Details

sample73.0ms

Algorithm

intervals

Results

34.0ms	90×	body	1280	valid
9.0ms	129×	body	80	valid
7.0ms	22×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
6	37
5	35
4	30
3	28
2	24
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize18.0ms

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))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `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 → 60

Calls

4 calls:

17.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms	(hypot 1.0 x)
8.0ms	(/ 1.0 (hypot 1.0 x))
9.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(hypot 1.0 x)
10.0ms	(/ 1.0 (hypot 1.0 x))
137.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	4651
2	762
1	220
0	101

prune380.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.7b

localize126.0ms

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

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
8×	`associate-*r/`
6×	`associate-/r/` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`distribute-rgt-in` `pow1` `distribute-lft-in` `frac-add` `associate--r+`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
2×	`flip3--` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 106

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
369.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
126.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

series788.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(/ 1.0 (hypot 1.0 x))
512.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))) (+ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))))
248.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

simplify3.2s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	3863
1	598
0	195

prune808.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.6b

localize146.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`sqrt-div`
9×	`times-frac`
8×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `flip3--` `add-cbrt-cube` `pow1/2` `swap-sqr` `add-exp-log` `flip--` `associate--r+` `add-log-exp`
6×	`associate-r` `associate-l`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `pow-sqr` `associate-/l`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 116

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
930.0ms	(* (sqrt (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))) (sqrt (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))
100.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
116.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
234.0ms	(* (sqrt (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))) (sqrt (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))
255.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
228.0ms	(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))

simplify2.1s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1646
1	356
0	156

prune841.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.6b

localize104.0ms

Local error

Found 4 expressions with local error:

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

rewrite807.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1` `flip3-+` `associate-*r/` `flip-+`
27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`associate-*l/` `associate-/r/`
18×	`times-frac`
17×	`add-cbrt-cube` `add-exp-log`
16×	`frac-times`
15×	`add-cube-cbrt`
13×	`sqr-pow`
12×	`pow-pow` `frac-add` `associate-/l*` `difference-of-squares`
9×	`pow-prod-down`
8×	`cube-div`
6×	`sqrt-pow1` `sqrt-div` `pow-prod-up` `add-log-exp`
4×	`associate-/r*` `prod-exp` `cbrt-unprod`
3×	`difference-cubes` `cbrt-undiv` `pow-unpow` `pow-plus` `pow1/2` `div-exp` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt`
2×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `diff-log` `unpow3` `div-sub` `cube-prod`

Counts

4 → 143

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
696.0ms	(/ (- (pow (* 1.0 (* 1.0 1.0)) 3) (pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3)) (* (+ (* (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0) 1.0) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (+ (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0))) (* (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (+ (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))))
86.0ms	(pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3)
15.0ms	(- (pow (* 1.0 (* 1.0 1.0)) 3) (pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3))

series3.1s

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1.0 (hypot 1.0 x))
2.4s	(/ (- (pow (* 1.0 (* 1.0 1.0)) 3) (pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3)) (* (+ (* (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0) 1.0) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (+ (* (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0))) (* (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (+ (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))))
272.0ms	(pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3)
376.0ms	(- (pow (* 1.0 (* 1.0 1.0)) 3) (pow (* (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 3))

simplify5.9s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
1	1317
0	353

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.6b

regimes192.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	25
1	25
0	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	2865×	body	1280	valid
313.0ms	599×	body	640	valid
244.0ms	4052×	body	80	valid
61.0ms	327×	body	320	valid
19.0ms	157×	body	160	valid