Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	48	7
2	104	7
3	196	7
4	359	7
5	686	7
6	1343	7
7	5001	7

prune3.0ms

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: 18.9b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
18.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+ (* x x) (* y y))
16.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series16.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	308	388
1	1848	330
2	5001	322

prune67.0ms

Filtered

48 candidates to 39 candidates (18.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.7b

Counts

49 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
18.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
18.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/l/`
19×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
9×	`cbrt-prod` `flip3--` `associate-/r*` `flip--`
8×	`associate-/r/`
6×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`cbrt-div` `pow1/3`

Counts

4 → 111

Calls

4 calls:

8.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
15.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
12.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
11.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))
10.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	321	1177
1	1613	1020
2	5002	984

prune142.0ms

Filtered

123 candidates to 103 candidates (16.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Merged error: 0.7b

Counts

127 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.2b	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
18.5b	(/ (+ x y) (+ (pow x 2) (pow y 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
41×	`times-frac`
32×	`add-sqr-sqrt`
31×	`distribute-lft-out`
26×	`associate-r`
25×	`add-cube-cbrt`
20×	`unpow-prod-down`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3-+` `associate-/r/` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 109

Calls

3 calls:

7.0ms	(+ (pow x 2) (pow y 2))
20.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
11.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

series27.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (pow x 2) (pow y 2))
14.0ms	(* (- x y) (/ (+ x y) (+ (pow x 2) (pow y 2))))
7.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	390	902
1	1953	823
2	5002	822

prune153.0ms

Filtered

118 candidates to 69 candidates (41.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	118	4	122

Merged error: 0.7b

Counts

122 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow x 2) (pow y 2))
0.0b	(/ (* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2)))) (+ x y))
18.5b	(/ (+ x y) (+ (pow x 2) (pow y 2)))
18.5b	(* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity`
45×	`times-frac`
33×	`add-sqr-sqrt` `distribute-lft-out`
28×	`add-cube-cbrt`
26×	`associate-r`
20×	`add-exp-log` `unpow-prod-down` `add-cbrt-cube`
9×	`associate-/r*`
7×	`associate-/l/`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `add-log-exp`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`frac-times` `flip3--` `associate-l` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod`
3×	`div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `difference-of-squares`

Counts

4 → 140

Calls

4 calls:

7.0ms	(+ (pow x 2) (pow y 2))
19.0ms	(/ (* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2)))) (+ x y))
11.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))
20.0ms	(* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (pow x 2) (pow y 2))
10.0ms	(/ (* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2)))) (+ x y))
7.0ms	(/ (+ x y) (+ (pow x 2) (pow y 2)))
14.0ms	(* (- (* x x) (* y y)) (/ (+ x y) (+ (pow x 2) (pow y 2))))

simplify98.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	553	1470
1	3176	1267
2	5001	1235

prune194.0ms

Filtered

152 candidates to 96 candidates (36.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	151	5	156

Merged error: 0.7b

Counts

156 → 5

regimes155.0ms

Accuracy

73% (5.3b remaining)

Error of 5.7b against oracle of 0.4b and baseline of 19.9b

bsearch64.0ms

Steps

Iters	Range		Point
8	9.248213857936598e-181	1.422664319248497e-177	9.347269768670303e-181
5	1.0895834673440059e-218	2.453862316361132e-218	2.412798504692918e-218
8	-2.1710675002639838e-161	-8.148337209962211e-164	-2.4992551874327323e-162
10	-5.4775306096553096e+162	-6.717857725957104e+151	-1.7974365593801703e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	52
1	32	52

end0.0ms

sample712.0ms

Algorithm

intervals

Results

322.0ms	8000×	body	80	valid
165.0ms	8000×	pre	80	true

Details

sample24.0ms

simplify70.0ms

prune3.0ms

localize9.0ms

rewrite22.0ms

series16.0ms

simplify50.0ms

prune67.0ms

localize12.0ms

rewrite51.0ms

series54.0ms

simplify56.0ms

prune142.0ms

localize10.0ms

rewrite43.0ms

series27.0ms

simplify63.0ms

prune153.0ms

localize14.0ms

rewrite66.0ms

series37.0ms

simplify98.0ms

prune194.0ms

regimes155.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample712.0ms

Profiling