Details

sample164.0ms

Algorithm

intervals

Results

83.0ms	1730×	body	80	nan
15.0ms	259×	body	80	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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))

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))
7.0ms	(+ (log (+ x y)) (log z))

series334.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(- (+ (log (+ x y)) (log z)) t)
90.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
75.0ms	(+ (log (+ x y)) (log z))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

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

prune298.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log (+ x y)) (log (+ x y)))
0.5b	(- (log z) (log (+ x y)))
0.7b	(pow (log (+ x y)) 3)
0.7b	(pow (log z) 3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
36×	`pow1`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
23×	`log-pow`
16×	`prod-diff`
15×	`log-prod`
8×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
6×	`pow-unpow` `swap-sqr`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u` `associate--r+` `distribute-lft-out--` `add-log-exp`
3×	`associate--l+` `distribute-lft-out`
2×	`cube-mult` `pow-to-exp` `log-div` `pow-pow` `unpow3` `pow-exp` `associate--r-` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

7.0ms	(* (log (+ x y)) (log (+ x y)))
7.0ms	(- (log z) (log (+ x y)))
2.0ms	(pow (log (+ x y)) 3)
2.0ms	(pow (log z) 3)

series754.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (log (+ x y)) (log (+ x y)))
78.0ms	(- (log z) (log (+ x y)))
319.0ms	(pow (log (+ x y)) 3)
178.0ms	(pow (log z) 3)

simplify75.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	395	865
1	1936	708
2	5002	674

prune530.0ms

Pruning

7 alts after pruning (6 fresh and 1 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))

rewrite25.0ms

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:

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

series933.0ms

Counts

4 → 12

Calls

4 calls:

707.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
77.0ms	(+ (log (+ x y)) (log z))
77.0ms	(+ (log (+ x y)) (log z))
72.0ms	(+ (log (+ x y)) (log z))

simplify60.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (49.0ms)

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

prune591.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))
0.7b	(pow (+ (log (+ x y)) (log z)) 3)
23.5b	(/ (- (pow (+ (log (+ x y)) (log z)) 3) (pow t 3)) (+ (* (+ (log (+ x y)) (log z)) (+ (+ (log (+ x y)) (log z)) t)) (* t t)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

247×	`*-un-lft-identity`
155×	`add-sqr-sqrt`
123×	`times-frac`
119×	`unpow-prod-down` `cube-prod`
87×	`pow1`
84×	`distribute-lft-out--`
82×	`log-pow` `distribute-lft-out`
64×	`difference-of-squares`
59×	`add-cube-cbrt`
41×	`associate-/l*`
33×	`sqr-pow`
14×	`log-prod`
8×	`associate-+l+` `fma-def`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+r+` `flip3-+` `flip-+`
4×	`difference-cubes` `expm1-log1p-u` `associate-+l-` `log-div` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`+-commutative` `cube-div` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip--` `div-inv` `rem-cube-cbrt`

Counts

4 → 281

Calls

4 calls:

7.0ms	(+ (log (+ x y)) (log z))
6.0ms	(+ (log (+ x y)) (log z))
7.0ms	(pow (+ (log (+ x y)) (log z)) 3)
213.0ms	(/ (- (pow (+ (log (+ x y)) (log z)) 3) (pow t 3)) (+ (* (+ (log (+ x y)) (log z)) (+ (+ (log (+ x y)) (log z)) t)) (* t t)))

series2.0m

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ (log (+ x y)) (log z))
75.0ms	(+ (log (+ x y)) (log z))
331.0ms	(pow (+ (log (+ x y)) (log z)) 3)
2.0m	(/ (- (pow (+ (log (+ x y)) (log z)) 3) (pow t 3)) (+ (* (+ (log (+ x y)) (log z)) (+ (+ (log (+ x y)) (log z)) t)) (* t t)))

simplify143.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	837	7055
1	3684	6870
2	5002	6804

prune882.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes550.0ms

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	23	22
1	23	22

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	55656×	body	80	nan
460.0ms	8030×	body	80	valid