Details

sample77.0ms

Algorithm

intervals

Results

21.0ms	40×	body	2560	valid
16.0ms	186×	body	80	valid
8.0ms	19×	body	1280	valid
7.0ms	256×	pre	80	true
2.0ms	6×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	3×	body	320	valid

simplify46.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `flip-+`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 79

Calls

4 calls:

31.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms	(+ (* (* 4.0 p) p) (* x x))
69.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
36.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
57.0ms	(+ (* (* 4.0 p) p) (* x x))
91.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.7s

Counts: 91 → 91

prune347.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.3b	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

24.0ms	(+ (* (* 4.0 p) p) (* x x))
56.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
270.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
39.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* (* 4.0 p) p) (* x x))
100.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
85.0ms	(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts: 67 → 67

prune342.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

62.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
43.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
35.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
77.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify1.3s

Counts: 66 → 66

prune331.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
26×	`sqrt-prod`
24×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`sqrt-div` `associate-/r*` `add-log-exp`
5×	`unswap-sqr`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip-+`
3×	`pow-flip` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 122

Calls

4 calls:

35.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
25.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
59.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
83.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
64.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify609.0ms

Counts: 134 → 134

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

regimes126.0ms

Accuracy

0% (2.0b remaining)

Error of 15.0b against oracle of 13.0b and baseline of 15.0b

bsearch0.0ms

simplify828.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

472.0ms	8000×	pre	80	true
469.0ms	5998×	body	80	valid
319.0ms	808×	body	2560	valid
194.0ms	633×	body	1280	valid
61.0ms	58×	body	5120	valid
58.0ms	288×	body	640	valid
21.0ms	142×	body	320	valid
8.0ms	73×	body	160	valid