Details

sample179.0ms

Algorithm

intervals

Results

71.0ms	1294×	body	80	nan
26.0ms	393×	body	80	valid
5.0ms	11×	body	320	valid
5.0ms	13×	body	640	valid
1.0ms	9×	body	160	valid
1.0ms	1×	body	1280	valid

simplify415.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	18
1	31	17
2	62	17
3	120	17
4	310	17
5	1060	17
done	5001	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.0b	(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
0.6b	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
6.8b	(log (- 1.0 z))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
24×	`add-cube-cbrt` `prod-diff`
19×	`distribute-rgt-in` `distribute-lft-in`
15×	`log-prod`
14×	`pow1`
10×	`associate--l+`
8×	`log-pow`
7×	`add-exp-log`
6×	`associate-r` `add-cbrt-cube`
5×	`distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`sub-neg` `log-div` `flip3--` `associate-*r/` `flip--` `fma-udef`
1×	`rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

19.0ms	(* a (- (log (- 1.0 z)) b))
1.0ms	(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
0.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series447.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* a (- (log (- 1.0 z)) b))
135.0ms	(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
187.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
48.0ms	(log (- 1.0 z))

simplify686.0ms

Counts

117 → 117

Iterations

Useful iterations: done (682.0ms)

Iter	Nodes	Cost
0	247	2045
1	527	1768
2	1752	1486
done	5000	1438

prune373.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
0.0b	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
60×	`prod-diff`
43×	`add-cube-cbrt`
40×	`associate--l+`
37×	`distribute-rgt-in` `distribute-lft-in`
21×	`pow1`
17×	`distribute-lft-out--`
13×	`log-pow`
10×	`associate-r`
8×	`add-cbrt-cube`
7×	`add-exp-log` `associate-l` `difference-of-squares`
6×	`log-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`exp-prod` `fma-udef`
2×	`associate-r/` `exp-sum` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `flip--` `rem-exp-log`

Counts

4 → 145

Calls

4 calls:

6.0ms	(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
1.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
65.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series838.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
179.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
108.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
245.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify888.0ms

Counts

157 → 157

Iterations

Useful iterations: done (881.0ms)

Iter	Nodes	Cost
0	288	6764
1	541	5392
2	1891	4393
done	5000	4321

prune484.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
72×	`prod-diff`
68×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
43×	`associate--l+`
37×	`distribute-rgt-in` `distribute-lft-in`
24×	`pow1`
19×	`distribute-lft-out--`
18×	`log-pow`
9×	`log-prod`
8×	`difference-of-squares`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`exp-prod` `associate-l`
2×	`flip3--` `associate-*r/` `flip--` `fma-udef`
1×	`diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 160

Calls

4 calls:

5.0ms	(- (log z) t)
1.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
66.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (log z) t)
178.0ms	(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
108.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
256.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify1.1s

Counts

172 → 172

Iterations

Useful iterations: done (895.0ms)

Iter	Nodes	Cost
0	318	6407
1	579	4936
2	1952	3962
done	5001	3890

prune500.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
0.6b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
60×	`prod-diff`
56×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `associate--l+`
37×	`distribute-rgt-in` `distribute-lft-in`
19×	`pow1`
17×	`distribute-lft-out--`
13×	`log-pow`
7×	`associate-r` `difference-of-squares`
6×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `fma-udef`
2×	`associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

64.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
0.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
0.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
248.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
236.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))
240.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify803.0ms

Counts

142 → 142

Iterations

Useful iterations: done (796.0ms)

Iter	Nodes	Cost
0	232	6185
1	410	4822
2	1435	3884
done	5001	3802

prune547.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes216.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	28
1	26	28
done	26	28

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.3s	40731×	body	80	nan
780.0ms	12420×	body	80	valid
137.0ms	395×	body	640	valid
82.0ms	383×	body	320	valid
52.0ms	73×	body	1280	valid
41.0ms	297×	body	160	valid