Details

sample327.0ms

Algorithm

intervals

Results

165.0ms	1547×	body	80	nan
26.0ms	259×	body	80	valid

simplify9.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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))

rewrite125.0ms

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:

104.0ms	(- (+ (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))

series570.0ms

Counts

3 → 9

Calls

3 calls:

305.0ms	(- (+ (log (+ x y)) (log z)) t)
166.0ms	(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
98.0ms	(+ (log (+ x y)) (log z))

simplify2.7s

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

prune520.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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:

8.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))

series1.0s

Counts

4 → 12

Calls

4 calls:

262.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
228.0ms	(cbrt z)
305.0ms	(cbrt z)
207.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))

simplify3.1s

Counts

73 → 73

Iterations

Useful iterations: done (3.1s)

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

prune501.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

22×	`log-prod`
20×	`*-un-lft-identity`
18×	`associate-+l+`
15×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
7×	`add-log-exp`
6×	`distribute-rgt-in` `associate-+r-` `fma-def` `distribute-lft-in` `log-pow`
5×	`associate-+r+` `distribute-lft-out`
4×	`add-exp-log` `expm1-log1p-u` `log-div` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`pow1/3`
2×	`+-commutative`

Counts

4 → 90

Calls

4 calls:

20.0ms	(+ (log (cbrt z)) (log (+ x y)))
2.0ms	(cbrt z)
1.0ms	(cbrt z)
56.0ms	(+ (* 2 (log (cbrt z))) (+ (log (cbrt z)) (log (+ x y))))

series1.0s

Counts

4 → 12

Calls

4 calls:

204.0ms	(+ (log (cbrt z)) (log (+ x y)))
284.0ms	(cbrt z)
336.0ms	(cbrt z)
191.0ms	(+ (* 2 (log (cbrt z))) (+ (log (cbrt z)) (log (+ x y))))

simplify3.3s

Counts

102 → 102

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	138	1073
1	363	928
2	988	845
3	3917	775
done	5000	774

prune793.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`pow1`
21×	`add-cube-cbrt` `log-prod`
16×	`cbrt-prod`
15×	`log-pow` `distribute-lft-out`
12×	`associate-+l+` `fma-def`
9×	`associate-+r+`
6×	`add-exp-log` `associate-+l-` `log-div` `flip3-+` `pow1/3` `swap-sqr` `associate-r` `associate-l` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

12.0ms	(* (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))))
13.0ms	(+ (log (+ x y)) (log z))
13.0ms	(+ (log (+ x y)) (log z))
30.0ms	(+ (log (+ x y)) (log z))

series2.1s

Counts

4 → 12

Calls

4 calls:

1.8s	(* (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))))
144.0ms	(+ (log (+ x y)) (log z))
97.0ms	(+ (log (+ x y)) (log z))
102.0ms	(+ (log (+ x y)) (log z))

simplify1.7s

Counts

144 → 144

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	285	3590
1	832	3330
2	3072	3030
done	5000	2745

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes1.3s

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	17	21
1	19	21
done	19	21

end0.0ms

sample13.4s

Algorithm

intervals

Results

7.8s	57030×	body	80	nan
1.1s	8036×	body	80	valid