Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize10.0ms

Local error

Found 1 expressions with local error:

15.9b

(/ x (+ (* x x) 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

28.0ms

(/ x (+ (* x x) 1.0))

series90.0ms

Counts

1 → 3

Calls

1 calls:

90.0ms

(/ x (+ (* x x) 1.0))

simplify131.0ms

Counts: 32 → 32

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
15.8b	(sqrt (+ (* x x) 1.0))
15.8b	(sqrt (+ (* x x) 1.0))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

110.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
27.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
10.0ms	(sqrt (+ (* x x) 1.0))
21.0ms	(sqrt (+ (* x x) 1.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
126.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
73.0ms	(sqrt (+ (* x x) 1.0))
54.0ms	(sqrt (+ (* x x) 1.0))

simplify80.0ms

Counts: 176 → 176

prune580.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

15.9b

(/ x (+ (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

15.0ms

(/ x (+ (* x x) 1.0))

series93.0ms

Counts

1 → 3

Calls

1 calls:

93.0ms

(/ x (+ (* x x) 1.0))

simplify115.0ms

Counts: 32 → 32

prune99.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
0.3b	(/ 1 (pow x 5))
0.4b	(/ 1 (pow x 3))
19.1b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-sqr-sqrt`
173×	`times-frac`
112×	`*-un-lft-identity`
63×	`difference-of-squares`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
40×	`sqr-pow`
26×	`cube-prod`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv` `associate-/l*`
4×	`pow1` `cube-mult` `associate-+r+` `unpow3`
3×	`sub-neg` `associate-*r/` `frac-add`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `frac-sub` `flip--` `inv-pow`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 227

Calls

4 calls:

42.0ms	(+ (/ 1 x) (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
9.0ms	(/ 1 (pow x 5))
17.0ms	(/ 1 (pow x 3))
138.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (/ 1 x) (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))))
82.0ms	(/ 1 (pow x 5))
39.0ms	(/ 1 (pow x 3))
162.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify86.0ms

Counts: 239 → 239

prune844.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch103.0ms

Steps

Iters	Range		Point
9	3.244205803610274e-06	1902.9075791774285	470.1828671092737
8	-2.6354521979890637e+33	-5.620501265456609e+28	-1.2032692145665368e+31

simplify33.0ms

end0.0ms

sample525.0ms

Algorithm

intervals

Results

339.0ms

8000×

body

valid