Details

sample109.0ms

Algorithm

intervals

Results

41.0ms	844×	body	80	nan
13.0ms	194×	body	80	valid
9.0ms	27×	body	640	valid
5.0ms	7×	body	1280	valid
3.0ms	17×	body	320	valid
2.0ms	13×	body	160	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

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: 6.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
6.7b	(log (- 1.0 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-*l/`
11×	`pow1`
10×	`associate-+r+` `associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
7×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
6×	`associate-+l+` `add-log-exp`
4×	`frac-add`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 109

Calls

4 calls:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
11.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series268.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
41.0ms	(* (- z 1.0) (log (- 1.0 y)))
59.0ms	(* (- x 1.0) (log y))
41.0ms	(log (- 1.0 y))

simplify67.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	621	970
1	2460	896
2	5003	883

prune396.0ms

Filtered

121 candidates to 91 candidates (75.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	7	122

Merged error: 0.1b

Counts

122 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (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)))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(* (- x 1.0) (log y))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
57×	`*-un-lft-identity`
56×	`unpow-prod-down`
50×	`add-cube-cbrt`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`associate-l` `add-cbrt-cube`
12×	`pow1` `frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`log-pow`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

12.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
20.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
16.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series328.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
48.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
61.0ms	(* (- x 1.0) (log y))

simplify58.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune929.0ms

Filtered

235 candidates to 163 candidates (69.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	7	235
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	233	9	242

Merged error: 0.0b

Counts

242 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(+ (* (log (sqrt y)) (- x 1.0)) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.1b	(* (log (sqrt y)) (- x 1.0))
0.1b	(* (log (sqrt y)) (- x 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

82×	`associate-*r/`
68×	`frac-add`
66×	`flip3--` `flip--`
26×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`frac-times`
17×	`associate-l`
16×	`associate-r`
15×	`pow1`
12×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`add-log-exp`
8×	`sub-neg`
7×	`log-pow`
6×	`log-prod` `associate--l+`
5×	`distribute-lft-out--`
4×	`associate-+l+` `difference-of-squares`
3×	`flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`sqrt-pow1` `pow1/2`
1×	`+-commutative` `associate-+r+`

Counts

4 → 152

Calls

4 calls:

12.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
16.0ms	(+ (* (log (sqrt y)) (- x 1.0)) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
7.0ms	(* (log (sqrt y)) (- x 1.0))
7.0ms	(* (log (sqrt y)) (- x 1.0))

series406.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
204.0ms	(+ (* (log (sqrt y)) (- x 1.0)) (+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
67.0ms	(* (log (sqrt y)) (- x 1.0))
67.0ms	(* (log (sqrt y)) (- x 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1556	4885
1	5003	4805

prune951.0ms

Filtered

164 candidates to 122 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	164	9	173

Merged error: 0.0b

Counts

173 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
52×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
22×	`pow1` `distribute-lft-out--`
18×	`cbrt-div`
15×	`add-cube-cbrt` `swap-sqr`
11×	`log-pow`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 111

Calls

4 calls:

15.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series952.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
217.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
222.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
259.0ms	(cbrt (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	508	2897
1	1877	2762
2	5001	2441

prune547.0ms

Filtered

123 candidates to 81 candidates (65.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	123	9	132

Merged error: 0.0b

Counts

132 → 9

regimes354.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	36
1	32	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	24041×	body	80	nan
328.0ms	5857×	body	80	valid
250.0ms	789×	body	640	valid
152.0ms	244×	body	1280	valid
137.0ms	720×	body	320	valid
50.0ms	419×	body	160	valid