Details

sample105.0ms

Algorithm

intervals

Results

39.0ms	822×	body	80	nan
9.0ms	182×	body	80	valid
9.0ms	15×	body	1280	valid
7.0ms	23×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	15×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	30	7
2	39	7
3	45	7
4	60	7
5	88	7
6	125	7
7	176	7
8	208	7
9	225	7
10	293	7
11	293	7

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: 10.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.2b	(* x (log y))
4.2b	(log (- 1.0 y))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

2×	`log-div` `flip3--` `associate--l+` `*-commutative` `flip--`
1×	`+-commutative` `sub-neg`

Counts

4 → 10

Calls

4 calls:

3.0ms	(* z (log (- 1.0 y)))
6.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
2.0ms	(* x (log y))
2.0ms	(log (- 1.0 y))

series242.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* z (log (- 1.0 y)))
87.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
42.0ms	(* x (log y))
43.0ms	(log (- 1.0 y))

simplify87.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	261	178
1	786	173
2	2771	156
3	5001	156

prune76.0ms

Filtered

22 candidates to 18 candidates (81.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Merged error: 0.2b

Counts

23 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.2b	(* x (log y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-*r/`
6×	`associate--l+` `unpow2` `sqr-pow`
5×	`sub-neg` `associate-r`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `times-frac`
3×	`*-commutative`
2×	`flip3--` `clear-num` `associate-/r` `flip--` `associate-/l`
1×	`+-commutative` `frac-2neg` `un-div-inv` `div-inv`

Counts

4 → 32

Calls

4 calls:

8.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
4.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
2.0ms	(* x (log y))

series386.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
110.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
44.0ms	(* x (log y))

simplify159.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	223	304
1	763	304
2	3869	287
3	5001	287

prune135.0ms

Filtered

44 candidates to 29 candidates (65.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	44	4	48

Merged error: 0.2b

Counts

48 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (log y))
0.3b	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
4.8b	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
31.7b	(/ (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

20×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-+r+`
12×	`associate--l+`
10×	`*-commutative`
9×	`sub-neg`
8×	`difference-of-squares`
7×	`flip3-+` `flip-+`
4×	`+-commutative` `frac-times` `associate-/l*`
2×	`flip3--` `associate-r/` `associate-l/` `associate-/r/` `flip--` `associate-/l/`
1×	`pow2` `frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

4 → 55

Calls

4 calls:

2.0ms	(* x (log y))
11.0ms	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
15.0ms	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
20.0ms	(/ (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

series2.4s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* x (log y))
244.0ms	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.2s	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
919.0ms	(/ (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))

simplify74.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	475	2032
1	1890	2006
2	5002	2001

prune239.0ms

Filtered

67 candidates to 37 candidates (55.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Merged error: 0.1b

Counts

71 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (log y))
0.3b	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
4.8b	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
31.6b	(* (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (/ 1 (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

20×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-+r+`
12×	`associate--l+`
11×	`*-commutative`
10×	`frac-times`
9×	`sub-neg`
8×	`difference-of-squares`
7×	`flip3-+` `flip-+`
5×	`flip3--` `associate-*r/` `flip--`
4×	`+-commutative` `associate-l` `associate-*l/` `clear-num`
3×	`frac-2neg` `associate-r`
2×	`associate-/r/` `un-div-inv`
1×	`pow2` `div-inv`

Counts

4 → 64

Calls

4 calls:

2.0ms	(* x (log y))
10.0ms	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
15.0ms	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
19.0ms	(* (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (/ 1 (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))

series2.5s

Counts

4 → 12

Calls

4 calls:

37.0ms	(* x (log y))
249.0ms	(* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.3s	(- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t))
924.0ms	(* (- (* (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (* t t)) (/ 1 (+ (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))

simplify92.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	505	2486
1	2283	2381
2	5001	2369

prune254.0ms

Filtered

76 candidates to 41 candidates (53.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	76	7	83

Merged error: 0.1b

Counts

83 → 7

regimes307.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	23996×	body	80	nan
273.0ms	5550×	body	80	valid
248.0ms	872×	body	640	valid
235.0ms	408×	body	1280	valid
130.0ms	758×	body	320	valid
46.0ms	444×	body	160	valid