Details

sample100.0ms

Algorithm

intervals

Results

49.0ms	77×	body	1280	valid
18.0ms	51×	body	640	valid
11.0ms	28×	body	2560	valid
5.0ms	26×	body	320	valid
3.0ms	62×	body	80	valid
1.0ms	12×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1.0)))
2.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.7b	(sqrt (+ (* x x) 1.0))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

33.0ms	(+ x (sqrt (+ (* x x) 1.0)))
25.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms	(sqrt (+ (* x x) 1.0))

series301.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1.0)))
182.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
59.0ms	(sqrt (+ (* x x) 1.0))

simplify61.0ms

Counts: 51 → 51

prune161.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 270

Calls

1 calls:

127.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series184.0ms

Counts

1 → 3

Calls

1 calls:

184.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify75.0ms

Counts: 273 → 273

prune597.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.0b	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.1b	(/ 0.125 (pow x 3))
12.9b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite576.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt`
18×	`add-log-exp`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`log-prod` `add-cbrt-cube` `distribute-lft-out--`
5×	`pow1` `sum-log` `difference-of-squares` `sqr-pow`
4×	`cube-mult` `diff-log` `unpow3`
3×	`associate-+r+` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`sub-neg` `log-div` `associate--l+` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 125

Calls

4 calls:

126.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
221.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
15.0ms	(/ 0.125 (pow x 3))
210.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
72.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
64.0ms	(/ 0.125 (pow x 3))
230.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify62.0ms

Counts: 137 → 137

prune442.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 0.0625) (pow x 5))
0.1b	(/ 0.125 (pow x 3))
15.3b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.6b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

13.0ms	(/ (- 0.0625) (pow x 5))
9.0ms	(/ 0.125 (pow x 3))
224.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
233.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (- 0.0625) (pow x 5))
41.0ms	(/ 0.125 (pow x 3))
285.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
67.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify81.0ms

Counts: 235 → 235

prune827.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes138.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.5b

bsearch114.0ms

Steps

Iters	Range		Point
9	8.845201659255268e-06	4.45864614599283	0.8818798333827608
10	-119.54622503529531	-1.822584514918214e-10	-1.016870309496291

simplify59.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	2294×	body	1280	valid
547.0ms	1583×	body	640	valid
380.0ms	802×	body	2560	valid
182.0ms	2176×	body	80	valid
145.0ms	751×	body	320	valid
46.0ms	394×	body	160	valid