Details

sample71.0ms

Algorithm

intervals

Results

36.0ms	91×	body	1280	valid
9.0ms	125×	body	80	valid
6.0ms	19×	body	640	valid
4.0ms	18×	body	320	valid
0.0ms	3×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-prod`
3×	`expm1-log1p-u` `fma-neg` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.0s

Counts

3 → 9

Calls

3 calls:

361.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
146.0ms	(/ 1.0 (hypot 1.0 x))
523.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.0s

Counts

84 → 84

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	207	2042
1	492	1618
2	1441	1398
done	5000	1265

prune345.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `prod-diff` `flip-+`

Counts

4 → 112

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
40.0ms	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
18.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.0s

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ 1.0 (hypot 1.0 x))
143.0ms	(/ 1.0 (hypot 1.0 x))
1.5s	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
145.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.1s

Counts

124 → 124

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	297	3324
1	869	3167
2	3510	2896
done	5002	2888

prune591.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.3b	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.3b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-pow`
18×	`exp-prod`
10×	`pow1` `associate-/l*`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
7×	`associate-/r*`
6×	`log-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-sum`
2×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `exp-diff` `div-exp` `prod-diff` `clear-num` `associate-/r/` `div-inv`
1×	`flip3--` `flip3-+` `fma-neg` `diff-log` `div-sub` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
68.0ms	(/ (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
15.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
16.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1.0 (hypot 1.0 x))
1.8s	(/ (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
159.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
159.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.7s

Counts

134 → 134

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	347	4444
1	895	4100
2	3448	3803
done	5001	3795

prune776.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (sqrt (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.3b	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.3b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
1.3b	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

544×	`times-frac`
390×	`*-un-lft-identity`
335×	`sqrt-prod`
258×	`add-sqr-sqrt` `add-cube-cbrt`
120×	`log-pow`
90×	`exp-prod`
66×	`distribute-lft-out`
34×	`pow1`
28×	`associate-/r*`
12×	`div-inv`
10×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
6×	`log-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `exp-sum`
2×	`sub-neg` `prod-diff`
1×	`log-div` `flip3--` `frac-2neg` `exp-diff` `fma-neg` `diff-log` `rem-log-exp` `clear-num` `associate-/r/` `flip--` `fma-udef`

Counts

4 → 382

Calls

4 calls:

70.0ms	(/ (sqrt (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (sqrt (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
20.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
16.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
0.0ms	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series3.8s

Counts

4 → 12

Calls

4 calls:

3.2s	(/ (sqrt (log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (/ (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (sqrt (fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
198.0ms	(log (exp (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
170.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))
211.0ms	(fma 1.0 1.0 (- (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.3s

Counts

394 → 394

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	633	29738
1	1529	26221
done	5000	24218

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes373.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 15.0b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	92
1	43	92
done	43	92

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.5s	2897×	body	1280	valid
386.0ms	4006×	body	80	valid
147.0ms	609×	body	640	valid
55.0ms	332×	body	320	valid
17.0ms	156×	body	160	valid