Details

sample58.0ms

Algorithm

intervals

Results

10.0ms	165×	body	80	valid
9.0ms	34×	body	1280	valid
7.0ms	30×	body	640	valid
4.0ms	100×	body	80	nan
3.0ms	17×	body	320	valid
2.0ms	8×	body	640	nan
1.0ms	10×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	1×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	2335
8	741
7	343
6	223
5	123
4	75
3	41
2	29
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp`

Counts

4 → 227

Calls

4 calls:

49.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
73.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
72.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
56.0ms	(/ (- x y) (- 1.0 y))
74.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
121.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify2.0s

Counts

239 → 239

Iterations

Iter	Nodes
done	5000
2	4243
1	1025
0	389

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
0.2b	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
202×	`*-un-lft-identity`
144×	`times-frac`
102×	`add-cube-cbrt`
93×	`prod-diff`
58×	`difference-of-squares`
50×	`distribute-lft-out--`
24×	`log-prod`
12×	`associate-/r/`
11×	`associate-/r*`
9×	`add-exp-log`
8×	`flip3--` `add-cbrt-cube` `flip--` `associate-/l*`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `rem-log-exp` `associate-/l/`
1×	`log-div` `sub-neg` `diff-log` `log-pow` `associate--r-`

Counts

4 → 248

Calls

4 calls:

30.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
22.0ms	(/ (- x y) (- 1.0 y))
97.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y)))))
46.0ms	(/ (- x y) (- 1.0 y))
184.0ms	(/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))
89.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify2.1s

Counts

260 → 260

Iterations

Iter	Nodes
done	5000
2	4483
1	1124
0	433

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
2.5b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
8.9b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
9.0b	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1072×	`add-sqr-sqrt`
1012×	`*-un-lft-identity`
828×	`prod-diff`
616×	`times-frac`
615×	`unpow-prod-down` `cube-prod`
498×	`add-cube-cbrt`
289×	`difference-of-squares`
256×	`distribute-lft-out--`
101×	`sqr-pow`
81×	`cube-mult` `unpow3`
48×	`associate-/r/`
39×	`log-prod`
27×	`flip3--` `flip--`
24×	`div-inv`
16×	`associate-+l+`
15×	`pow1`
12×	`fma-neg`
11×	`log-pow`
8×	`log-div` `add-log-exp`
6×	`fma-def` `add-exp-log` `distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate-+r+` `flip3-+` `flip-+`
2×	`difference-cubes` `associate-+r-` `sum-log` `sub-neg` `diff-log` `rem-log-exp` `associate--r-`
1×	`+-commutative` `associate-+l-`

Counts

4 → 982

Calls

4 calls:

138.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
141.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
600.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
88.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

482.0ms	(+ (- 1.0 (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))) (log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y)))))))
286.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
521.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
238.0ms	(log (+ (* 1.0 1.0) (+ (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))) (* 1.0 (/ (- x y) (- 1.0 y))))))

simplify1.1s

Counts

994 → 994

Iterations

Iter	Nodes
done	5000
1	1883
0	725

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
1.8b	(fma (/ x (pow y 2)) 1.0 (/ x y))
7.9b	(/ x (pow y 2))
15.7b	(log (/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
67×	`times-frac`
56×	`*-un-lft-identity`
42×	`add-cube-cbrt`
24×	`log-prod`
14×	`associate-/r*` `difference-of-squares`
12×	`unpow-prod-down` `add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-inv`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `rem-log-exp` `flip--`
1×	`pow-to-exp` `log-div` `pow-exp` `log-pow` `fma-udef`

Counts

4 → 141

Calls

4 calls:

24.0ms	(/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
0.0ms	(fma (/ x (pow y 2)) 1.0 (/ x y))
6.0ms	(/ x (pow y 2))
11.0ms	(log (/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
71.0ms	(fma (/ x (pow y 2)) 1.0 (/ x y))
30.0ms	(/ x (pow y 2))
204.0ms	(log (/ (exp 1.0) (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))))

simplify1.2s

Counts

153 → 153

Iterations

Iter	Nodes
done	5002
2	2114
1	565
0	271

prune966.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes382.0ms

Accuracy

95.4% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 18.7b

bsearch2.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
0	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

788.0ms	5642×	body	80	valid
376.0ms	778×	body	1280	valid
299.0ms	824×	body	640	valid
230.0ms	3828×	body	80	nan
129.0ms	391×	body	640	nan
106.0ms	350×	body	1280	nan
100.0ms	492×	body	320	valid
72.0ms	264×	body	160	valid
40.0ms	244×	body	320	nan
37.0ms	116×	body	160	nan