Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
5.0ms	24×	body	1280	valid
3.0ms	114×	body	80	nan
3.0ms	21×	body	640	valid
2.0ms	13×	body	1280	nan
2.0ms	16×	body	320	valid
1.0ms	12×	body	640	nan
0.0ms	7×	body	160	valid
0.0ms	3×	body	320	nan
0.0ms	3×	body	160	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
1.9b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.5b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite80.0ms

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:

15.0ms	(/ (- x y) (- 1.0 y))
26.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
28.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series180.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
88.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify88.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (60.0ms)

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

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 y))
0.3b	(cbrt (- 1.0 y))
3.5b	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
11.4b	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `prod-diff`
2×	`log-div` `pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (- 1.0 y))
2.0ms	(cbrt (- 1.0 y))
2.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
2.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series337.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (- 1.0 y))
96.0ms	(cbrt (- 1.0 y))
94.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
55.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	378	1088
1	1244	972
2	5001	950

prune279.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))) (log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))))))
11.4b	(- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))
12.5b	(log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))))
16.7b	(log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

112×	`prod-diff`
88×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`unpow-prod-down` `cube-prod`
39×	`sqr-pow`
32×	`log-prod`
25×	`difference-of-squares`
21×	`cube-mult` `unpow3`
19×	`pow1`
16×	`fma-neg`
15×	`log-pow`
13×	`associate--l+`
8×	`log-div`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`difference-cubes` `associate--r+`
2×	`associate--l-` `sub-neg` `flip3-+` `diff-log` `rem-log-exp` `flip-+` `associate--r-`

Counts

4 → 233

Calls

4 calls:

1.1s	(- (log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))) (log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))))))
16.0ms	(- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))
1.1s	(log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))))
15.0ms	(log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

431.0ms	(- (log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))) (log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))))))
277.0ms	(- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3))
236.0ms	(log (+ (* 1.0 1.0) (+ (* (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))) (* 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))))
301.0ms	(log (- (pow 1.0 3) (pow (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))) 3)))

simplify226.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	824	12881
1	3307	9630
2	5001	9621

prune619.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x y) (* 1.0 (/ 1 y)))
3.0b	(fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y))))
3.9b	(log (fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y)))))
8.3b	(/ x (pow y 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`fma-neg` `prod-diff`
12×	`unpow-prod-down`
10×	`add-exp-log`
8×	`associate-/r*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `sqr-pow`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`associate-*r/` `un-div-inv` `frac-sub` `sub-div`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip--` `fma-udef`

Counts

4 → 120

Calls

4 calls:

12.0ms	(- (/ x y) (* 1.0 (/ 1 y)))
0.0ms	(fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y))))
1.0ms	(log (fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y)))))
4.0ms	(/ x (pow y 2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ x y) (* 1.0 (/ 1 y)))
38.0ms	(fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y))))
64.0ms	(log (fma 1.0 (/ x (pow y 2)) (- (/ x y) (* 1.0 (/ 1 y)))))
27.0ms	(/ x (pow y 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	432	915
1	1639	768
2	5001	735

prune336.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 16.8b

bsearch131.0ms

Steps

Iters	Range		Point
10	0.00023067256624480483	29129170.846978452	28223629.68475053
8	-513705451564942.06	-1847211671904.2754	-1864702967354.4304

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	23
1	37	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

222.0ms	5692×	body	80	valid
164.0ms	808×	body	1280	valid
104.0ms	769×	body	640	valid
101.0ms	3880×	body	80	nan
60.0ms	388×	body	1280	nan
44.0ms	455×	body	320	valid
43.0ms	377×	body	640	nan
19.0ms	234×	body	320	nan
18.0ms	276×	body	160	valid
7.0ms	133×	body	160	nan