Details

sample281.0ms

Algorithm

intervals

Results

173.0ms	1968×	body	80	nan
28.0ms	257×	body	80	valid

simplify71.0ms

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: 0.3b

localize16.0ms

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))

rewrite44.0ms

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))

series353.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(- (+ (log (+ x y)) (log z)) t)
98.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
76.0ms	(+ (log (+ x y)) (log z))

simplify44.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

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

prune303.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.5b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-+r+` `log-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3` `fma-udef` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `log-pow` `flip-+`

Counts

4 → 61

Calls

4 calls:

4.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series744.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
162.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
191.0ms	(cbrt z)
186.0ms	(cbrt z)

simplify74.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	203	445
1	573	409
2	2204	368
3	5002	358

prune408.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x y)) (cbrt (+ x y)))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))

rewrite30.0ms

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:

20.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))

series627.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
149.0ms	(cbrt (+ x y))
144.0ms	(cbrt (+ x y))
152.0ms	(cbrt (+ x y))

simplify158.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	255	701
1	926	660
2	4357	610
3	5001	610

prune527.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
21×	`log-prod`
19×	`pow1`
15×	`log-pow` `distribute-lft-out`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`associate-+l+` `fma-def`
9×	`associate-+r+`
6×	`associate-+l-` `log-div` `flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `cbrt-prod` `sum-log`
1×	`pow1/3`

Counts

4 → 103

Calls

4 calls:

1.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
7.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))
10.0ms	(+ (log (+ x y)) (log z))

series1.0s

Counts

4 → 12

Calls

4 calls:

787.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
88.0ms	(+ (log (+ x y)) (log z))
82.0ms	(+ (log (+ x y)) (log z))
86.0ms	(+ (log (+ x y)) (log z))

simplify64.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	601	974
1	2133	892
2	5001	877

prune573.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes592.0ms

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	19	12
1	19	12

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.3s	56983×	body	80	nan
898.0ms	8033×	body	80	valid