot x y) (/ (hypot x y) (- x y)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	390	982
1	1715	849
2	5002	841

prune310.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

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	12	9
1	12	9

end0.0ms

sample468.0ms

Algorithm

intervals

Results

226.0ms	8000×	body	80	valid
109.0ms	8000×	pre	80	true