Details

sample108.0ms

Algorithm

intervals

Results

39.0ms	822×	body	80	nan
13.0ms	189×	body	80	valid
9.0ms	14×	body	1280	valid
7.0ms	21×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid

simplify133.0ms

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: 9.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
4.2b	(log (- 1.0 y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`log-prod`
13×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`flip3--` `associate-*l/` `flip--`
3×	`log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series311.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- z 1.0) (log (- 1.0 y)))
154.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
63.0ms	(* (- x 1.0) (log y))
48.0ms	(log (- 1.0 y))

simplify50.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune309.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

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))

rewrite65.0ms

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:

11.0ms	(+ (* (- 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)))
12.0ms	(* (- 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))

series334.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
56.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
69.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
55.0ms	(* (- x 1.0) (log y))

simplify65.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1332	2812
1	5001	2662

prune974.0ms

Filtered

235 candidates to 163 candidates (69.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	8	235
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	235	9	244

Merged error: 0.0b

Counts

244 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (- x 1.0) (log y))
0.5b	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
88×	`associate-r`
80×	`times-frac`
59×	`*-un-lft-identity`
56×	`unpow-prod-down`
45×	`add-cube-cbrt`
36×	`add-exp-log`
32×	`frac-times`
24×	`unpow2` `sqr-pow`
22×	`flip3--` `flip--`
19×	`unswap-sqr`
18×	`pow1` `associate-*l/` `add-cbrt-cube`
15×	`prod-exp`
14×	`associate-l`
12×	`flip3-+` `sqrt-prod` `flip-+`
11×	`associate-*r/`
9×	`div-exp`
7×	`cbrt-unprod`
6×	`distribute-rgt-in` `pow-to-exp` `log-prod` `distribute-lft-in` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`distribute-lft-out--`
4×	`*-commutative` `add-log-exp`
3×	`log-pow` `distribute-lft-out`
2×	`sub-neg`
1×	`cbrt-undiv` `div-inv`

Counts

4 → 227

Calls

4 calls:

19.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
16.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
7.0ms	(* (- x 1.0) (log y))
21.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
163.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* (- x 1.0) (log y))
274.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1308	3389
1	5002	2934

prune1.2s

Filtered

239 candidates to 164 candidates (68.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	239	9	248

Merged error: 0.0b

Counts

248 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series746.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (cbrt y) (cbrt y))
178.0ms	(cbrt y)
179.0ms	(cbrt y)
180.0ms	(cbrt y)

simplify90.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune416.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	85	9	94

Merged error: 0.0b

Counts

94 → 9

regimes324.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	44	24
2	44	24

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23996×	body	80	nan
330.0ms	5894×	body	80	valid
238.0ms	770×	body	640	valid
156.0ms	251×	body	1280	valid
135.0ms	693×	body	320	valid
49.0ms	424×	body	160	valid