Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	190×	body	80	valid
4.0ms	31×	body	640	valid
3.0ms	18×	body	1280	valid
3.0ms	103×	body	80	nan
1.0ms	14×	body	640	nan
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	nan
0.0ms	5×	body	160	nan
0.0ms	3×	body	320	nan
0.0ms	3×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
102×	`times-frac`
93×	`prod-diff`
81×	`add-cube-cbrt`
46×	`difference-of-squares`
44×	`distribute-lft-out--`
8×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `div-inv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`log-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `associate--r-`

Counts

3 → 187

Calls

3 calls:

25.0ms	(/ (- x y) (- 1.0 y))
48.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
50.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series186.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (- x y) (- 1.0 y))
58.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
90.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify83.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	847	3956
1	2766	2899
2	5001	2689

prune356.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
4.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-sqr-sqrt`
266×	`*-un-lft-identity`
186×	`prod-diff`
154×	`times-frac`
138×	`add-cube-cbrt`
68×	`difference-of-squares`
64×	`distribute-lft-out--`
18×	`log-prod`
12×	`sqrt-prod` `associate-/r/`
10×	`flip3--` `flip--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `log-pow` `div-inv`
4×	`expm1-log1p-u` `log-div` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 276

Calls

4 calls:

47.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
46.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
38.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
60.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
133.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
137.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	775	7342
1	2406	5244
2	5002	4770

prune586.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.9b	(log (sqrt (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
4.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

272×	`add-sqr-sqrt`
263×	`*-un-lft-identity`
186×	`prod-diff`
153×	`times-frac`
137×	`add-cube-cbrt`
66×	`difference-of-squares`
63×	`distribute-lft-out--`
54×	`cbrt-div`
36×	`flip3--` `flip--`
28×	`frac-times` `log-div` `sqrt-div`
27×	`pow1`
20×	`log-pow`
16×	`sqrt-pow1`
14×	`associate-*l/`
13×	`log-prod`
12×	`associate-/r/`
9×	`pow1/3` `pow-prod-up`
8×	`associate-*r/` `add-log-exp`
7×	`sqrt-prod`
6×	`add-exp-log` `pow-plus` `fma-neg` `div-inv`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-sqr`
2×	`pow2` `sub-neg` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`
1×	`pow3`

Counts

4 → 309

Calls

4 calls:

46.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
46.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
340.0ms	(log (sqrt (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
39.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
60.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
132.0ms	(log (sqrt (* (* (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y))))) (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))))
140.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	969	8928
1	2611	6791
2	5001	5966

prune767.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

4.9b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
4.9b	(log (sqrt (+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))) (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3))))))))
9.4b	(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
13.4b	(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

rewrite6.8s

Algorithm

rewrite-expression-head

Rules

3290×	`*-un-lft-identity`
2583×	`add-sqr-sqrt`
1950×	`times-frac`
1310×	`difference-of-squares`
1288×	`unpow-prod-down` `cube-prod`
1283×	`distribute-lft-out--`
1005×	`associate-r`
568×	`distribute-lft-neg-in` `distribute-rgt-out`
420×	`distribute-lft-out`
419×	`distribute-rgt-neg-in`
352×	`sqr-pow`
312×	`add-cube-cbrt`
30×	`difference-cubes`
25×	`associate-/r*`
15×	`log-prod`
14×	`neg-mul-1` `distribute-lft1-in`
13×	`add-exp-log`
11×	`associate-*r/` `add-cbrt-cube`
10×	`pow1` `log-div` `flip3--` `sqrt-div` `associate-/r/` `flip--`
9×	`frac-add` `sqrt-prod`
6×	`log-pow`
5×	`div-inv`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `distribute-neg-frac`
2×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 1149

Calls

4 calls:

37.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
297.0ms	(log (sqrt (+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))) (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3))))))))
6.1s	(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
60.0ms	(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
308.0ms	(log (sqrt (+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))) (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3))))))))
45.0ms	(* (fma 1.0 1.0 (fma y y (* 1.0 y))) (+ (- (/ (- x y) (- (pow 1.0 3) (pow y 3)))) (/ (- x y) (- (pow 1.0 3) (pow y 3)))))
84.0ms	(/ (* (fma 1.0 1.0 (fma y y (* 1.0 y))) (- x y)) (- (pow 1.0 3) (pow y 3)))

simplify192.0ms

Algorithm

egg-herbie

Counts

1161 → 1161

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1607	13282
1	5003	12969

prune2.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes210.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 18.7b

bsearch179.0ms

Steps

Iters	Range		Point
11	0.01509307947529729	2.6456288670904664e+20	3758135.545993155
9	-8425493960980.196	-11523406.719001934	-125230047.99645755

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	50
1	61	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

215.0ms	5655×	body	80	valid
152.0ms	811×	body	1280	valid
106.0ms	821×	body	640	valid
89.0ms	3558×	body	80	nan
47.0ms	474×	body	320	valid
46.0ms	328×	body	1280	nan
45.0ms	374×	body	640	nan
18.0ms	225×	body	320	nan
15.0ms	239×	body	160	valid
6.0ms	119×	body	160	nan