Details

sample420.0ms

Algorithm

intervals

Results

222.0ms	1715×	body	80	nan
29.0ms	257×	body	80	valid

simplify9.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

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))
0.7b	(+ (log (+ x y)) (log z))

rewrite137.0ms

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:

113.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
17.0ms	(+ (log (+ x y)) (log z))

series520.0ms

Counts

3 → 9

Calls

3 calls:

288.0ms	(- (+ (log (+ x y)) (log z)) t)
137.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
95.0ms	(+ (log (+ x y)) (log z))

simplify2.6s

Counts

101 → 101

Iterations

Useful iterations: 3 (1.2s)

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

prune463.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.5b	(cbrt z)
0.5b	(cbrt z)
0.6b	(fma 2 (log (cbrt z)) (log (+ x y)))

rewrite22.0ms

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:

16.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
2.0ms	(cbrt z)
2.0ms	(cbrt z)
1.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

307.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
318.0ms	(cbrt z)
282.0ms	(cbrt z)
240.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))

simplify3.5s

Counts

73 → 73

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	99	750
1	205	706
2	525	648
3	1954	517
done	5000	495

prune579.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt z))
0.6b	(cbrt (pow z 2/3))
0.6b	(fma 2 (log (* (cbrt (pow z 2/3)) (cbrt (cbrt z)))) (log (+ x y)))
6.0b	(pow z 2/3)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow1/3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (cbrt z))
2.0ms	(cbrt (pow z 2/3))
0.0ms	(fma 2 (log (* (cbrt (pow z 2/3)) (cbrt (cbrt z)))) (log (+ x y)))
3.0ms	(pow z 2/3)

series1.2s

Counts

4 → 12

Calls

4 calls:

358.0ms	(cbrt (cbrt z))
301.0ms	(cbrt (pow z 2/3))
260.0ms	(fma 2 (log (* (cbrt (pow z 2/3)) (cbrt (cbrt z)))) (log (+ x y)))
301.0ms	(pow z 2/3)

simplify3.1s

Counts

74 → 74

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	128	634
1	233	593
2	444	527
3	1095	512
4	4055	500
done	5000	490

prune689.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite743.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
117×	`distribute-lft-out`
91×	`pow1`
87×	`log-pow`
39×	`prod-diff`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
16×	`log-prod`
13×	`fma-neg`
12×	`associate-+r+`
11×	`fma-def` `distribute-lft-out--`
10×	`associate-+l-` `add-log-exp`
7×	`sum-log`
6×	`log-div` `sqrt-prod`
5×	`associate-+l+` `flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`diff-log`
2×	`+-commutative` `associate--l-`
1×	`sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

4 → 166

Calls

4 calls:

583.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
0.0ms	(fma (- a 0.5) (log t) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
17.0ms	(+ (log (+ x y)) (log (sqrt z)))
122.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
176.0ms	(fma (- a 0.5) (log t) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
205.0ms	(+ (log (+ x y)) (log (sqrt z)))
260.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

simplify1.4s

Counts

178 → 178

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	230	3321
1	588	2630
2	1687	2243
done	5001	2051

prune595.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes579.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	27
1	26	27
done	26	27

end0.0ms

sample13.6s

Algorithm

intervals

Results

7.4s	56347×	body	80	nan
1.6s	8033×	body	80	valid