Details

sample65.0ms

Algorithm

intervals

Results

38.0ms	92×	body	1280	valid
6.0ms	123×	body	80	valid
6.0ms	25×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid

simplify46.0ms

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	43	12
done	43	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `hypot-udef` `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

4 → 85

Calls

4 calls:

29.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(hypot 1.0 x)
8.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series981.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
80.0ms	(hypot 1.0 x)
115.0ms	(/ 1.0 (hypot 1.0 x))
406.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.7s

Counts

97 → 97

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	225	2149
1	563	1727
2	2461	1491
done	5002	1474

prune364.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize24.0ms

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
19.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
10.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series850.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ 1.0 (hypot 1.0 x))
148.0ms	(/ 1.0 (hypot 1.0 x))
397.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
156.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify1.9s

Counts

104 → 104

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	190	1534
1	516	1451
2	2582	1318
done	5001	1313

prune475.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize32.0ms

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	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.6b	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
56×	`prod-diff`
46×	`add-cube-cbrt`
45×	`unpow-prod-down`
42×	`sqr-pow`
30×	`times-frac` `difference-of-squares`
10×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cube-mult` `unpow3` `cube-prod` `add-log-exp`
7×	`pow1` `fma-neg`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `flip3-+` `associate-*l/` `pow-exp` `flip--` `flip-+` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `sqrt-prod` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 188

Calls

4 calls:

19.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
82.0ms	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
16.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
37.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series4.2s

Counts

4 → 12

Calls

4 calls:

504.0ms	(+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
2.9s	(/ (- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
310.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
537.0ms	(- (pow 1.0 6) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify987.0ms

Counts

200 → 200

Iterations

Useful iterations: done (975.0ms)

Iter	Nodes	Cost
0	526	11409
1	1537	9323
done	5000	7890

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.5b	(expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
1.6b	(- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-cube-cbrt`
21×	`times-frac` `prod-diff`
18×	`unpow-prod-down`
15×	`difference-of-squares`
10×	`sqr-pow`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `fma-neg` `associate-/l*` `add-log-exp`
5×	`log1p-expm1-u` `distribute-lft-out--`
4×	`expm1-log1p-u`
3×	`pow-unpow` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `diff-log` `associate-*l/` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `log1p-udef` `expm1-log1p` `frac-2neg` `flip3-+` `unpow3` `div-sub` `cube-prod` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 132

Calls

4 calls:

49.0ms	(/ (- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
16.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0ms	(expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
20.0ms	(- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

series6.9s

Counts

4 → 12

Calls

4 calls:

3.7s	(/ (- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (pow 1.0 3))))
387.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
896.0ms	(expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))
1.9s	(- (pow 1.0 6) (log1p (expm1 (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))))

simplify935.0ms

Counts

144 → 144

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	463	8075
1	1393	6451
done	5000	5770

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

regimes618.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	92
1	32	92
done	32	92

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.7s	2816×	body	1280	valid
332.0ms	4088×	body	80	valid
163.0ms	624×	body	640	valid
63.0ms	324×	body	320	valid
16.0ms	148×	body	160	valid