Details

sample97.0ms

Algorithm

intervals

Results

34.0ms	741×	body	80	nan
11.0ms	19×	body	1280	valid
8.0ms	172×	body	80	valid
7.0ms	24×	body	640	valid
5.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0b	(log (- 1.0 y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`log-div` `log-pow`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

7.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
3.0ms	(log (- 1.0 y))

series234.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* z (log (- 1.0 y)))
116.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify112.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune225.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

111×	`add-sqr-sqrt`
80×	`times-frac`
76×	`*-un-lft-identity`
74×	`associate-r`
73×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
34×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`pow1`
18×	`unswap-sqr`
13×	`log-pow`
12×	`log-prod`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
6×	`pow-to-exp` `associate-l` `pow-exp` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--`
1×	`cbrt-undiv` `fma-neg` `diff-log` `fma-udef` `div-inv` `difference-of-squares`

Counts

4 → 233

Calls

4 calls:

19.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
32.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
31.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series443.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
99.0ms	(* z (- (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)))
171.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify116.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	936	3375
1	3893	2186
2	5001	2179

prune798.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(+ (* (log y) x) (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.3b	(* (log y) x)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
80×	`times-frac`
78×	`*-un-lft-identity`
77×	`associate-r`
75×	`add-cube-cbrt`
56×	`unpow-prod-down`
51×	`prod-diff`
46×	`associate--l+`
39×	`associate-+r+`
34×	`distribute-rgt-in` `distribute-lft-in`
31×	`add-exp-log`
24×	`pow1` `unpow2` `sqr-pow`
19×	`unswap-sqr`
14×	`log-pow`
13×	`add-cbrt-cube`
12×	`log-prod` `prod-exp`
10×	`associate-l`
9×	`div-exp` `add-log-exp`
6×	`pow-to-exp` `pow-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-r/` `pow-prod-down` `-commutative`
2×	`sum-log` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `flip3--` `fma-def` `flip3-+` `diff-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 247

Calls

4 calls:

32.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
35.0ms	(+ (* (log y) x) (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
31.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
3.0ms	(* (log y) x)

series382.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
163.0ms	(+ (* (log y) x) (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
56.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
59.0ms	(* (log y) x)

simplify118.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	1065	3154
1	4243	2171
2	5002	2162

prune804.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (log y)) (cbrt (log y)))
0.5b	(cbrt (log y))
0.5b	(cbrt (log y))
0.5b	(cbrt (log y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`pow1/3` `swap-sqr` `log-pow`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 89

Calls

4 calls:

11.0ms	(* (cbrt (log y)) (cbrt (log y)))
1.0ms	(cbrt (log y))
1.0ms	(cbrt (log y))
1.0ms	(cbrt (log y))

series1.3s

Counts

4 → 12

Calls

4 calls:

463.0ms	(* (cbrt (log y)) (cbrt (log y)))
265.0ms	(cbrt (log y))
314.0ms	(cbrt (log y))
263.0ms	(cbrt (log y))

simplify85.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	125	517
1	435	446
2	2997	388
3	5001	381

prune333.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes221.0ms

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

sample2.8s

Algorithm

intervals

Results

1.0s	24930×	body	80	nan
266.0ms	5534×	body	80	valid
255.0ms	886×	body	640	valid
238.0ms	409×	body	1280	valid
121.0ms	723×	body	320	valid
50.0ms	479×	body	160	valid