Details

sample167.0ms

Algorithm

intervals

Results

80.0ms	1737×	body	80	nan
17.0ms	257×	body	80	valid

simplify66.0ms

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

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))
0.6b	(+ (log (+ x y)) (log z))

rewrite47.0ms

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:

34.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series332.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(- (+ (log (+ x y)) (log z)) t)
94.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
70.0ms	(+ (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

prune314.0ms

Filtered

101 candidates to 61 candidates (60.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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) (fma (- t) 1 t)))
0.6b	(+ (log (+ x y)) (log z))

rewrite47.0ms

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:

34.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))
6.0ms	(+ (log (+ x y)) (log z))

series355.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(- (+ (log (+ x y)) (log z)) t)
118.0ms	(fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))
69.0ms	(+ (log (+ x y)) (log z))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	394	888
1	1247	691
2	5001	681

prune337.0ms

Filtered

101 candidates to 60 candidates (59.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (log (+ x y)))
0.6b	(cbrt (log (+ x y)))
0.6b	(cbrt (log (+ x y)))
0.7b	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `log-pow`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (log (+ x y)))
1.0ms	(cbrt (log (+ x y)))
1.0ms	(cbrt (log (+ x y)))
0.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

series2.0s

Counts

4 → 12

Calls

4 calls:

469.0ms	(cbrt (log (+ x y)))
474.0ms	(cbrt (log (+ x y)))
461.0ms	(cbrt (log (+ x y)))
565.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

simplify64.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (53.0ms)

Iter	Nodes	Cost
0	97	446
1	173	386
2	488	377
3	1652	351
4	5002	350

prune337.0ms

Filtered

64 candidates to 54 candidates (84.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))) (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`pow1`
21×	`add-cube-cbrt` `log-prod`
16×	`cbrt-prod`
15×	`log-pow` `distribute-lft-out`
12×	`associate-+l+` `fma-def`
9×	`associate-+r+`
6×	`add-exp-log` `associate-+l-` `log-div` `flip3-+` `pow1/3` `swap-sqr` `associate-r` `associate-l` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))) (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))))
6.0ms	(+ (log (+ x y)) (log z))
6.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))

series968.0ms

Counts

4 → 12

Calls

4 calls:

748.0ms	(* (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))) (cbrt (fma (log t) (- a 0.5) (+ (- (+ (log (+ x y)) (log z)) t) (fma (- t) 1 t)))))
70.0ms	(+ (log (+ x y)) (log z))
74.0ms	(+ (log (+ x y)) (log z))
75.0ms	(+ (log (+ x y)) (log z))

simplify90.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	713	1951
1	2813	1774
2	5002	1627

prune734.0ms

Filtered

144 candidates to 105 candidates (72.9%)

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.0b

regimes871.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	55312×	body	80	nan
445.0ms	8035×	body	80	valid