Details

sample394.0ms

Algorithm

intervals

Results

143.0ms	1404×	body	80	nan
42.0ms	4×	body	1280	valid
41.0ms	410×	body	80	valid
6.0ms	11×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	17	18
1	31	17
2	62	17
3	135	17
4	379	17
5	1360	17
done	5000	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize32.0ms

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)))) x)
0.3b	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
6.1b	(log (- 1.0 z))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

48.0ms	(* a (- (log (- 1.0 z)) b))
13.0ms	(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
0.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
12.0ms	(log (- 1.0 z))

series858.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* a (- (log (- 1.0 z)) b))
456.0ms	(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
237.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
73.0ms	(log (- 1.0 z))

simplify1.4s

Counts

124 → 124

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	265	2242
1	627	1976
2	2143	1675
done	5002	1609

prune579.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
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)
0.3b	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 167

Calls

4 calls:

16.0ms	(- (log z) t)
209.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
20.0ms	(* (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	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series1.0s

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (log z) t)
138.0ms	(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
442.0ms	(* (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)
357.0ms	(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify2.4s

Counts

179 → 179

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	338	6726
1	749	5266
2	2601	4268
done	5000	3643

prune826.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))
0.0b	(* (exp (log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))) x)
0.2b	(* y (- (log z) t))
0.3b	(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

1.0ms	(log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))
24.0ms	(* (exp (log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))) x)
71.0ms	(* y (- (log z) t))
1.0ms	(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))

series1.3s

Counts

4 → 12

Calls

4 calls:

375.0ms	(log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))
507.0ms	(* (exp (log1p (expm1 (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))))) x)
92.0ms	(* y (- (log z) t))
359.0ms	(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* y (- (log z) t)))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	223	2588
1	501	2273
2	1693	1906
done	5001	1861

prune783.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
0.3b	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
6.1b	(log (- 1.0 z))
6.1b	(log (- 1.0 z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `log-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `rem-log-exp` `log-pow` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

1.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
1.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
10.0ms	(log (- 1.0 z))
15.0ms	(log (- 1.0 z))

series713.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
287.0ms	(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
87.0ms	(log (- 1.0 z))
82.0ms	(log (- 1.0 z))

simplify2.1s

Counts

68 → 68

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	101	868
1	219	828
2	642	736
3	2480	730
done	5001	728

prune871.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes229.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	29
1	26	29
done	26	29

end0.0ms

sample12.8s

Algorithm

intervals

Results

6.2s	40674×	body	80	nan
1.7s	12356×	body	80	valid
209.0ms	395×	body	640	valid
154.0ms	384×	body	320	valid
126.0ms	296×	body	160	valid
105.0ms	75×	body	1280	valid