Details

sample89.0ms

Algorithm

intervals

Results

23.0ms	195×	body	80	valid
17.0ms	21×	body	2560	valid
12.0ms	20×	body	1280	valid
10.0ms	256×	pre	80	true
6.0ms	9×	body	640	valid
4.0ms	10×	body	320	valid
0.0ms	1×	body	160	valid

simplify118.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

118.0ms

(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize23.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* x x) (* p (* 4 p))))
0.8b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.0b	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
0.0b	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 86

Calls

4 calls:

Slowest

21.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
18.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
17.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
9.0ms	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
86.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
63.0ms	(/ x (sqrt (+ (* x x) (* p (* 4 p)))))
59.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify10.5s

Counts

124 → 98

Calls

124 calls:

Slowest

642.0ms	(+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3))
573.0ms	(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
469.0ms	(/ 1 (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
451.0ms	(/ x (sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p))))))
415.0ms	(- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.5b

localize43.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* x x) (* p (* 4 p))))
0.8b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
0.5b	(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
0.0b	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
7×	`pow1` `log-pow`
6×	`exp-prod` `add-log-exp`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`log-prod` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `rem-log-exp`

Counts

4 → 63

Calls

4 calls:

Slowest

35.0ms	(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
17.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
11.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

294.0ms	(sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))
277.0ms	(log (exp (sqrt (+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5))))
96.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)
47.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify9.1s

Counts

84 → 75

Calls

84 calls:

Slowest

594.0ms	(+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3))
544.0ms	(sqrt (+ (pow (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) 3) (pow 0.5 3)))
435.0ms	(sqrt (- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5)))
385.0ms	(sqrt (- (* (* x x) (* x x)) (* (* p (* 4 p)) (* p (* 4 p)))))
371.0ms	(- (* (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p)))))) (* 0.5 (/ x (sqrt (+ (* x x) (* p (* 4 p))))))) (* 0.5 0.5))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize36.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* x x) (* p (* p 4))))
13.8b	(sqrt (+ (* x x) (* p (* p 4))))
3.0b	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
3.0b	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 56

Calls

4 calls:

Slowest

9.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
6.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
6.0ms	(sqrt (+ (* x x) (* p (* p 4))))
6.0ms	(sqrt (+ (* x x) (* p (* p 4))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
99.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
55.0ms	(sqrt (+ (* x x) (* p (* p 4))))
54.0ms	(sqrt (+ (* x x) (* p (* p 4))))

simplify8.1s

Counts

76 → 68

Calls

76 calls:

Slowest

550.0ms	(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))
453.0ms	(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
415.0ms	(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))
413.0ms	(* (exp 0.5) (exp (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))))
407.0ms	(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.5b

localize78.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* x x) (* p (* p 4))))
13.8b	(sqrt (+ (* x x) (* p (* p 4))))
3.0b	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
3.0b	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+` `insert-posit16`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 56

Calls

4 calls:

Slowest

12.0ms	(sqrt (+ (* x x) (* p (* p 4))))
11.0ms	(sqrt (+ (* x x) (* p (* p 4))))
9.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
9.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

108.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
90.0ms	(+ 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))
81.0ms	(sqrt (+ (* x x) (* p (* p 4))))
75.0ms	(sqrt (+ (* x x) (* p (* p 4))))

simplify8.1s

Counts

76 → 68

Calls

76 calls:

Slowest

527.0ms	(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))
507.0ms	(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
504.0ms	(+ (* 0.5 0.5) (- (* (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4))))))) (* 0.5 (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))))))
464.0ms	(+ (pow 0.5 3) (pow (* x (/ 0.5 (sqrt (+ (* x x) (* p (* p 4)))))) 3))
431.0ms	(sqrt (- (* (* x x) (* x x)) (* (* p (* p 4)) (* p (* p 4)))))

prune1.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 13.5b

regimes238.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch5.0ms

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	5943×	body	80	valid
931.0ms	8000×	pre	80	true
841.0ms	796×	body	2560	valid
493.0ms	634×	body	1280	valid
198.0ms	301×	body	640	valid
74.0ms	76×	body	5120	valid
66.0ms	153×	body	320	valid
26.0ms	97×	body	160	valid