Details

sample20.0ms

Algorithm

intervals

Results

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

simplify69.0ms

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: 20.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.0b	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
20.1b	(/ (fma x x (* y y)) (+ x y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 178

Calls

3 calls:

0.0ms	(fma x x (* y y))
17.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
6.0ms	(/ (fma x x (* y y)) (+ x y))

series180.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma x x (* y y))
73.0ms	(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
72.0ms	(/ (fma x x (* y y)) (+ x y))

simplify85.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	652	2043
1	2939	1866
2	5001	1860

prune388.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x y)
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))

rewrite38.0ms

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×	`associate-/r*` `associate-/r/`
4×	`expm1-log1p-u` `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×	`hypot-udef` `flip3--` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 117

Calls

4 calls:

0.0ms	(hypot x y)
13.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
15.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))

series318.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot x y)
91.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
88.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
94.0ms	(/ (hypot x y) (+ x y))

simplify48.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	378	858
1	1715	740
2	5001	733

prune463.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize15.0ms

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

13.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
16.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
5.0ms	(/ (hypot x y) (+ x y))
12.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)

series374.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
90.0ms	(* (hypot x y) (/ (hypot x y) (+ x y)))
86.0ms	(/ (hypot x y) (+ x y))
102.0ms	(pow (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))) 3)

simplify75.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	528	1247
1	2697	1134
2	5001	1132

prune385.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

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	(pow (log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))) 3)
0.3b	(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
17×	`times-frac`
16×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
5×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*` `log1p-expm1-u`
4×	`expm1-log1p-u` `distribute-lft-out` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `associate-/r/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`cube-mult` `pow-to-exp` `expm1-log1p` `flip3--` `pow-pow` `flip3-+` `unpow3` `div-sub` `associate-*r/` `pow-exp` `flip--` `flip-+` `expm1-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
5.0ms	(/ (hypot x y) (+ x y))
1.0ms	(pow (log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))) 3)
0.0ms	(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
94.0ms	(/ (hypot x y) (+ x y))
149.0ms	(pow (log1p (expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))) 3)
122.0ms	(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	392	969
1	1732	822
2	5002	814

prune328.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes37.0ms

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	17	13
1	17	13

end0.0ms

sample497.0ms

Algorithm

intervals

Results

243.0ms	8000×	body	80	valid
112.0ms	8000×	pre	80	true