Details

sample173.0ms

Algorithm

intervals

Results

56.0ms	663×	body	80	nan
21.0ms	184×	body	80	valid
13.0ms	24×	body	640	valid
10.0ms	11×	body	1280	valid
6.0ms	19×	body	320	valid
4.0ms	19×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	27	16
2	57	16
3	135	16
4	388	16
5	1306	16
6	3670	16
done	5000	16

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
6.3b	(log (- 1.0 y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

14.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
1.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
13.0ms	(log (- 1.0 y))

series453.0ms

Counts

3 → 9

Calls

3 calls:

226.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
154.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
73.0ms	(log (- 1.0 y))

simplify663.0ms

Counts

66 → 66

Iterations

Useful iterations: done (660.0ms)

Iter	Nodes	Cost
0	159	1368
1	371	1224
2	1143	1077
done	5000	954

prune510.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
70×	`*-un-lft-identity`
63×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`pow1`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`flip3--` `associate--l+` `log-pow` `flip--`
6×	`pow-to-exp` `log-prod` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `fma-neg` `associate-*r/` `cbrt-unprod` `difference-of-squares`
2×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`
1×	`cbrt-undiv` `diff-log` `div-inv`

Counts

4 → 218

Calls

4 calls:

58.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
87.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
252.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
95.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
141.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify694.0ms

Counts

230 → 230

Iterations

Useful iterations: done (678.0ms)

Iter	Nodes	Cost
0	445	6887
1	1145	5504
done	5001	4761

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(* (- x 1.0) (log y))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
76×	`*-un-lft-identity`
67×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
31×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`unswap-sqr`
18×	`pow1`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod` `prod-exp`
9×	`div-exp` `add-log-exp`
8×	`flip3--` `log-pow` `flip--`
7×	`associate--l+`
6×	`pow-to-exp` `pow-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `fma-neg` `associate-r/` `pow-prod-down` `-commutative`
2×	`diff-log`
1×	`cbrt-undiv` `sum-log` `div-inv`

Counts

4 → 240

Calls

4 calls:

108.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
43.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
55.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
29.0ms	(* (- x 1.0) (log y))

series594.0ms

Counts

4 → 12

Calls

4 calls:

338.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
90.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
101.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
65.0ms	(* (- x 1.0) (log y))

simplify689.0ms

Counts

252 → 252

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	509	6932
1	1305	5538
done	5001	4602

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

54.0ms	(* (- x 1.0) (log (cbrt y)))
63.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series908.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (- x 1.0) (log (cbrt y)))
187.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
292.0ms	(cbrt y)
288.0ms	(cbrt y)

simplify1.8s

Counts

131 → 131

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	212	1942
1	638	1652
2	3159	1351
done	5000	1341

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes436.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	38
1	29	38
done	29	38

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	23684×	body	80	nan
1.3s	5830×	body	80	valid
553.0ms	788×	body	640	valid
268.0ms	679×	body	320	valid
229.0ms	257×	body	1280	valid
89.0ms	468×	body	160	valid