Details

sample184.0ms

Algorithm

intervals

Results

94.0ms	1828×	body	80	nan
16.0ms	258×	body	80	valid

simplify61.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 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)
0.1b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (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:

33.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
8.0ms	(+ (log (+ x y)) (log z))

series326.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(- (+ (log (+ x y)) (log z)) t)
90.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
69.0ms	(+ (log (+ x y)) (log z))

simplify44.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

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

prune288.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
22.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (+ x y))
137.0ms	(cbrt (+ x y))
124.0ms	(cbrt (+ x y))
162.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

simplify133.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	255	701
1	933	660
2	4363	610
3	5001	610

prune505.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(* (cbrt (+ x y)) (pow (+ x y) 1/3))
5.1b	(pow (+ x y) 1/3)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-cube-cbrt`
10×	`add-exp-log` `unpow-prod-down`
8×	`associate-r`
7×	`associate-l`
6×	`cbrt-div` `unswap-sqr`
5×	`pow1` `pow1/3` `add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `flip3-+` `prod-exp` `flip-+`
2×	`pow-to-exp` `unpow1/3` `associate-*l/` `pow-exp` `cbrt-unprod`
1×	`pow-pow` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 94

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
29.0ms	(* (cbrt (+ x y)) (pow (+ x y) 1/3))
5.0ms	(pow (+ x y) 1/3)

series577.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ x y))
132.0ms	(cbrt (+ x y))
184.0ms	(* (cbrt (+ x y)) (pow (+ x y) 1/3))
138.0ms	(pow (+ x y) 1/3)

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	323	562
1	1263	449
2	5001	429

prune517.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (log (+ x y)) (log z))
0.5b	(* (log (+ x y)) (log (+ x y)))
0.6b	(* (log z) (log z))
0.6b	(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
43×	`pow1`
37×	`add-sqr-sqrt`
35×	`log-prod`
31×	`add-cube-cbrt`
25×	`log-pow`
17×	`prod-diff`
14×	`distribute-rgt-in` `distribute-lft-in`
12×	`swap-sqr` `associate--l+`
9×	`associate--r+`
8×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
6×	`add-log-exp`
5×	`fma-neg` `distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--`
2×	`associate--l-` `pow2` `sub-neg` `log-div` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 157

Calls

4 calls:

7.0ms	(- (log (+ x y)) (log z))
8.0ms	(* (log (+ x y)) (log (+ x y)))
4.0ms	(* (log z) (log z))
8.0ms	(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (log (+ x y)) (log z))
165.0ms	(* (log (+ x y)) (log (+ x y)))
151.0ms	(* (log z) (log z))
168.0ms	(- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	446	1242
1	1661	1012
2	5001	875

prune511.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes334.0ms

Accuracy

0% (0.1b 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	24	16
1	24	16

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.7s	54507×	body	80	nan
498.0ms	8030×	body	80	valid