Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	93×	body	1280	valid
7.0ms	129×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

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: 16.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l` `difference-of-squares`
2×	`pow1` `sqrt-prod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

2 → 43

Calls

2 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series91.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	166	342
1	498	320
2	1423	318
3	5001	318

prune110.0ms

Filtered

49 candidates to 35 candidates (71.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Merged error: 16.4b

Counts

50 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`associate-*r/`
36×	`*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`frac-sub`
20×	`times-frac`
14×	`associate-/l*`
12×	`flip3--` `associate-/r*` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`clear-num` `difference-of-squares`
4×	`pow1` `frac-2neg` `associate-l` `associate--l+` `un-div-inv` `distribute-lft-out--`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 114

Calls

4 calls:

10.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
30.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
10.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify78.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	542	1148
1	2248	1096
2	5003	1094

prune338.0ms

Filtered

126 candidates to 87 candidates (69.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Merged error: 16.4b

Counts

129 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
0.0b	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
0.1b	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.5b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

10836×	`associate-*r/`
4768×	`frac-add`
3572×	`frac-times`
3311×	`*-un-lft-identity`
3006×	`flip3--` `flip--`
2911×	`add-sqr-sqrt`
2394×	`associate-/r/`
1856×	`associate-/l*`
1574×	`associate-l`
1350×	`associate-/r*`
1063×	`times-frac`
1011×	`add-cube-cbrt`
893×	`clear-num`
892×	`un-div-inv`
723×	`unpow-prod-down` `cube-prod`
697×	`associate-*l/`
672×	`difference-of-squares`
661×	`distribute-lft-out`
571×	`unswap-sqr`
447×	`frac-2neg`
238×	`distribute-lft-out--`
197×	`sqr-pow`
109×	`flip3-+` `flip-+`
99×	`cube-div`
59×	`pow-unpow`
56×	`difference-cubes`
46×	`associate-r`
44×	`frac-sub`
24×	`associate-/l/`
21×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-+r+`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sub-neg`
4×	`pow-prod-down` `*-commutative` `div-inv`
3×	`cbrt-undiv` `div-exp` `pow-exp` `rem-cube-cbrt`
2×	`+-commutative` `pow-pow`
1×	`cube-mult` `pow-to-exp` `diff-log` `unpow3` `div-sub`

Counts

4 → 3921

Calls

4 calls:

47.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
411.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
11.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
81.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series340.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
177.0ms	(/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5)))))
33.0ms	(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
73.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify1.7s

Algorithm

egg-herbie

Counts

3933 → 3933

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	6720	171506

prune18.0s

Filtered

3933 candidates to 2181 candidates (55.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	3930	3	3933
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	3933	4	3937

Merged error: 16.1b

Counts

3937 → 4

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (hypot 1.0 x))
1.5b	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
1.5b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
1.5b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

1896×	`associate-*r/`
929×	`add-sqr-sqrt`
634×	`flip3--` `flip--`
632×	`frac-times`
582×	`frac-sub`
418×	`unswap-sqr`
320×	`associate-*l/`
293×	`*-un-lft-identity`
200×	`associate-/l*`
178×	`difference-of-squares`
150×	`associate-/r*`
136×	`associate-r`
117×	`add-cube-cbrt`
100×	`clear-num` `un-div-inv`
74×	`associate-l`
60×	`distribute-rgt-out--`
51×	`distribute-lft-out--`
50×	`unpow-prod-down` `frac-2neg` `cube-prod`
48×	`times-frac`
44×	`cube-div`
32×	`distribute-rgt-in` `distribute-lft-in`
30×	`*-commutative`
28×	`swap-sqr`
19×	`sub-neg`
16×	`associate--l+` `associate--r+`
14×	`sqr-pow`
10×	`add-log-exp`
8×	`sub-div`
4×	`pow1` `difference-cubes` `add-exp-log` `pow-unpow` `add-cbrt-cube`
3×	`cbrt-prod` `diff-log`
1×	`pow1/3`

Counts

4 → 946

Calls

4 calls:

1.0ms	(cbrt (hypot 1.0 x))
81.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
139.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
140.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (hypot 1.0 x))
69.0ms	(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
37.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
46.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

simplify367.0ms

Algorithm

egg-herbie

Counts

958 → 958

Iterations

Useful iterations: 1 (88.0ms)

Iter	Nodes	Cost
0	4248	27815
1	5002	27459

prune5.1s

Filtered

958 candidates to 391 candidates (40.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	957	1	958
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	958	4	962

Merged error: 16.1b

Counts

962 → 4

regimes144.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	114
1	66	114

end0.0ms

sample845.0ms

Algorithm

intervals

Results

492.0ms	2908×	body	1280	valid
118.0ms	3983×	body	80	valid
85.0ms	614×	body	640	valid
31.0ms	313×	body	320	valid
11.0ms	182×	body	160	valid