Details

sample92.0ms

Algorithm

intervals

Results

53.0ms	95×	body	1280	valid
9.0ms	121×	body	80	valid
7.0ms	20×	body	640	valid
4.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

Local error

Found 3 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)))))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`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

3 → 54

Calls

3 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
20.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series647.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
96.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
544.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.7s

Counts

63 → 63

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	105	855
1	202	779
2	471	735
3	1197	733
4	4096	731
done	5001	731

prune208.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.4b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
43.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
13.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
107.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
230.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
62.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	149	2415
1	354	2319
2	1206	2115
done	5000	1912

prune473.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
23×	`times-frac`
19×	`add-cube-cbrt`
11×	`sqrt-prod`
10×	`difference-of-squares`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`associate-r` `associate-/l*`
5×	`distribute-lft-out--`
4×	`unswap-sqr`
3×	`flip3-+` `pow-prod-down` `associate-/r*` `flip-+`
2×	`flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `div-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

11.0ms	(+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5)))
73.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))))
73.0ms	(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
16.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5)))
218.0ms	(/ (- 0.5 (/ 0.5 (hypot 1.0 x))) (+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))))
100.0ms	(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
57.0ms	(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify2.6s

Counts

115 → 115

Iterations

Useful iterations: 3 (962.0ms)

Iter	Nodes	Cost
0	167	2692
1	393	2576
2	1042	2414
3	3151	2412
done	5000	2412

prune487.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
0.5b	(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
1.6b	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`unpow-prod-down` `cube-prod`
26×	`times-frac`
25×	`add-cube-cbrt`
24×	`difference-of-squares`
11×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `sqr-pow`
10×	`associate-l`
9×	`associate-r`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`distribute-lft-out--` `unswap-sqr`
4×	`frac-times` `pow-prod-down` `associate-*l/`
3×	`pow-unpow`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-r/` `pow-exp` `prod-exp` `-commutative` `cbrt-unprod` `div-inv` `rem-cube-cbrt`
1×	`difference-cubes` `cbrt-undiv` `cube-div` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `distribute-lft-in` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `flip--` `distribute-lft-out`

Counts

4 → 149

Calls

4 calls:

55.0ms	(* (+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
8.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
62.0ms	(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
52.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series512.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (+ 1.0 (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
48.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)
93.0ms	(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
98.0ms	(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify2.4s

Counts

161 → 161

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	269	3759
1	802	3454
2	3416	3174
done	5001	3172

prune742.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

regimes96.0ms

Accuracy

0% (0.3b remaining)

Error of 15.4b against oracle of 15.2b and baseline of 15.4b

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	50
1	31	50
done	31	50

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	2831×	body	1280	valid
313.0ms	4019×	body	80	valid
224.0ms	656×	body	640	valid
54.0ms	336×	body	320	valid
16.0ms	158×	body	160	valid