Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify1.1s

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
16.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 42

Calls

2 calls:

17.0ms	(+ (* x x) (* y y))
76.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series145.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x x) (* y y))
112.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify735.0ms

Counts: 48 → 48

prune152.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.0b	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
16.0b	(sqrt (+ (* x x) (* y y)))
16.0b	(sqrt (+ (* x x) (* y y)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt`
96×	`times-frac`
95×	`*-un-lft-identity`
57×	`add-cube-cbrt` `sqrt-prod`
36×	`associate-l`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `associate-/r/` `distribute-lft-out`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 183

Calls

4 calls:

39.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
131.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
8.0ms	(sqrt (+ (* x x) (* y y)))
10.0ms	(sqrt (+ (* x x) (* y y)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
65.0ms	(* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (/ (+ x y) (sqrt (+ (* x x) (* y y)))))
41.0ms	(sqrt (+ (* x x) (* y y)))
38.0ms	(sqrt (+ (* x x) (* y y)))

simplify1.0s

Counts: 195 → 195

prune563.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
0.0b	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
16.6b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`pow-unpow` `add-cbrt-cube`
8×	`associate-/l/`
7×	`log-prod`
6×	`unpow-prod-down` `flip3-+` `times-frac` `flip-+` `add-log-exp`
5×	`pow1`
4×	`frac-times` `pow-pow` `associate-/r/`
3×	`exp-prod` `flip3--` `rem-log-exp` `associate-/r*` `flip--`
2×	`cbrt-undiv` `pow-to-exp` `associate-r/` `div-exp` `associate-l/` `pow-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `log-pow` `cbrt-unprod` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

11.0ms	(+ (* x x) (* y y))
10.0ms	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
18.0ms	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
35.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x x) (* y y))
127.0ms	(log (pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))))
120.0ms	(pow (exp 1) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))))
102.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify895.0ms

Counts: 98 → 98

prune453.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify16.0ms

Counts: 0 → 0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes124.0ms

Accuracy

78.4% (4.2b remaining)

Error of 4.6b against oracle of 0.4b and baseline of 20.0b

bsearch125.0ms

Steps

Iters	Range	Point
7	1.270532878618462e-164	1.8595605403829251e-162	1.8282600166370302e-162
7	-9.040093718271735e-161	-4.482309770999907e-162	-1.937646393364571e-161
10	-3.6321213431321147e+161	-2.5300323932420435e+146	-9.82178231331464e+153

Iters

Range

Point

1.270532878618462e-164

1.8595605403829251e-162

1.8282600166370302e-162

-9.040093718271735e-161

-4.482309770999907e-162

-1.937646393364571e-161

-3.6321213431321147e+161

-2.5300323932420435e+146

-9.82178231331464e+153

simplify643.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

798.0ms	8000×	body	80	valid
227.0ms	8000×	pre	80	true