Details

sample27.0ms

Algorithm

intervals

Results

14.0ms

442×

body

valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.0b	(- (+ (* x x) (* y y)) (* z z))
26.2b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

817×	`*-un-lft-identity`
337×	`associate-l`
335×	`add-sqr-sqrt`
228×	`times-frac`
211×	`distribute-lft-out`
154×	`distribute-lft-out--`
137×	`add-cube-cbrt`
120×	`prod-diff`
117×	`swap-sqr`
87×	`associate-r`
70×	`difference-of-squares`
43×	`*-commutative` `unswap-sqr`
19×	`associate-/l*`
15×	`fma-def`
12×	`associate-/r*`
10×	`add-log-exp`
8×	`add-exp-log` `fma-neg` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `+-commutative` `flip3--` `diff-log` `div-exp` `associate--l+` `sum-log` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 472

Calls

3 calls:

17.0ms	(+ (* x x) (* y y))
33.0ms	(- (+ (* x x) (* y y)) (* z z))
49.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series186.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
52.0ms	(- (+ (* x x) (* y y)) (* z z))
102.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify172.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	1009	5363
1	4167	4308
2	5001	4296

prune342.0ms

Filtered

481 candidates to 136 candidates (71.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	473	8	481
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	474	8	482

Merged error: 0.0b

Counts

482 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ z (hypot x y))
0.0b	(- (/ (hypot x y) y) (/ z y))
0.0b	(/ (hypot x y) y)
0.1b	(* (/ (+ z (hypot x y)) (* 2.0 1)) (- (/ (hypot x y) y) (/ z y)))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

2674×	`associate-/r*`
2243×	`*-un-lft-identity`
2194×	`add-sqr-sqrt`
1980×	`frac-times`
1944×	`frac-sub`
1873×	`add-cube-cbrt`
1663×	`associate-/l*`
795×	`times-frac`
572×	`frac-2neg`
524×	`clear-num`
507×	`prod-diff`
341×	`associate-l`
297×	`associate-r`
196×	`unswap-sqr`
182×	`associate-/l/`
171×	`distribute-rgt-in` `distribute-lft-in`
168×	`sub-div`
105×	`distribute-lft-out`
96×	`*-commutative`
92×	`flip3-+` `flip-+`
90×	`associate-*r/`
85×	`div-inv`
24×	`flip3--` `flip--`
22×	`associate-*l/`
18×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`fma-neg`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `fma-def`
2×	`distribute-rgt-out--`
1×	`+-commutative` `diff-log` `1-exp` `pow-prod-down` `sum-log`

Counts

4 → 2863

Calls

4 calls:

3.0ms	(+ z (hypot x y))
29.0ms	(- (/ (hypot x y) y) (/ z y))
3.0ms	(/ (hypot x y) y)
110.0ms	(* (/ (+ z (hypot x y)) (* 2.0 1)) (- (/ (hypot x y) y) (/ z y)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ z (hypot x y))
82.0ms	(- (/ (hypot x y) y) (/ z y))
91.0ms	(/ (hypot x y) y)
204.0ms	(* (/ (+ z (hypot x y)) (* 2.0 1)) (- (/ (hypot x y) y) (/ z y)))

simplify620.0ms

Algorithm

egg-herbie

Counts

2875 → 2875

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5001	59298

prune4.8s

Filtered

2875 candidates to 1316 candidates (54.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	2869	6	2875
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	2876	7	2883

Merged error: 0b

Counts

2883 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ z (hypot x y))
0.0b	(- (/ (hypot x y) y) (/ z y))
0.0b	(/ (hypot x y) y)
0.1b	(* (+ z (hypot x y)) (* (/ 1 (* 2.0 1)) (- (/ (hypot x y) y) (/ z y))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

8768×	`frac-times`
7334×	`associate-/r*`
5269×	`add-sqr-sqrt`
4941×	`frac-sub`
4798×	`*-un-lft-identity`
4370×	`add-cube-cbrt`
4116×	`associate-/l*`
2089×	`associate-*r/`
1821×	`flip3-+` `flip-+`
1494×	`frac-2neg`
1372×	`clear-num`
1259×	`times-frac`
907×	`associate-r`
875×	`associate-l`
845×	`prod-diff`
684×	`distribute-rgt-in` `distribute-lft-in`
582×	`unswap-sqr`
427×	`sub-div`
278×	`*-commutative`
137×	`div-inv`
61×	`flip3--` `flip--`
59×	`associate-*l/`
44×	`add-exp-log`
27×	`prod-exp`
20×	`add-cbrt-cube`
13×	`fma-neg`
9×	`pow1`
8×	`cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`div-exp`
6×	`1-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-def` `pow-prod-down`
2×	`distribute-rgt-out--` `distribute-lft-out`
1×	`+-commutative` `diff-log` `sum-log`

Counts

4 → 6588

Calls

4 calls:

3.0ms	(+ z (hypot x y))
30.0ms	(- (/ (hypot x y) y) (/ z y))
3.0ms	(/ (hypot x y) y)
402.0ms	(* (+ z (hypot x y)) (* (/ 1 (* 2.0 1)) (- (/ (hypot x y) y) (/ z y))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ z (hypot x y))
76.0ms	(- (/ (hypot x y) y) (/ z y))
82.0ms	(/ (hypot x y) y)
197.0ms	(* (+ z (hypot x y)) (* (/ 1 (* 2.0 1)) (- (/ (hypot x y) y) (/ z y))))

simplify1.7s

Algorithm

egg-herbie

Counts

6600 → 6600

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	8806	167282

prune22.0s

Filtered

6600 candidates to 5097 candidates (22.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	6598	2	6600
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	6600	7	6607

Merged error: 0b

Counts

6607 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ 1 (* 2.0 1)) (fma (/ 1 1) (/ (hypot x y) y) (- (* (/ 1 y) z)))) (+ z (hypot x y)))
0.2b	(* (/ 1 y) z)
0.2b	(* (/ 1 y) z)
51.7b	(fma (- (/ 1 y)) z (* (/ 1 y) z))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

145×	`associate-l`
141×	`add-sqr-sqrt`
94×	`associate-*l/`
82×	`*-un-lft-identity`
73×	`times-frac`
62×	`add-cube-cbrt`
60×	`add-exp-log`
48×	`unswap-sqr`
45×	`associate-/r*`
38×	`frac-times`
35×	`prod-exp`
31×	`associate-r`
28×	`add-cbrt-cube`
20×	`flip3-+` `flip-+`
15×	`associate-/l*`
13×	`pow1`
12×	`cbrt-unprod`
10×	`div-exp` `*-commutative`
8×	`1-exp`
5×	`rec-exp` `frac-2neg` `pow-prod-down` `clear-num`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*r/`
1×	`fma-udef` `distribute-lft-out`

Counts

4 → 260

Calls

4 calls:

41.0ms	(* (* (/ 1 (* 2.0 1)) (fma (/ 1 1) (/ (hypot x y) y) (- (* (/ 1 y) z)))) (+ z (hypot x y)))
8.0ms	(* (/ 1 y) z)
8.0ms	(* (/ 1 y) z)
1.0ms	(fma (- (/ 1 y)) z (* (/ 1 y) z))

series274.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (* (/ 1 (* 2.0 1)) (fma (/ 1 1) (/ (hypot x y) y) (- (* (/ 1 y) z)))) (+ z (hypot x y)))
9.0ms	(* (/ 1 y) z)
10.0ms	(* (/ 1 y) z)
21.0ms	(fma (- (/ 1 y)) z (* (/ 1 y) z))

simplify78.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	1591	3033
1	5001	2685

prune836.0ms

Filtered

272 candidates to 181 candidates (33.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	271	1	272
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	272	7	279

Merged error: 0b

Counts

279 → 7

regimes124.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	22	10
2	22	10

end0.0ms

sample732.0ms

Algorithm

intervals

Results

457.0ms

13633×

body

valid