Details

sample343.0ms

Algorithm

intervals

Results

172.0ms	1360×	body	80	nan
44.0ms	418×	body	80	valid
6.0ms	18×	body	320	valid
4.0ms	8×	body	640	valid
4.0ms	2×	body	1280	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1044
4	347
3	135
2	62
1	31
0	17

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(exp (fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a)))
0.1b	(fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a))
4.6b	(log (- 1.0 z))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`prod-diff`
10×	`pow1`
8×	`log-prod`
6×	`log-pow` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `log1p-expm1-u`
3×	`exp-prod` `associate--l+` `distribute-lft-out--`
2×	`log-div` `flip3--` `fma-udef` `flip--` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `exp-sum` `rem-exp-log`

Counts

4 → 78

Calls

4 calls:

11.0ms	(- (log z) t)
2.0ms	(exp (fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a)))
0.0ms	(fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a))
8.0ms	(log (- 1.0 z))

series545.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (log z) t)
168.0ms	(exp (fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a)))
222.0ms	(fma y (- (log z) t) (* (- (log (- 1.0 z)) b) a))
70.0ms	(log (- 1.0 z))

simplify2.1s

Counts

90 → 90

Iterations

Iter	Nodes
done	5016
3	2994
2	1001
1	425
0	187

prune706.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)
0.0b	(- (log z) t)
0.1b	(exp (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
0.1b	(fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`prod-diff`
11×	`pow1`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`associate-l` `log-pow`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`log-prod` `exp-prod` `associate-r` `associate--l+` `distribute-lft-out--`
2×	`flip3--` `associate-*l/` `fma-udef` `flip--` `difference-of-squares`
1×	`sub-neg` `diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 84

Calls

4 calls:

23.0ms	(* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)
15.0ms	(- (log z) t)
4.0ms	(exp (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
1.0ms	(fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))

series753.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)
93.0ms	(- (log z) t)
235.0ms	(exp (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
307.0ms	(fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))

simplify2.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	3683
2	930
1	379
0	175

prune830.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))) (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))))
12.2b	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
12.2b	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
12.2b	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

24.0ms	(* (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))) (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))))
1.0ms	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
1.0ms	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
1.0ms	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))

series25.7s

Counts

4 → 12

Calls

4 calls:

20.9s	(* (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))) (cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a))))
1.6s	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
1.6s	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))
1.6s	(cbrt (fma y (- (log z) t) (* (- (fma (* (/ z 1.0) (/ z 1.0)) -1/2 (- (log 1.0) (* 1.0 z))) b) a)))

simplify2.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
3	3397
2	1084
1	409
0	166

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.3b	(cbrt (exp (* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))))
0.3b	(* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))
0.5b	(fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

44.0ms	(* y (- (log z) t))
4.0ms	(cbrt (exp (* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))))
11.0ms	(* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))
1.0ms	(fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t)))

series1.2s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* y (- (log z) t))
321.0ms	(cbrt (exp (* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))))
401.0ms	(* 3 (fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t))))
335.0ms	(fma a (fma -1/2 (* (/ z 1.0) (/ z 1.0)) (- (log 1.0) (fma z 1.0 b))) (* y (- (log z) t)))

simplify3.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
3	4881
2	1306
1	509
0	239

prune906.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes475.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	21

end0.0ms

sample11.2s

Algorithm

intervals

Results

6.5s	41239×	body	80	nan
1.5s	12486×	body	80	valid
272.0ms	353×	body	640	valid
137.0ms	410×	body	320	valid
85.0ms	60×	body	1280	valid
79.0ms	269×	body	160	valid