Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	35×	body	1280	valid
7.0ms	178×	body	80	valid
4.0ms	27×	body	640	valid
3.0ms	128×	body	80	nan
2.0ms	12×	body	1280	nan
1.0ms	12×	body	320	valid
1.0ms	11×	body	320	nan
1.0ms	6×	body	640	nan
0.0ms	4×	body	160	valid
0.0ms	3×	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

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: 19.3b

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))
1.5b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`flip3--` `flip--`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `div-sub` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 21

Calls

4 calls:

3.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
4.0ms	(/ (- x y) (- 1.0 y))
2.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
2.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
35.0ms	(/ (- x y) (- 1.0 y))
51.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
81.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	300	267
1	892	255
2	3820	245
3	5001	244

prune97.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 0.0b

Counts

34 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
2.9b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`flip3--` `flip--`
6×	`frac-times`
4×	`log-div` `clear-num`
3×	`frac-2neg` `associate-r/` `associate-r*`
2×	`sub-neg` `associate-*l/` `associate-/r/` `un-div-inv` `associate--r-`
1×	`*-commutative` `div-inv`

Counts

4 → 29

Calls

4 calls:

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

series262.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
39.0ms	(* (- x y) (/ 1 (- 1.0 y)))
82.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
52.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify36.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	333	330
1	1292	312
2	5001	302

prune94.0ms

Filtered

41 candidates to 30 candidates (73.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Merged error: 0.0b

Counts

44 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
1.5b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.1b	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
12.8b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

14×	`sqr-pow`
10×	`prod-diff`
8×	`log-div` `unpow3`
6×	`unpow-prod-down`
5×	`flip3--` `flip--`
4×	`associate-+l+` `log-prod` `associate-/r/`
3×	`difference-cubes` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`
2×	`associate-+r-` `sub-neg` `fma-neg` `div-inv` `associate--r+` `associate--r-`
1×	`+-commutative`

Counts

4 → 36

Calls

4 calls:

39.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
10.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
13.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
6.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

313.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
304.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
161.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
381.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	561	1083
1	2012	989
2	5003	984

prune204.0ms

Filtered

48 candidates to 39 candidates (81.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	48	3	51

Merged error: 0.0b

Counts

51 → 3

localize52.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3))
12.1b	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
12.8b	(log (/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6))))
13.9b	(/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

60×	`unpow-prod-down`
48×	`sqr-pow`
28×	`prod-diff`
24×	`unpow3`
12×	`log-div` `difference-of-squares`
10×	`associate-/l*`
8×	`associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv`
4×	`fma-neg` `associate-/l/`
3×	`difference-cubes` `clear-num`
2×	`frac-2neg`
1×	`sub-neg` `log-prod` `flip3-+` `div-sub` `log-rec` `flip-+`

Counts

4 → 66

Calls

4 calls:

11.0ms	(- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3))
15.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
10.0ms	(log (/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6))))
12.0ms	(/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6)))

series6.4s

Counts

4 → 12

Calls

4 calls:

1.5s	(- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3))
160.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))
3.8s	(log (/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6))))
977.0ms	(/ (- (pow (pow 1.0 3) 3) (pow (pow (/ (- x y) (- 1.0 y)) 3) 3)) (fma (pow (/ (- x y) (- 1.0 y)) 3) (+ (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (pow 1.0 6)))

simplify86.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	678	2108
1	2584	1669
2	5001	1662

prune366.0ms

Filtered

78 candidates to 51 candidates (65.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	78	3	81

Merged error: 0.0b

Counts

81 → 3

regimes82.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 18.1b

bsearch121.0ms

Steps

Iters	Range		Point
11	3.88064682879673e-06	2.996660094541056e+24	34062684.84310692
7	-4.2197574811023237e+18	-23086016024645856.0	-2.361719426239133e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

219.0ms	5669×	body	80	valid
178.0ms	873×	body	1280	valid
110.0ms	797×	body	640	valid
109.0ms	3793×	body	80	nan
62.0ms	399×	body	1280	nan
51.0ms	411×	body	640	nan
45.0ms	430×	body	320	valid
19.0ms	221×	body	320	nan
16.0ms	231×	body	160	valid
6.0ms	102×	body	160	nan