Details

sample239.0ms

Algorithm

intervals

Results

147.0ms	1761×	body	80	nan
26.0ms	256×	body	80	valid

simplify63.0ms

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

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))

rewrite43.0ms

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))
6.0ms	(+ (log (+ x y)) (log z))

series333.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(- (+ (log (+ x y)) (log z)) t)
91.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
68.0ms	(+ (log (+ x y)) (log z))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (35.0ms)

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

prune268.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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:

35.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series318.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(- (+ (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))

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (31.0ms)

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

prune281.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

6.0ms	(+ (log (+ x y)) (log z))
0.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
0.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
1.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))

series2.0s

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ (log (+ x y)) (log z))
663.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
647.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
664.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))

simplify64.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	601	1546
1	2133	1428
2	5001	1415

prune499.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
0.6b	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
0.6b	(cbrt (fma (log t) (- a 0.5) (- (fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z)) t)))
0.7b	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
0.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
1.0ms	(cbrt (fma (log t) (- a 0.5) (- (fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z)) t)))
0.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

series2.7s

Counts

4 → 12

Calls

4 calls:

687.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
683.0ms	(cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t)))
749.0ms	(cbrt (fma (log t) (- a 0.5) (- (fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z)) t)))
569.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

simplify68.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	531	1703
1	1966	1552
2	5002	1413

prune462.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes484.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	23	8
2	23	8

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.8s	55455×	body	80	nan
823.0ms	8031×	body	80	valid