Details

sample118.0ms

Algorithm

intervals

Results

40.0ms	883×	body	80	nan
9.0ms	16×	body	1280	valid
8.0ms	174×	body	80	valid
8.0ms	26×	body	640	valid
5.0ms	29×	body	320	valid
1.0ms	12×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

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))
4.5b	(log (- 1.0 y))

rewrite23.0ms

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:

15.0ms	(* z (log (- 1.0 y)))
0.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0ms	(log (- 1.0 y))

series242.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* z (log (- 1.0 y)))
124.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
47.0ms	(log (- 1.0 y))

simplify106.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (100.0ms)

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

prune217.0ms

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

rewrite166.0ms

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:

71.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
37.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
42.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series465.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
51.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
136.0ms	(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
173.0ms	(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify323.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 2 (86.0ms)

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

prune803.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 132

Calls

3 calls:

0.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
38.0ms	(* 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)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
54.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
179.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	616	990
1	2555	827
2	5002	826

prune512.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
76×	`add-sqr-sqrt`
71×	`associate-r`
56×	`unpow-prod-down`
40×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
11×	`prod-exp` `add-cbrt-cube`
9×	`pow1` `div-exp`
7×	`associate-l`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `fma-def` `flip3-+` `associate-*r/` `sum-log` `log-pow` `flip-+` `div-inv`

Counts

4 → 158

Calls

4 calls:

11.0ms	(+ (* (log y) x) (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))
0.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
38.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
8.0ms	(* (log y) x)

series404.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(+ (* (log y) x) (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))
112.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
55.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
59.0ms	(* (log y) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	748	1234
1	3506	1013
2	5002	996

prune560.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	25	13

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	24530×	body	80	nan
266.0ms	5489×	body	80	valid
249.0ms	431×	body	1280	valid
242.0ms	864×	body	640	valid
124.0ms	765×	body	320	valid
49.0ms	473×	body	160	valid