Details

sample46.0ms

Algorithm

intervals

Results

20.0ms	90×	body	1280	valid
6.0ms	129×	body	80	valid
4.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `fma-neg` `sqrt-prod` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `hypot-udef` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

17.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms	(hypot 1.0 x)
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
98.0ms	(hypot 1.0 x)
131.0ms	(/ 1.0 (hypot 1.0 x))
498.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2439
1	564
0	223

prune613.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.8b	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

15.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series938.0ms

Counts

4 → 12

Calls

4 calls:

493.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
134.0ms	(/ 1.0 (hypot 1.0 x))
172.0ms	(/ 1.0 (hypot 1.0 x))
138.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	2670
1	544
0	194

prune796.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
1.8b	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
19.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
32.0ms	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

series1.6s

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ 1.0 (hypot 1.0 x))
158.0ms	(/ 1.0 (hypot 1.0 x))
794.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1))
498.0ms	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 3 1)))

simplify1.8s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	3432
1	704
0	247

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
1.8b	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))
1.8b	(log (exp (- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`prod-diff`
13×	`log-prod`
12×	`unpow-prod-down`
10×	`exp-sum`
9×	`pow1` `times-frac`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `log-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `associate-/r` `sqrt-prod` `associate-/l` `sqr-pow`
2×	`sub-neg` `sqrt-pow1`
1×	`pow-to-exp` `cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3--` `pow1/2` `exp-diff` `fma-neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `div-inv` `sqrt-pow2` `flip--`

Counts

4 → 104

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
21.0ms	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))
46.0ms	(log (exp (- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))

series1.8s

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ 1.0 (hypot 1.0 x))
765.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4)
467.0ms	(- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))
461.0ms	(log (exp (- (* 1.0 (pow 1.0 3)) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 4))))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	3616
1	733
0	298

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

regimes287.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	2865×	body	1280	valid
301.0ms	4052×	body	80	valid
262.0ms	599×	body	640	valid
114.0ms	327×	body	320	valid
18.0ms	157×	body	160	valid