Details

sample58.0ms

Algorithm

intervals

Results

28.0ms	92×	body	1280	valid
7.0ms	123×	body	80	valid
6.0ms	25×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	24	12
3	28	12
4	30	12
5	35	12
6	36	12
done	36	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize27.0ms

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))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`times-frac`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `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` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 61

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0ms	(hypot 1.0 x)
5.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(hypot 1.0 x)
12.0ms	(/ 1.0 (hypot 1.0 x))
94.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.1s

Counts

73 → 73

Iterations

Useful iterations: 3 (929.0ms)

Iter	Nodes	Cost
0	106	904
1	218	828
2	717	778
3	4234	776
done	5001	776

prune207.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.4b

localize18.0ms

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`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`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `associate--r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
14.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
106.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
57.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

92 → 92

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	109	1174
1	277	1112
2	1368	1008
done	5002	1003

prune387.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.4b

localize40.0ms

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

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`times-frac` `difference-of-squares`
26×	`sqr-pow`
20×	`add-cube-cbrt`
11×	`unpow-prod-down`
10×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
5×	`distribute-lft-out--`
3×	`pow-unpow` `flip3-+` `associate-/r*` `flip-+`
2×	`cube-div` `flip3--` `pow-pow` `associate-*r/` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `cube-prod` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 115

Calls

4 calls:

7.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
73.0ms	(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 1.0 1.0)))))
32.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
31.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series841.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
428.0ms	(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (* (pow 1.0 3) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 1.0 1.0)))))
105.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
198.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify2.1s

Counts

127 → 127

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	243	6010
1	713	5581
2	3432	5261
done	5000	5257

prune920.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

50×	`sqrt-prod`
32×	`add-sqr-sqrt`
18×	`associate-*r/`
17×	`pow1`
16×	`cube-div`
15×	`swap-sqr`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqr-pow`
12×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
11×	`associate-r` `associate-l`
9×	`unpow-prod-down` `unswap-sqr`
8×	`flip3-+` `cube-prod` `flip-+`
6×	`cube-mult` `pow-unpow` `sqrt-pow1` `pow1/2` `unpow3` `add-log-exp`
5×	`pow-prod-down`
4×	`frac-times` `pow-pow` `pow-exp` `rem-cube-cbrt`
3×	`prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod` `difference-of-squares`
2×	`pow-to-exp` `associate-*l/`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `rem-square-sqrt` `*-commutative` `flip--`

Counts

4 → 140

Calls

4 calls:

17.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
18.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
54.0ms	(* (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
28.0ms	(- (pow 1.0 6) (* (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))))

series673.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
144.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
158.0ms	(* (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
225.0ms	(- (pow 1.0 6) (* (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (sqrt (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))))

simplify1.3s

Counts

152 → 152

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	178	4312
1	462	2863
2	2063	2639
done	5002	2595

prune926.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.3b

regimes327.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	72
1	31	72
done	31	72

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	2816×	body	1280	valid
346.0ms	4088×	body	80	valid
256.0ms	624×	body	640	valid
60.0ms	324×	body	320	valid
16.0ms	148×	body	160	valid