Details

sample50.0ms

Algorithm

intervals

Results

29.0ms	95×	body	1280	valid
5.0ms	121×	body	80	valid
4.0ms	20×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite57.0ms

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:

9.0ms	(/ 1.0 (hypot 1.0 x))
36.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ 1.0 (hypot 1.0 x))
403.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
525.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	207	2042
1	492	1618
2	1444	1398
done	5000	1265

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 16.2b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
37.0ms	(/ (- (* 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))

series2.3s

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1.0 (hypot 1.0 x))
416.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.6s	(/ (- (* 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)))))))
153.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	330	3402
1	971	3222
2	3887	2952
done	5000	2951

prune538.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 16.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (exp (log (- (* 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)))))))
0.1b	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.7b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
45.0ms	(/ (exp (log (- (* 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)))))))
20.0ms	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
18.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.6s

Counts

4 → 12

Calls

4 calls:

463.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.8s	(/ (exp (log (- (* 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)))))))
191.0ms	(exp (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
177.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.1s

Counts

116 → 116

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	318	4398
1	872	3998
2	3464	3594
done	5000	3579

prune632.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 16.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ (pow E (log (- (* 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)))))))
0.1b	(pow E (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.7b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
40×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-up` `unpow-prod-down` `log-prod`
12×	`distribute-lft-out`
11×	`add-exp-log`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`pow1` `add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `log-div` `pow-unpow` `div-exp` `pow-exp` `associate-/r*` `log1p-expm1-u` `pow-sub`
3×	`flip3--` `fma-def` `flip--`
2×	`pow-to-exp` `e-exp-1` `flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `pow-pow` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `sum-log` `log-pow` `div-inv`

Counts

4 → 134

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
70.0ms	(/ (pow E (log (- (* 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)))))))
11.0ms	(pow E (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series3.7s

Counts

4 → 12

Calls

4 calls:

493.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.5s	(/ (pow E (log (- (* 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)))))))
570.0ms	(pow E (log (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
164.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify3.0s

Counts

146 → 146

Iterations

Useful iterations: 2 (1.3s)

Iter	Nodes	Cost
0	378	5975
1	1049	5605
2	4022	5262
done	5000	5262

prune821.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes445.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.4b

bsearch3.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	100
1	46	100
2	48	100
done	48	100

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2831×	body	1280	valid
387.0ms	4019×	body	80	valid
180.0ms	656×	body	640	valid
59.0ms	336×	body	320	valid
19.0ms	158×	body	160	valid