Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	29×	body	1280	valid
7.0ms	190×	body	80	valid
3.0ms	120×	body	80	nan
3.0ms	19×	body	1280	nan
3.0ms	20×	body	640	valid
1.0ms	11×	body	640	nan
1.0ms	12×	body	320	valid
0.0ms	4×	body	320	nan
0.0ms	5×	body	160	valid
0.0ms	4×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
1.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
5.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--` `add-log-exp`
8×	`associate-/r/`
7×	`add-exp-log`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`diff-log` `associate--r-`
2×	`sub-neg` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 228

Calls

4 calls:

20.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
16.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
39.0ms	(/ (- x y) (- 1.0 y))
58.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
92.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify111.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	981	4627
1	3211	3350
2	5001	3140

prune342.0ms

Filtered

240 candidates to 126 candidates (52.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	236	4	240
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	4	241

Merged error: 0.1b

Counts

241 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b	(- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y)))))
5.7b	(log (+ (- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y))))) (* (/ (- x y) (- (* 1.0 1.0) (* y y))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
11.8b	(/ (- x y) (- (* 1.0 1.0) (* y y)))
11.8b	(/ (- x y) (- (* 1.0 1.0) (* y y)))

rewrite999.0ms

Algorithm

rewrite-expression-head

Rules

2855×	`add-sqr-sqrt`
1310×	`*-un-lft-identity`
1209×	`difference-of-squares`
966×	`frac-add`
829×	`times-frac`
616×	`log-div`
546×	`prod-diff`
528×	`associate-/r*`
516×	`frac-times`
513×	`associate-r`
492×	`swap-sqr`
441×	`flip3-+` `flip-+`
419×	`add-cube-cbrt`
418×	`unswap-sqr`
413×	`*-commutative`
395×	`distribute-lft-out--`
352×	`distribute-neg-frac`
329×	`flip3--` `flip--`
186×	`associate-l`
86×	`associate-*l/`
80×	`associate-/l*`
32×	`associate-/l/`
16×	`frac-2neg` `clear-num`
14×	`distribute-lft-out`
12×	`associate-*r/`
11×	`log-prod`
10×	`associate-/r/`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`cbrt-undiv` `div-sub` `div-exp`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 1651

Calls

4 calls:

112.0ms	(- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y)))))
374.0ms	(log (+ (- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y))))) (* (/ (- x y) (- (* 1.0 1.0) (* y y))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
30.0ms	(/ (- x y) (- (* 1.0 1.0) (* y y)))
27.0ms	(/ (- x y) (- (* 1.0 1.0) (* y y)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y)))))
149.0ms	(log (+ (- 1.0 (* (+ 1.0 y) (/ (- x y) (- (* 1.0 1.0) (* y y))))) (* (/ (- x y) (- (* 1.0 1.0) (* y y))) (+ (- (+ 1.0 y)) (+ 1.0 y)))))
74.0ms	(/ (- x y) (- (* 1.0 1.0) (* y y)))
76.0ms	(/ (- x y) (- (* 1.0 1.0) (* y y)))

simplify792.0ms

Algorithm

egg-herbie

Counts

1663 → 1663

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	82997

prune2.7s

Filtered

1663 candidates to 483 candidates (29.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1660	3	1663
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	1663	4	1667

Merged error: 0.1b

Counts

1667 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

12.1b	(cbrt (- (* 1.0 1.0) (* y y)))
12.1b	(cbrt (- (* 1.0 1.0) (* y y)))
12.1b	(cbrt (- (* 1.0 1.0) (* y y)))
26.0b	(fma (- (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y))))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y)))))) (* (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y))))))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
99×	`cbrt-prod`
75×	`difference-of-squares`
43×	`*-un-lft-identity`
36×	`swap-sqr`
30×	`*-commutative` `unswap-sqr`
15×	`distribute-lft-out--`
12×	`associate-l`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 145

Calls

4 calls:

18.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
17.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
17.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
1.0ms	(fma (- (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y))))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y)))))) (* (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y))))))))

series915.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
203.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
206.0ms	(cbrt (- (* 1.0 1.0) (* y y)))
299.0ms	(fma (- (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y))))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y)))))) (* (/ (- x y) (cbrt (- (* 1.0 1.0) (* y y)))) (* (+ 1.0 y) (/ 1 (* (cbrt (- (* 1.0 1.0) (* y y))) (cbrt (- (* 1.0 1.0) (* y y))))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	323	1580
1	1104	1470
2	5001	1409

prune524.0ms

Filtered

157 candidates to 71 candidates (45.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	157	4	161

Merged error: 0.1b

Counts

161 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
1.2b	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
3.8b	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
5.8b	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

4589×	`*-un-lft-identity`
3942×	`add-sqr-sqrt`
2492×	`times-frac`
1890×	`prod-diff`
1552×	`add-cube-cbrt`
1303×	`swap-sqr`
1291×	`distribute-lft-out--`
922×	`difference-of-squares`
885×	`associate-l`
877×	`associate-r`
249×	`unswap-sqr`
225×	`frac-times`
171×	`*-commutative`
162×	`associate-/l*`
160×	`associate-/r*`
128×	`associate-/r/`
98×	`flip3--` `flip--`
64×	`div-inv` `associate-/l/`
57×	`log-prod`
33×	`clear-num`
32×	`frac-2neg`
18×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`fma-neg` `associate-r/` `associate-l/`
13×	`pow1`
6×	`add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log-div` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`un-div-inv`
2×	`rem-log-exp` `log-pow`
1×	`pow2` `sub-neg` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 2454

Calls

4 calls:

43.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
147.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
187.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
13.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
107.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
345.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
93.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

simplify1.2s

Algorithm

egg-herbie

Counts

2466 → 2466

Iterations

Useful iterations: 1 (82.0ms)

Iter	Nodes	Cost
0	4476	104562
1	5001	102013

prune2.6s

Filtered

2466 candidates to 597 candidates (24.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	2465	1	2466
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	2467	3	2470

Merged error: 0.1b

Counts

2470 → 3

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.6b

bsearch195.0ms

Steps

Iters	Range		Point
10	2.622148067335985e-09	55266295.648746796	27970212.32870033
9	-21360866922585.72	-5585.32673263024	-68337904.12502125

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	99
1	79	99
2	81	99
3	81	99

end0.0ms

sample1.0s

Algorithm

intervals

Results

222.0ms	5737×	body	80	valid
160.0ms	785×	body	1280	valid
111.0ms	778×	body	640	valid
103.0ms	3602×	body	80	nan
55.0ms	361×	body	1280	nan
46.0ms	463×	body	320	valid
46.0ms	380×	body	640	nan
19.0ms	220×	body	320	nan
16.0ms	237×	body	160	valid
6.0ms	105×	body	160	nan