Details

sample75.0ms

Algorithm

intervals

Results

37.0ms	86×	body	1280	valid
10.0ms	130×	body	80	valid
6.0ms	19×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	8×	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	43	12
done	43	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.8b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
22.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1.0 (hypot 1.0 x))
155.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
395.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
560.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts

104 → 104

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	223	2270
1	564	1839
2	2485	1595
done	5000	1579

prune451.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize18.0ms

Local error

Found 4 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)))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.3b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

10.0ms	(/ 1.0 (hypot 1.0 x))
24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(+ 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))

series1.2s

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1.0 (hypot 1.0 x))
411.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
459.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
178.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.3s

Counts

89 → 89

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	218	1545
1	590	1428
2	2860	1328
done	5000	1323

prune534.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))) (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
2.3b	(- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac` `prod-diff`
8×	`pow1` `unpow-prod-down` `add-log-exp`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `pow-pow` `log1p-expm1-u`
3×	`fma-def` `associate-/r` `associate-/l`
2×	`unpow-prod-up` `flip3--` `sqrt-pow1` `sqrt-prod` `flip--` `associate-/l/` `distribute-lft-out` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

70.0ms	(/ (- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))) (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
43.0ms	(- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

series4.0s

Counts

4 → 12

Calls

4 calls:

2.1s	(/ (- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))) (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))
499.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
868.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
502.0ms	(- (* (pow 1.0 3) 1.0) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

simplify888.0ms

Counts

111 → 111

Iterations

Useful iterations: done (879.0ms)

Iter	Nodes	Cost
0	385	4706
1	1189	3849
done	5000	3515

prune831.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

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))))))
0.2b	(exp (log (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
2.3b	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

75×	`unpow-prod-down`
65×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`*-un-lft-identity`
41×	`add-cube-cbrt`
29×	`sqr-pow`
18×	`difference-of-squares`
14×	`log-prod` `exp-sum`
9×	`pow1`
8×	`sqrt-prod` `add-log-exp`
7×	`fma-neg`
5×	`add-exp-log`
4×	`expm1-log1p-u` `exp-prod` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-unpow` `fma-def`
2×	`log-div` `flip3--` `sqrt-pow1` `exp-diff` `flip--`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `pow-exp` `sum-log` `log-pow` `sqrt-pow2` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 159

Calls

4 calls:

14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
23.0ms	(exp (log (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
22.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
37.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

series2.1s

Counts

4 → 12

Calls

4 calls:

466.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
434.0ms	(exp (log (- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))
732.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
448.0ms	(- (pow 1.0 4) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))

simplify2.0s

Counts

171 → 171

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	368	8041
1	890	6060
2	3653	4764
done	5000	4756

prune952.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

regimes423.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 15.0b and baseline of 15.2b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	45
1	25	45
2	27	45
done	27	45

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2812×	body	1280	valid
669.0ms	4036×	body	80	valid
291.0ms	660×	body	640	valid
68.0ms	332×	body	320	valid
21.0ms	160×	body	160	valid