Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	98×	body	1280	valid
6.0ms	123×	body	80	valid
4.0ms	18×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify57.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

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:

0.0ms	(hypot 1.0 x)
24.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot 1.0 x)
107.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(/ 1.0 (hypot 1.0 x))
149.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.6s

Counts

73 → 73

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	106	904
1	203	828
2	472	778
3	1201	776
4	4065	774
done	5000	774

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.7b

localize35.0ms

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	(/ 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)))))

rewrite50.0ms

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:

11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
10.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(/ 1.0 (hypot 1.0 x))
15.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
19.0ms	(/ 1.0 (hypot 1.0 x))
16.0ms	(/ 1.0 (hypot 1.0 x))
58.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.3s

Counts

92 → 92

Iterations

Useful iterations: 3 (905.0ms)

Iter	Nodes	Cost
0	109	1174
1	245	1108
2	749	1004
3	2941	995
done	5002	995

prune330.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 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 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
1.7b	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
30×	`times-frac` `difference-of-squares`
26×	`sqr-pow`
21×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
11×	`unpow-prod-down`
10×	`associate-/l*`
8×	`flip3-+` `associate-*l/` `flip-+`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`frac-times` `associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`pow-unpow` `associate-r` `associate-/r*`
2×	`cube-div` `flip3--` `pow-pow` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `cube-prod` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 131

Calls

4 calls:

138.0ms	(* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
121.0ms	(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
16.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
18.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series710.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
327.0ms	(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
102.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
178.0ms	(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify2.7s

Counts

143 → 143

Iterations

Useful iterations: 2 (904.0ms)

Iter	Nodes	Cost
0	281	6665
1	815	6316
2	3896	5900
done	5000	5900

prune952.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.7b

localize63.0ms

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)
0.0b	(* (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
1.7b	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `flip3-+` `flip-+`
6×	`pow-unpow` `associate-*r/` `add-log-exp`
4×	`cube-div` `frac-times` `pow-pow` `associate-r` `pow-exp` `rem-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-*l/` `sqr-pow`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `*-commutative` `flip--` `distribute-lft-out` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

17.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
15.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
124.0ms	(* (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
25.0ms	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
133.0ms	(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
382.0ms	(* (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))
544.0ms	(- (* (pow 1.0 6) (pow 1.0 6)) (* (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)))

simplify2.3s

Counts

102 → 102

Iterations

Useful iterations: 2 (512.0ms)

Iter	Nodes	Cost
0	201	3802
1	663	3228
2	3207	2846
done	5000	2846

prune754.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.7b

regimes328.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.8b and baseline of 14.8b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	168
1	53	168
done	53	168

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	2834×	body	1280	valid
338.0ms	4075×	body	80	valid
254.0ms	609×	body	640	valid
72.0ms	155×	body	160	valid
61.0ms	327×	body	320	valid