Details

sample162.0ms

Algorithm

intervals

Results

82.0ms	1708×	body	80	nan
14.0ms	256×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.5b	(+ (log (+ x y)) (log z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
28×	`pow1`
25×	`log-pow` `distribute-lft-out`
21×	`prod-diff`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
7×	`log-prod` `fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-+l-` `log-div` `associate-+l+` `fma-def`
3×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate--l-` `diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 92

Calls

3 calls:

35.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series325.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(- (+ (log (+ x y)) (log z)) t)
90.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
71.0ms	(+ (log (+ x y)) (log z))

simplify42.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	388	866
1	1209	661
2	5001	650

prune292.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log z) t)
0.2b	(fma (log t) (- a 0.5) (+ (log (+ x y)) (- (log z) t)))
0.3b	(+ (log (+ x y)) (- (log z) t))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`add-sqr-sqrt` `prod-diff`
22×	`add-cube-cbrt`
17×	`pow1` `associate-+r+`
14×	`log-pow`
10×	`log-prod`
7×	`distribute-lft-out`
6×	`associate--l+` `distribute-lft-out--` `add-log-exp`
4×	`associate-+l+` `fma-def` `fma-neg`
3×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate-+l-` `sub-neg` `log-div` `flip3-+` `diff-log` `sum-log` `flip-+`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 94

Calls

3 calls:

4.0ms	(- (log z) t)
0.0ms	(fma (log t) (- a 0.5) (+ (log (+ x y)) (- (log z) t)))
14.0ms	(+ (log (+ x y)) (- (log z) t))

series319.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(- (log z) t)
93.0ms	(fma (log t) (- a 0.5) (+ (log (+ x y)) (- (log z) t)))
166.0ms	(+ (log (+ x y)) (- (log z) t))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	420	756
1	1251	585
2	5001	554

prune321.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t))
0.5b	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
0.5b	(+ (log (+ x y)) (log z))
0.7b	(pow (+ (log (+ x y)) (log z)) 3)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
26×	`pow1`
21×	`log-pow` `distribute-lft-out`
20×	`cbrt-prod`
14×	`unpow-prod-down` `cube-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`log-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `associate-+l+` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-+r+`
2×	`cube-mult` `associate-+l-` `log-div` `cbrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

0.0ms	(fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t))
7.0ms	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
6.0ms	(+ (log (+ x y)) (log z))
7.0ms	(pow (+ (log (+ x y)) (log z)) 3)

series546.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t))
72.0ms	(cbrt (pow (+ (log (+ x y)) (log z)) 3))
74.0ms	(+ (log (+ x y)) (log z))
312.0ms	(pow (+ (log (+ x y)) (log z)) 3)

simplify51.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	388	875
1	1379	809
2	5002	796

prune378.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t)))
0.7b	(pow (+ (log (+ x y)) (log z)) 3)
0.7b	(pow (+ (log (+ x y)) (log z)) 3)
0.7b	(pow (+ (log (+ x y)) (log z)) 3)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
31×	`pow1`
24×	`log-pow` `distribute-lft-out`
21×	`unpow-prod-down` `cube-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow-unpow`
7×	`add-exp-log` `add-cbrt-cube`
6×	`cube-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cube-mult` `pow-to-exp` `pow-pow` `flip3-+` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`pow1/3`

Counts

4 → 118

Calls

4 calls:

0.0ms	(cbrt (fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t)))
7.0ms	(pow (+ (log (+ x y)) (log z)) 3)
7.0ms	(pow (+ (log (+ x y)) (log z)) 3)
7.0ms	(pow (+ (log (+ x y)) (log z)) 3)

series1.6s

Counts

4 → 12

Calls

4 calls:

673.0ms	(cbrt (fma (log t) (- a 0.5) (- (cbrt (pow (+ (log (+ x y)) (log z)) 3)) t)))
308.0ms	(pow (+ (log (+ x y)) (log z)) 3)
316.0ms	(pow (+ (log (+ x y)) (log z)) 3)
312.0ms	(pow (+ (log (+ x y)) (log z)) 3)

simplify74.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	642	1319
1	2624	1196
2	5002	1179

prune515.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes424.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	56228×	body	80	nan
450.0ms	8025×	body	80	valid