Details

sample25.0ms

Algorithm

intervals

Results

10.0ms

272×

body

valid

simplify16.0ms

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

prune3.0ms

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: 26.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.1b	(- (* b c) (* a d))
26.0b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite104.0ms

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:

16.0ms	(+ (* c c) (* d d))
17.0ms	(- (* b c) (* a d))
45.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (* c c) (* d d))
44.0ms	(- (* b c) (* a d))
100.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify113.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	798	4080
1	2578	3154
2	5001	2994

prune345.0ms

Filtered

346 candidates to 112 candidates (32.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	338	8	346
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	339	8	347

Merged error: 10.3b

Counts

347 → 8

localize14.0ms

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)))
1.1b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

rewrite383.0ms

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:

9.0ms	(/ 1 (/ (hypot c d) 1))
181.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
20.0ms	(- (* b c) (* a d))
36.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

series811.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (/ (hypot c d) 1))
198.0ms	(* (/ 1 (/ (hypot c d) 1)) (/ (- (* b c) (* a d)) (* (hypot c d) 1)))
48.0ms	(- (* b c) (* a d))
501.0ms	(/ (- (* b c) (* a d)) (* (hypot c d) 1))

simplify226.0ms

Algorithm

egg-herbie

Counts

1364 → 1364

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	17154

prune1.9s

Filtered

1364 candidates to 583 candidates (42.7%)

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	0	0	0
Total	1366	6	1372

Merged error: 0.1b

Counts

1372 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (hypot c d) d)
0.2b	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
2.1b	(/ a (/ (hypot c d) d))
3.4b	(/ b (/ (hypot c d) c))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

24113×	`times-frac`
16885×	`add-sqr-sqrt`
16853×	`*-un-lft-identity`
16828×	`add-cube-cbrt`
15274×	`associate-/r*`
7220×	`frac-sub`
6897×	`frac-times`
5408×	`prod-diff`
4015×	`associate-/l*`
2706×	`distribute-rgt-in` `distribute-lft-in`
1973×	`div-inv`
1900×	`associate-/r/`
1338×	`frac-2neg` `clear-num`
363×	`associate-*r/`
52×	`associate-l`
42×	`add-exp-log`
25×	`add-cbrt-cube`
20×	`flip3--` `flip--`
19×	`div-exp` `associate-*l/`
18×	`associate-r`
10×	`cbrt-undiv` `prod-exp`
9×	`difference-of-squares`
8×	`unswap-sqr`
6×	`pow1` `1-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `cbrt-unprod`
2×	`sub-neg`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 12982

Calls

4 calls:

3.0ms	(/ (hypot c d) d)
532.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
7.0ms	(/ a (/ (hypot c d) d))
6.0ms	(/ b (/ (hypot c d) c))

series547.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (hypot c d) d)
315.0ms	(* (/ 1 (/ (hypot c d) 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d))))
71.0ms	(/ a (/ (hypot c d) d))
82.0ms	(/ b (/ (hypot c d) c))

simplify5.0s

Algorithm

egg-herbie

Counts

12994 → 12994

Iterations

Useful iterations: 0 (276.0ms)

Iter	Nodes	Cost
0	19792	514508

prune45.3s

Filtered

12994 candidates to 9656 candidates (74.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	12989	5	12994
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	12993	7	13000

Merged error: 0b

Counts

13000 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (hypot c d) d)
0.1b	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
2.1b	(/ a (/ (hypot c d) d))
3.4b	(/ b (/ (hypot c d) c))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

18444×	`times-frac`
13033×	`add-sqr-sqrt`
9215×	`*-un-lft-identity`
6393×	`add-cube-cbrt`
6092×	`cbrt-prod`
3154×	`associate-l`
2739×	`unswap-sqr`
1992×	`associate-r`
747×	`swap-sqr` `difference-of-squares`
714×	`div-inv`
620×	`associate-/r*`
498×	`distribute-lft-out--`
372×	`associate-/l/`
363×	`associate-*r/`
361×	`frac-sub`
249×	`*-commutative`
215×	`associate-/l*`
125×	`add-cbrt-cube`
73×	`cbrt-undiv`
64×	`add-exp-log`
49×	`associate-/r/`
46×	`frac-2neg` `clear-num`
45×	`cbrt-unprod`
34×	`div-exp`
12×	`prod-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`1-exp`
1×	`flip3--` `flip--`

Counts

4 → 6529

Calls

4 calls:

3.0ms	(/ (hypot c d) d)
614.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
6.0ms	(/ a (/ (hypot c d) d))
7.0ms	(/ b (/ (hypot c d) c))

series467.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (hypot c d) d)
242.0ms	(/ (* (* (cbrt 1) (cbrt 1)) (- (/ b (/ (hypot c d) c)) (/ a (/ (hypot c d) d)))) (/ (/ (hypot c d) 1) (cbrt 1)))
69.0ms	(/ a (/ (hypot c d) d))
80.0ms	(/ b (/ (hypot c d) c))

simplify2.1s

Algorithm

egg-herbie

Counts

6541 → 6541

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	7648	205414

prune21.8s

Filtered

6541 candidates to 4862 candidates (74.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	6540	1	6541
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	6541	7	6548

Merged error: 0b

Counts

6548 → 7

regimes137.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms

sample503.0ms

Algorithm

intervals

Results

291.0ms

8490×

body

valid