Details

sample35.0ms

Algorithm

intervals

Results

18.0ms	94×	body	1280	valid
4.0ms	118×	body	80	valid
3.0ms	23×	body	640	valid
2.0ms	18×	body	320	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (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: 18.1b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
15×	`add-cube-cbrt` `sqrt-prod`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l` `associate-/r` `associate-/l` `difference-of-squares` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 82

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
74.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
87.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	269	634
1	861	604
2	2863	601
3	5001	601

prune151.0ms

Filtered

94 candidates to 65 candidates (30.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 17.7b

Counts

95 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b	(+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

127×	`*-un-lft-identity`
54×	`times-frac`
46×	`distribute-lft-out`
35×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`associate-l`
24×	`distribute-rgt-neg-in`
15×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`add-log-exp`
4×	`pow1` `associate-+r+` `distribute-neg-in`
3×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`
2×	`neg-sub0` `distribute-rgt-in` `associate-+r-` `distribute-lft-in` `unsub-neg` `sum-log` `associate-/r/` `associate-/l/`
1×	`neg-log`

Counts

4 → 147

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
42.0ms	(/ (+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms	(+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
164.0ms	(/ (+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
34.0ms	(+ (* 1.0 1.0) (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	356	1923
1	1441	1773
2	5001	1707

prune265.0ms

Filtered

159 candidates to 90 candidates (43.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	159	4	163

Merged error: 17.7b

Counts

163 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot 1.0 x))
0.0b	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
0.6b	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
1.1b	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
141×	`*-un-lft-identity`
97×	`times-frac`
54×	`add-cube-cbrt`
46×	`associate-l`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`distribute-lft-out`
29×	`sqrt-prod`
28×	`unswap-sqr`
25×	`associate-r`
24×	`*-commutative`
15×	`associate-/l*`
14×	`distribute-rgt-out` `distribute-lft1-in`
12×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`pow1` `associate-/r*`
8×	`distribute-rgt-out--`
6×	`add-log-exp`
3×	`div-exp` `pow-prod-down`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*r/` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `rec-exp` `pow-flip` `sqrt-unprod` `diff-log` `1-exp` `div-sub` `prod-exp` `cbrt-unprod` `inv-pow`

Counts

4 → 197

Calls

4 calls:

4.0ms	(/ 1 (hypot 1.0 x))
46.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
22.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
11.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (hypot 1.0 x))
162.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ (* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0))) 1.0))
77.0ms	(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
33.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

simplify90.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	606	2979
1	2285	2847
2	5002	2796

prune375.0ms

Filtered

209 candidates to 121 candidates (42.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	209	4	213

Merged error: 17.7b

Counts

213 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.2b	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

635×	`associate-/l*`
555×	`*-un-lft-identity`
484×	`frac-sub`
446×	`add-sqr-sqrt`
279×	`add-cube-cbrt`
202×	`associate-/r*`
174×	`associate-r`
171×	`associate-l`
145×	`times-frac`
107×	`distribute-lft-out`
69×	`swap-sqr`
58×	`unswap-sqr`
52×	`*-commutative`
49×	`frac-2neg`
47×	`clear-num`
46×	`associate-*r/` `associate-/l/`
26×	`flip3-+` `flip-+`
25×	`distribute-lft-out--`
18×	`difference-of-squares`
13×	`add-exp-log` `add-cbrt-cube`
12×	`sub-div`
6×	`associate-/r/` `add-log-exp`
5×	`div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`distribute-rgt-out--`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 695

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
24.0ms	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
194.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
187.0ms	(/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
341.0ms	(- (/ (* 1.0 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify336.0ms

Algorithm

egg-herbie

Counts

707 → 707

Iterations

Useful iterations: 1 (95.0ms)

Iter	Nodes	Cost
0	4386	26275
1	5002	26198

prune1.1s

Filtered

707 candidates to 341 candidates (51.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	702	5	707
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	705	6	711

Merged error: 17.4b

Counts

711 → 6

regimes158.0ms

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	18	30
1	18	30

end0.0ms

sample830.0ms

Algorithm

intervals

Results

477.0ms	2830×	body	1280	valid
114.0ms	4035×	body	80	valid
86.0ms	640×	body	640	valid
32.0ms	327×	body	320	valid
10.0ms	168×	body	160	valid