Details

sample156.0ms

Algorithm

intervals

Results

73.0ms	886×	body	80	nan
18.0ms	181×	body	80	valid
10.0ms	13×	body	1280	valid
9.0ms	24×	body	640	valid
6.0ms	23×	body	320	valid
3.0ms	17×	body	160	valid

simplify36.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize12.0ms

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))
8.0b	(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))

series249.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(* z (log (- 1.0 y)))
125.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
50.0ms	(log (- 1.0 y))

simplify121.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (114.0ms)

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

prune250.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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:

29.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
19.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
34.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 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))

series488.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
139.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
111.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
183.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify137.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (97.0ms)

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

prune934.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

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	(+ (* (log y) x) (- (* 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))))))
0.3b	(* (log y) x)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

86×	`associate--l+`
78×	`prod-diff`
64×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
58×	`add-cube-cbrt`
51×	`distribute-rgt-in` `distribute-lft-in`
39×	`associate-+r+`
28×	`pow1`
20×	`log-pow`
18×	`log-prod`
11×	`add-log-exp`
9×	`associate-r`
8×	`add-exp-log` `sub-neg` `add-cbrt-cube`
7×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+` `difference-of-squares`

Counts

4 → 187

Calls

4 calls:

18.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
37.0ms	(+ (* (log y) x) (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
31.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* (log y) x)

series506.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
183.0ms	(+ (* (log y) x) (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
111.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
73.0ms	(* (log y) x)

simplify94.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	651	3520
1	2309	2269
2	5001	2251

prune780.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
64×	`*-un-lft-identity`
57×	`add-cube-cbrt`
56×	`unpow-prod-down`
29×	`add-exp-log`
24×	`prod-diff` `unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`pow1`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`add-log-exp`
7×	`log-pow`
6×	`pow-to-exp` `log-prod` `associate-l` `pow-exp` `associate--l+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-*r/` `cbrt-unprod`
2×	`sub-neg` `pow-prod-down` `sum-log` `*-commutative` `fma-udef` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `associate-+l+` `flip3--` `distribute-rgt-neg-in` `flip3-+` `unsub-neg` `neg-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 204

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
5.0ms	(+ (fma (log y) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- t))
31.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 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)))))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
207.0ms	(+ (fma (log y) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- t))
114.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
141.0ms	(fma (log y) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify126.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	893	2664
1	3788	1866
2	5001	1848

prune761.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes241.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.0s	24375×	body	80	nan
537.0ms	5478×	body	80	valid
365.0ms	907×	body	640	valid
300.0ms	414×	body	1280	valid
191.0ms	748×	body	320	valid
84.0ms	480×	body	160	valid