Details

sample150.0ms

Algorithm

intervals

Results

53.0ms	802×	body	80	nan
12.0ms	185×	body	80	valid
12.0ms	29×	body	640	valid
8.0ms	10×	body	1280	valid
5.0ms	18×	body	320	valid
2.0ms	16×	body	160	valid

simplify14.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	27	16
2	57	16
3	130	16
4	281	16
5	649	16
6	1372	16
7	2484	16
8	3329	16
9	3557	16
10	3561	16
done	3561	16

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.1b	(* (- x 1.0) (log y))
5.1b	(log (- 1.0 y))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`log-prod`
20×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
10×	`associate-+r+` `associate-*l/`
9×	`prod-diff`
8×	`pow1`
7×	`add-exp-log` `flip3--` `flip--`
6×	`associate-+l+` `add-cbrt-cube`
5×	`associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-r` `frac-add` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `diff-log` `sum-log` `log-pow`
1×	`+-commutative` `sub-neg` `fma-def` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

129.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
50.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
48.0ms	(* (- x 1.0) (log y))
12.0ms	(log (- 1.0 y))

series487.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
150.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
80.0ms	(* (- x 1.0) (log y))
69.0ms	(log (- 1.0 y))

simplify1.8s

Counts

125 → 125

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	281	2381
1	741	2087
2	2455	1887
done	5000	1787

prune430.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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)))))))
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)))
0.1b	(* (- x 1.0) (log y))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
80×	`times-frac`
72×	`associate-r`
71×	`*-un-lft-identity`
67×	`add-cube-cbrt`
56×	`unpow-prod-down`
34×	`associate-+r+`
33×	`prod-diff`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
23×	`distribute-rgt-in` `distribute-lft-in`
22×	`flip3--` `associate-*l/` `flip--`
18×	`log-prod` `unswap-sqr`
16×	`frac-add`
15×	`pow1`
11×	`prod-exp` `add-cbrt-cube` `add-log-exp`
9×	`div-exp`
8×	`frac-times` `associate-l`
7×	`associate--l+` `log-pow`
6×	`pow-to-exp` `associate-+l+` `pow-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `cbrt-unprod`
2×	`diff-log` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `flip-+` `div-inv`

Counts

4 → 243

Calls

4 calls:

34.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
121.0ms	(- (+ (* (- 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)
46.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
26.0ms	(* (- x 1.0) (log y))

series672.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
329.0ms	(- (+ (* (- 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)
59.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
61.0ms	(* (- x 1.0) (log y))

simplify786.0ms

Counts

255 → 255

Iterations

Useful iterations: done (770.0ms)

Iter	Nodes	Cost
0	564	7141
1	1464	6037
done	5000	5472

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

2.0ms	(log (sqrt y))
5.0ms	(log (sqrt y))
0.0ms	(fma (- x 1.0) (log (sqrt y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
32.0ms	(* (log (sqrt y)) (- x 1.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log (sqrt y))
106.0ms	(log (sqrt y))
203.0ms	(fma (- x 1.0) (log (sqrt y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
77.0ms	(* (log (sqrt y)) (- x 1.0))

simplify2.1s

Counts

109 → 109

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	186	1625
1	389	1420
2	1012	1214
3	3282	1152
done	5000	1151

prune637.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x 1.0) (cbrt (pow (log (sqrt y)) 3)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (log (sqrt y)) (- x 1.0))
0.5b	(cbrt (pow (log (sqrt y)) 3))
0.7b	(pow (log (sqrt y)) 3)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`cbrt-prod` `prod-diff`
17×	`pow1`
15×	`log-pow`
12×	`unpow-prod-down` `cube-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
5×	`sqrt-pow1` `pow1/2` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `unpow3` `associate-*r/` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

0.0ms	(fma (- x 1.0) (cbrt (pow (log (sqrt y)) 3)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
45.0ms	(* (log (sqrt y)) (- x 1.0))
6.0ms	(cbrt (pow (log (sqrt y)) 3))
7.0ms	(pow (log (sqrt y)) 3)

series572.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(fma (- x 1.0) (cbrt (pow (log (sqrt y)) 3)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
92.0ms	(* (log (sqrt y)) (- x 1.0))
74.0ms	(cbrt (pow (log (sqrt y)) 3))
202.0ms	(pow (log (sqrt y)) 3)

simplify1.5s

Counts

131 → 131

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	269	2160
1	655	1721
2	2153	1510
done	5000	1480

prune577.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes429.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	39
1	30	39
done	30	39

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.6s	24165×	body	80	nan
449.0ms	5908×	body	80	valid
337.0ms	771×	body	640	valid
226.0ms	257×	body	1280	valid
169.0ms	663×	body	320	valid
71.0ms	435×	body	160	valid