Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

263×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 24.3b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (* b c) (* a d))
23.8b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

322×	`*-un-lft-identity`
268×	`add-sqr-sqrt`
163×	`associate-l`
144×	`prod-diff`
98×	`add-cube-cbrt`
88×	`times-frac`
75×	`associate-r`
65×	`unswap-sqr`
60×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares`
25×	`*-commutative`
24×	`swap-sqr`
12×	`fma-neg`
11×	`associate-/l*`
8×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 304

Calls

2 calls:

17.0ms	(- (* b c) (* a d))
44.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (* b c) (* a d))
92.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify101.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	752	3996
1	2226	3080
2	5002	2923

prune244.0ms

Filtered

310 candidates to 86 candidates (72.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	302	8	310
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	302	9	311

Merged error: 10.0b

Counts

311 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot c d) 1))
0.3b	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
1.0b	(- (* b c) (* a d))
15.6b	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

1448×	`add-sqr-sqrt`
1042×	`*-un-lft-identity`
761×	`times-frac`
682×	`associate-/r*`
577×	`add-cube-cbrt`
551×	`frac-times`
452×	`associate-l`
351×	`associate-r` `unswap-sqr`
340×	`associate-/l*`
196×	`distribute-lft-out--`
192×	`difference-of-squares`
170×	`add-exp-log`
144×	`prod-diff`
93×	`div-exp`
69×	`*-commutative`
62×	`prod-exp`
56×	`clear-num`
54×	`frac-2neg`
50×	`add-cbrt-cube`
42×	`associate-/l/`
41×	`1-exp` `div-inv`
29×	`associate-*r/`
22×	`flip3--` `associate-/r/` `flip--`
20×	`cbrt-undiv`
19×	`associate-*l/`
15×	`rec-exp`
13×	`cbrt-unprod`
12×	`fma-neg`
7×	`pow1`
6×	`un-div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`remove-double-div`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `pow-prod-down` `inv-pow`

Counts

4 → 1352

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot c d) 1))
149.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
20.0ms	(- (* b c) (* a d))
31.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

series418.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (/ (hypot c d) 1))
190.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
45.0ms	(- (* b c) (* a d))
124.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

simplify209.0ms

Algorithm

egg-herbie

Counts

1364 → 1364

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	17154

prune2.0s

Filtered

1364 candidates to 583 candidates (57.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1359	5	1364
Fresh	6	1	7
Picked	1	0	1
Done	1	0	1
Total	1367	6	1373

Merged error: 0.1b

Counts

1373 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot c d) 1))
0.3b	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
2.3b	(/ b (/ (hypot c d) c))
4.3b	(/ a (/ (hypot c d) d))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

24179×	`times-frac`
16921×	`add-sqr-sqrt`
16890×	`*-un-lft-identity`
16864×	`add-cube-cbrt`
15287×	`associate-/r*`
7220×	`frac-sub`
6897×	`frac-times`
5408×	`prod-diff`
4019×	`associate-/l*`
2706×	`distribute-rgt-in` `distribute-lft-in`
1977×	`div-inv`
1909×	`associate-/r/`
1340×	`clear-num`
1339×	`frac-2neg`
363×	`associate-*r/`
55×	`add-exp-log`
52×	`associate-l`
30×	`div-exp`
28×	`add-cbrt-cube`
20×	`flip3--` `flip--`
19×	`associate-*l/`
18×	`associate-r`
12×	`cbrt-undiv` `1-exp`
10×	`prod-exp`
9×	`difference-of-squares`
8×	`unswap-sqr`
7×	`pow1`
6×	`rec-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-unprod`
2×	`sub-neg` `remove-double-div`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 13044

Calls

4 calls:

7.0ms	(/ 1 (/ (hypot c d) 1))
553.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
6.0ms	(/ b (/ (hypot c d) c))
7.0ms	(/ a (/ (hypot c d) d))

series811.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (/ (hypot c d) 1))
313.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
368.0ms	(/ b (/ (hypot c d) c))
75.0ms	(/ a (/ (hypot c d) d))

simplify4.7s

Algorithm

egg-herbie

Counts

13056 → 13056

Iterations

Useful iterations: 0 (298.0ms)

Iter	Nodes	Cost
0	19813	514997

prune46.7s

Filtered

13056 candidates to 9706 candidates (25.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	13051	5	13056
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	13056	6	13062

Merged error: 0b

Counts

13062 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
0.0b	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
2.3b	(/ b (/ (hypot c d) c))
4.3b	(/ a (/ (hypot c d) d))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

25741×	`times-frac`
17252×	`add-sqr-sqrt`
13418×	`*-un-lft-identity`
10576×	`add-cube-cbrt`
6092×	`cbrt-prod`
3154×	`associate-l`
2739×	`unswap-sqr`
2704×	`prod-diff`
1992×	`associate-r`
1426×	`associate-/r*`
1173×	`div-inv`
994×	`associate-/r/`
756×	`difference-of-squares`
747×	`swap-sqr`
722×	`frac-sub`
641×	`associate-/l*`
504×	`distribute-lft-out--`
372×	`associate-/l/`
363×	`associate-*r/`
249×	`*-commutative`
188×	`frac-2neg` `clear-num`
123×	`add-cbrt-cube`
72×	`cbrt-undiv`
62×	`add-exp-log`
52×	`fma-neg`
45×	`cbrt-unprod`
33×	`div-exp`
12×	`prod-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`1-exp`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log`

Counts

4 → 9646

Calls

4 calls:

185.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
631.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
6.0ms	(/ b (/ (hypot c d) c))
7.0ms	(/ a (/ (hypot c d) d))

series566.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
237.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
68.0ms	(/ b (/ (hypot c d) c))
72.0ms	(/ a (/ (hypot c d) d))

simplify3.2s

Algorithm

egg-herbie

Counts

9658 → 9658

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	11354	333785

prune36.2s

Filtered

9658 candidates to 7412 candidates (23.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	9655	3	9658
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	9658	6	9664

Merged error: 0b

Counts

9664 → 6

regimes151.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample506.0ms

Algorithm

intervals

Results

300.0ms

8440×

body

valid