Details

sample113.0ms

Algorithm

intervals

Results

47.0ms	839×	body	80	nan
11.0ms	187×	body	80	valid
8.0ms	25×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	6×	body	1280	valid
2.0ms	13×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
5.2b	(log (- 1.0 y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
1.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms	(log (- 1.0 y))

series300.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- z 1.0) (log (- 1.0 y)))
209.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
44.0ms	(log (- 1.0 y))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune237.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

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

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 189

Calls

3 calls:

21.0ms

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

14.0ms

(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

1.0ms

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

series346.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

65.0ms

(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

225.0ms

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

simplify114.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	933	2642
1	4282	1844
2	5001	1841

prune667.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
0.0b	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
0.1b	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
5.8b	(* z (pow y 2))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`add-exp-log`
8×	`associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-l` `prod-exp` `fma-udef`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
1.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
1.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
6.0ms	(* z (pow y 2))

series269.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
38.0ms	(fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))))
109.0ms	(fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
34.0ms	(* z (pow y 2))

simplify106.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	187	518
1	674	444
2	3223	442
3	5002	436

prune280.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t)))
5.8b	(* z (pow y 2))
5.8b	(* z (pow y 2))
5.8b	(* z (pow y 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
19×	`add-exp-log`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`associate-l` `prod-exp`
6×	`unpow2` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt (fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t)))
6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))
6.0ms	(* z (pow y 2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (fma (log y) (- x 1.0) (- (fma 0.5 (pow y 2) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t)))
29.0ms	(* z (pow y 2))
34.0ms	(* z (pow y 2))
29.0ms	(* z (pow y 2))

simplify133.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	278	668
1	879	595
2	4199	590
3	5001	590

prune525.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes203.0ms

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	21	12
1	21	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	24011×	body	80	nan
345.0ms	5938×	body	80	valid
266.0ms	820×	body	640	valid
145.0ms	233×	body	1280	valid
124.0ms	628×	body	320	valid
51.0ms	409×	body	160	valid