Details

sample110.0ms

Algorithm

intervals

Results

39.0ms	831×	body	80	nan
14.0ms	22×	body	1280	valid
9.0ms	178×	body	80	valid
9.0ms	30×	body	640	valid
4.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify27.0ms

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: 8.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.3b	(* x (log y))
4.0b	(log (- 1.0 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg` `log-pow`
2×	`log-div` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 106

Calls

4 calls:

7.0ms	(* z (log (- 1.0 y)))
19.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
4.0ms	(* x (log y))
3.0ms	(log (- 1.0 y))

series245.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* z (log (- 1.0 y)))
89.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
38.0ms	(* x (log y))
47.0ms	(log (- 1.0 y))

simplify56.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	519	871
1	1908	704
2	5001	676

prune323.0ms

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 223

Calls

4 calls:

13.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
27.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
23.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
4.0ms	(* x (log y))

series412.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
185.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
44.0ms	(* x (log y))

simplify123.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	1034	2311
1	3973	1857
2	5001	1843

prune820.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt` `times-frac`
72×	`associate-r`
56×	`unpow-prod-down`
44×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
12×	`log-prod`
11×	`prod-exp`
10×	`add-cbrt-cube`
9×	`div-exp`
8×	`pow1`
6×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `associate-l` `pow-exp` `associate--l+`
5×	`add-log-exp`
3×	`expm1-log1p-u` `prod-diff` `cbrt-unprod` `log1p-expm1-u`
2×	`pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `sub-neg` `flip3--` `fma-neg` `diff-log` `associate-*r/` `log-pow` `flip--` `div-inv`

Counts

3 → 163

Calls

3 calls:

4.0ms	(- (* x (log y)) t)
30.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
4.0ms	(* x (log y))

series147.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* x (log y)) t)
56.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
37.0ms	(* x (log y))

simplify81.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	747	909
1	3085	760
2	5002	759

prune681.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (log (cbrt y)))
0.3b	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `associate-+l+` `*-un-lft-identity`
12×	`associate-+r+`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow1/3` `associate-l`
2×	`log-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* x (log (cbrt y)))
13.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series559.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* x (log (cbrt y)))
101.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
179.0ms	(cbrt y)
185.0ms	(cbrt y)

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	384	753
1	1636	640
2	5001	570

prune716.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes156.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24079×	body	80	nan
283.0ms	5544×	body	80	valid
257.0ms	860×	body	640	valid
243.0ms	415×	body	1280	valid
127.0ms	725×	body	320	valid
51.0ms	478×	body	160	valid