Details

sample159.0ms

Algorithm

intervals

Results

81.0ms	1740×	body	80	nan
14.0ms	257×	body	80	valid

simplify68.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
48×	`pow1`
43×	`add-sqr-sqrt`
42×	`prod-diff` `log-pow`
41×	`distribute-lft-out`
35×	`add-cube-cbrt`
28×	`associate-+l+`
19×	`log-prod`
14×	`add-log-exp`
13×	`fma-def`
11×	`distribute-lft-out--`
9×	`associate-+r+`
7×	`fma-neg`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--`
5×	`associate-+l-` `associate-l`
4×	`expm1-log1p-u` `log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

33.0ms	(- (+ (log (+ x y)) (log z)) t)
115.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
10.0ms	(* (- a 0.5) (log t))
6.0ms	(+ (log (+ x y)) (log z))

series487.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(- (+ (log (+ x y)) (log z)) t)
193.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
59.0ms	(* (- a 0.5) (log t))
70.0ms	(+ (log (+ x y)) (log z))

simplify78.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	706	1592
1	2722	1253
2	5001	1237

prune510.0ms

Filtered

184 candidates to 109 candidates (59.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.4b	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
0.5b	(+ (log (sqrt (+ x y))) (log z))

rewrite615.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
96×	`distribute-lft-out`
80×	`pow1`
76×	`log-pow`
56×	`associate-+l+`
40×	`add-sqr-sqrt`
39×	`prod-diff`
34×	`add-cube-cbrt`
29×	`log-prod`
27×	`fma-def`
15×	`add-log-exp`
12×	`distribute-lft-out--`
11×	`sum-log`
10×	`associate-+r+`
8×	`sqrt-prod`
7×	`associate-+l-`
6×	`add-exp-log` `distribute-rgt-in` `log-div` `distribute-lft-in` `flip3-+` `sqrt-div` `associate-*l/` `add-cbrt-cube` `flip-+`
5×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `associate-r` `frac-add` `log1p-expm1-u`
3×	`+-commutative` `diff-log`
2×	`associate-+r-` `sqrt-pow1` `pow1/2` `difference-of-squares`
1×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

565.0ms	(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
10.0ms	(* (- a 0.5) (log t))
21.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
8.0ms	(+ (log (sqrt (+ x y))) (log z))

series592.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(+ (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t) (* (- a 0.5) (log t)))
55.0ms	(* (- a 0.5) (log t))
131.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
110.0ms	(+ (log (sqrt (+ x y))) (log z))

simplify88.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	849	1962
1	3278	1529
2	5002	1476

prune666.0ms

Filtered

204 candidates to 125 candidates (61.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log z) t)
0.1b	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.3b	(fma (log t) (- a 0.5) (- (log z) t))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

4.0ms	(- (log z) t)
5.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.0ms	(fma (log t) (- a 0.5) (- (log z) t))

series279.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(- (log z) t)
162.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
54.0ms	(fma (log t) (- a 0.5) (- (log z) t))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	393	634
1	1179	513
2	5001	502

prune284.0ms

Filtered

81 candidates to 58 candidates (71.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
0.5b	(+ (log (sqrt (+ x y))) (log z))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
25×	`pow1`
24×	`distribute-lft-out`
23×	`log-pow`
17×	`log-prod`
14×	`associate-+l+`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`fma-def`
8×	`sqrt-prod`
6×	`cbrt-prod` `associate-+l-` `log-div` `sqrt-div`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `associate-+r-` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 103

Calls

4 calls:

23.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
8.0ms	(+ (log (sqrt (+ x y))) (log z))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series604.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
112.0ms	(+ (log (sqrt (+ x y))) (log z))
179.0ms	(cbrt t)
179.0ms	(cbrt t)

simplify89.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	388	704
1	1060	619
2	3807	597
3	5001	594

prune516.0ms

Filtered

115 candidates to 88 candidates (76.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes551.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b 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

sample4.8s

Algorithm

intervals

Results

2.5s	55681×	body	80	nan
436.0ms	8024×	body	80	valid