Details

sample108.0ms

Algorithm

intervals

Results

39.0ms	858×	body	80	nan
10.0ms	16×	body	1280	valid
9.0ms	30×	body	640	valid
9.0ms	174×	body	80	valid
4.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify30.0ms

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: 8.2b

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))
5.8b	(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))

series233.0ms

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))
46.0ms	(log (- 1.0 y))

simplify111.0ms

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

prune221.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))

rewrite97.0ms

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:

26.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
18.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
35.0ms	(* 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))

series451.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
122.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
108.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
165.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify122.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (91.0ms)

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

prune840.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
70×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`pow1`
3×	`associate-l`
2×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

2 → 122

Calls

2 calls:

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

series233.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
184.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify66.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	597	828
1	2509	688
2	5002	687

prune472.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
0.5b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.5b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.5b	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

rewrite9.0ms

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×	`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 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

series1.4s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
338.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
333.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
334.0ms	(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	421	2516
1	1538	2319
2	5002	2069

prune450.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes246.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24019×	body	80	nan
279.0ms	5540×	body	80	valid
257.0ms	864×	body	640	valid
226.0ms	375×	body	1280	valid
134.0ms	760×	body	320	valid
54.0ms	487×	body	160	valid