Details

sample223.0ms

Algorithm

intervals

Results

96.0ms	1820×	body	80	nan
15.0ms	257×	body	80	valid

simplify8.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	61	15
3	155	15
4	356	15
5	858	15
6	1598	15
7	2194	15
8	2618	15
9	2630	15
done	2630	15

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite89.0ms

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:

72.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
14.0ms	(+ (log (+ x y)) (log z))

series390.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(- (+ (log (+ x y)) (log z)) t)
118.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
89.0ms	(+ (log (+ x y)) (log z))

simplify2.9s

Counts

101 → 101

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	170	1568
1	388	1337
2	1000	1146
3	3921	1059
done	5000	1059

prune430.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt z))
0.2b	(fma (- a 0.5) (log t) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
0.4b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

2.0ms	(log (sqrt z))
0.0ms	(fma (- a 0.5) (log t) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
77.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
19.0ms	(+ (log (+ x y)) (log (sqrt z)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log (sqrt z))
165.0ms	(fma (- a 0.5) (log t) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
165.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
150.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify2.2s

Counts

114 → 114

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	186	1467
1	467	1306
2	1279	1164
3	4675	1113
done	5000	1109

prune583.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

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:

16.0ms	(+ (log (+ x y)) (log z))
1.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))

series4.1s

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (log (+ x y)) (log z))
1.3s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.4s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.3s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))

simplify1.4s

Counts

81 → 81

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	236	3757
1	701	3570
2	2602	3262
done	5000	3159

prune803.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
2.0ms	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
2.0ms	(cbrt (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))))

series5.7s

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.5s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.4s	(cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t)))
1.3s	(cbrt (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))))

simplify2.3s

Counts

67 → 67

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	304	4747
1	1000	4510
2	4221	4161
done	5000	4149

prune749.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	19	20
done	19	20

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.0s	55308×	body	80	nan
695.0ms	8027×	body	80	valid