Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (0.0%)

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: 24.9b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(- (* b c) (* a d))
24.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

340×	`*-un-lft-identity`
276×	`add-sqr-sqrt`
170×	`associate-l`
144×	`prod-diff`
104×	`add-cube-cbrt`
88×	`times-frac`
78×	`associate-r`
66×	`unswap-sqr`
65×	`distribute-lft-out`
40×	`distribute-lft-out--` `difference-of-squares`
29×	`swap-sqr`
26×	`*-commutative`
15×	`fma-def`
12×	`fma-neg`
11×	`associate-/l*`
8×	`associate-/r*`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 337

Calls

3 calls:

19.0ms	(+ (* c c) (* d d))
17.0ms	(- (* b c) (* a d))
41.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* c c) (* d d))
40.0ms	(- (* b c) (* a d))
92.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify103.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	810	4080
1	2677	3154
2	5001	2993

prune407.0ms

Filtered

346 candidates to 112 candidates (32.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	337	9	346
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	337	10	347

Merged error: 11.0b

Counts

347 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (hypot c d) 1))
0.2b	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

rewrite324.0ms

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))
153.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
18.0ms	(- (* b c) (* a d))
35.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

series413.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (/ (hypot c d) 1))
191.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
39.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

simplify197.0ms

Algorithm

egg-herbie

Counts

1364 → 1364

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5001	17154

prune2.5s

Filtered

1364 candidates to 583 candidates (42.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1360	4	1364
Fresh	7	1	8
Picked	1	0	1
Done	0	1	1
Total	1368	6	1374

Merged error: 0.1b

Counts

1374 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
0.2b	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
2.4b	(/ b (/ (hypot c d) c))
3.6b	(/ a (/ (hypot c d) d))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

31410×	`times-frac`
21104×	`add-sqr-sqrt`
21056×	`*-un-lft-identity`
21011×	`add-cube-cbrt`
16080×	`associate-/r*`
8112×	`prod-diff`
7581×	`frac-sub`
6897×	`frac-times`
4441×	`associate-/l*`
2845×	`associate-/r/`
2706×	`distribute-rgt-in` `distribute-lft-in`
2432×	`div-inv`
1480×	`frac-2neg` `clear-num`
363×	`associate-*r/`
52×	`fma-neg` `associate-l`
40×	`add-exp-log`
23×	`add-cbrt-cube`
21×	`flip3--` `flip--`
19×	`associate-*l/`
18×	`div-exp` `associate-r` `difference-of-squares`
12×	`distribute-lft-out--`
10×	`prod-exp`
9×	`cbrt-undiv`
8×	`unswap-sqr`
6×	`pow1` `1-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `rec-exp` `cbrt-unprod`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 16099

Calls

4 calls:

186.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
547.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
7.0ms	(/ b (/ (hypot c d) c))
7.0ms	(/ a (/ (hypot c d) d))

series620.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
293.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
69.0ms	(/ b (/ (hypot c d) c))
74.0ms	(/ a (/ (hypot c d) d))

simplify5.5s

Algorithm

egg-herbie

Counts

16111 → 16111

Iterations

Useful iterations: 0 (269.0ms)

Iter	Nodes	Cost
0	19802	648277

prune1.3m

Filtered

16111 candidates to 14677 candidates (91.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	16107	4	16111
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	16111	6	16117

Merged error: 0b

Counts

16117 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
0.1b	(/ (* (/ 1 1) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (hypot c d) 1))
2.4b	(/ b (/ (hypot c d) c))
3.6b	(/ a (/ (hypot c d) d))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

12445×	`times-frac`
9181×	`add-sqr-sqrt`
8857×	`*-un-lft-identity`
8501×	`add-cube-cbrt`
6889×	`associate-/r*`
3971×	`frac-sub`
3639×	`associate-/l/`
3267×	`frac-times`
2717×	`associate-/l*`
2704×	`prod-diff`
972×	`associate-/r/`
935×	`div-inv`
893×	`frac-2neg` `clear-num`
363×	`associate-*r/`
252×	`associate-r`
182×	`associate-l`
135×	`difference-of-squares`
90×	`distribute-lft-out--`
88×	`add-exp-log`
70×	`unswap-sqr`
58×	`div-exp`
52×	`fma-neg`
35×	`add-cbrt-cube`
23×	`1-exp`
21×	`prod-exp`
17×	`cbrt-undiv`
14×	`*-commutative`
11×	`flip3--` `flip--`
9×	`associate-*l/`
6×	`rec-exp` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
1×	`sub-neg` `diff-log`

Counts

4 → 7583

Calls

4 calls:

177.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
761.0ms	(/ (* (/ 1 1) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (hypot c d) 1))
8.0ms	(/ b (/ (hypot c d) c))
8.0ms	(/ a (/ (hypot c d) d))

series557.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))
229.0ms	(/ (* (/ 1 1) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (hypot c d) 1))
70.0ms	(/ b (/ (hypot c d) c))
73.0ms	(/ a (/ (hypot c d) d))

simplify1.9s

Algorithm

egg-herbie

Counts

7595 → 7595

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	9211	187167

prune29.1s

Filtered

7595 candidates to 5848 candidates (77.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	7594	1	7595
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	7596	5	7601

Merged error: 0b

Counts

7601 → 5

regimes112.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	20	11
2	20	11

end0.0ms

sample498.0ms

Algorithm

intervals

Results

293.0ms

8500×

body

valid