Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	192×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	95×	body	80	nan
2.0ms	15×	body	640	nan
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	nan
0.0ms	5×	body	320	nan
0.0ms	5×	body	160	valid
0.0ms	1×	body	160	nan

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: 16.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite78.0ms

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:

12.0ms	(/ (- x y) (- 1.0 y))
28.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
27.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series172.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify97.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (61.0ms)

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

prune337.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1.0 y))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
3.9b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.1b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`times-frac`
27×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-l` `associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `prod-diff` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `log-div` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `log-pow` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 131

Calls

4 calls:

5.0ms	(/ 1 (- 1.0 y))
23.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (- 1.0 y))
36.0ms	(* (- x y) (/ 1 (- 1.0 y)))
81.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
53.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	521	939
1	2201	815
2	5001	760

prune306.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
1.7b	(expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y)))))
2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
24.0b	(log (expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 193

Calls

4 calls:

12.0ms	(/ (- x y) (- 1.0 y))
0.0ms	(expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y)))))
25.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
1.0ms	(log (expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y))))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- x y) (- 1.0 y))
148.0ms	(expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y)))))
49.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
288.0ms	(log (expm1 (log1p (- 1.0 (/ (- x y) (- 1.0 y))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1002	4167
1	3319	3084
2	5002	2858

prune427.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x y) (/ 1 (- 1.0 y)))
3.9b	(log (/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
5.0b	(- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3))
11.5b	(/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

183×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
96×	`prod-diff`
95×	`times-frac`
88×	`add-cube-cbrt`
69×	`sqr-pow`
68×	`difference-of-squares`
55×	`unpow-prod-down` `cube-prod`
43×	`log-prod`
21×	`cube-mult` `unpow3` `associate-r`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`fma-neg` `distribute-lft-out--`
11×	`add-cbrt-cube`
8×	`difference-cubes`
7×	`pow1`
6×	`add-log-exp`
5×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`associate-/r*` `div-inv` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rem-log-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `log-div` `rec-exp` `frac-2neg` `diff-log` `1-exp` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `log-pow` `un-div-inv` `-commutative`

Counts

4 → 312

Calls

4 calls:

24.0ms	(* (- x y) (/ 1 (- 1.0 y)))
11.0ms	(log (/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
20.0ms	(- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3))
42.0ms	(/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

series828.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- x y) (/ 1 (- 1.0 y)))
349.0ms	(log (/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
178.0ms	(- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3))
257.0ms	(/ (- (pow 1.0 3) (pow (* (- x y) (/ 1 (- 1.0 y))) 3)) (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

simplify109.0ms

Algorithm

egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1131	7019
1	5001	6155

prune841.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes149.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 18.3b

bsearch109.0ms

Steps

Iters	Range		Point
10	1050.8208076513	6622766257468.929	39316813.46217899
6	-1419131402.1388264	-110051303.36362042	-244170417.41587064

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample1.0s

Algorithm

intervals

Results

222.0ms	5689×	body	80	valid
157.0ms	779×	body	1280	valid
111.0ms	807×	body	640	valid
104.0ms	3853×	body	80	nan
55.0ms	363×	body	1280	nan
49.0ms	427×	body	640	nan
46.0ms	472×	body	320	valid
19.0ms	224×	body	320	nan
17.0ms	253×	body	160	valid
6.0ms	106×	body	160	nan