Details

sample211.0ms

Algorithm

intervals

Results

75.0ms	124×	body	320	valid
56.0ms	230×	body	80	nan
54.0ms	129×	body	160	valid
1.0ms	3×	body	80	valid

simplify408.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

407.0ms

(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.9b

localize45.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
8.6b	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
6.6b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `frac-times` `flip3--` `add-cbrt-cube` `sqrt-div` `associate-*r/` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `associate-*l/` `flip-+` `difference-of-squares`

Counts

4 → 72

Calls

4 calls:

Slowest

47.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
46.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
9.0ms	(sqrt (- (* g g) (* h h)))
9.0ms	(sqrt (- (* g g) (* h h)))

series912.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

395.0ms	(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
366.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(sqrt (- (* g g) (* h h)))
72.0ms	(sqrt (- (* g g) (* h h)))

simplify6.2s

Counts

40 → 84

Calls

40 calls:

Slowest

439.0ms	(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
360.0ms	(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
353.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
342.0ms	(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))))
318.0ms	(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 28.0b

localize68.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
6.6b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
2.5b	(- (sqrt (- (* g g) (* h h))) g)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`sqrt-prod`
23×	`*-un-lft-identity`
21×	`prod-diff` `add-cube-cbrt`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`pow1` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

Slowest

60.0ms	(- (sqrt (- (* g g) (* h h))) g)
30.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(sqrt (- (* g g) (* h h)))
10.0ms	(sqrt (- (* g g) (* h h)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

355.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
79.0ms	(- (sqrt (- (* g g) (* h h))) g)
72.0ms	(sqrt (- (* g g) (* h h)))
62.0ms	(sqrt (- (* g g) (* h h)))

simplify9.4s

Counts

88 → 113

Calls

88 calls:

Slowest

369.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
348.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
337.0ms	(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
274.0ms	(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
272.0ms	(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))

prune2.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 26.6b

localize69.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
2.5b	(- (sqrt (- (* g g) (* h h))) g)
2.2b	(- (* g g) (* h h))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`sqrt-prod`
23×	`*-un-lft-identity`
22×	`prod-diff`
21×	`add-cube-cbrt`
9×	`difference-of-squares`
8×	`fma-neg` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`
1×	`distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

Slowest

81.0ms	(- (sqrt (- (* g g) (* h h))) g)
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))
11.0ms	(- (* g g) (* h h))

series247.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(- (sqrt (- (* g g) (* h h))) g)
67.0ms	(sqrt (- (* g g) (* h h)))
65.0ms	(sqrt (- (* g g) (* h h)))
34.0ms	(- (* g g) (* h h))

simplify8.0s

Counts

87 → 114

Calls

87 calls:

Slowest

346.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
311.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
259.0ms	(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
258.0ms	(fma (* (cbrt (sqrt (- (* g g) (* h h)))) (cbrt (sqrt (- (* g g) (* h h))))) (cbrt (sqrt (- (* g g) (* h h)))) (- (* (cbrt g) (* (cbrt g) (cbrt g)))))
252.0ms	(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune2.3s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 26.6b

localize85.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* g g) (* h h)))
27.8b	(sqrt (- (* g g) (* h h)))
6.6b	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
2.5b	(+ (- g) (sqrt (- (* g g) (* h h))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def`
9×	`add-cube-cbrt`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1`
5×	`cbrt-div`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`distribute-lft-neg-in`
2×	`frac-times` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-*r/` `distribute-lft-out` `difference-of-squares`
1×	`cbrt-prod` `neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `pow1/3` `neg-log` `associate-*l/` `associate-+l-` `flip-+`

Counts

4 → 83

Calls

4 calls:

Slowest

51.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(sqrt (- (* g g) (* h h)))
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

419.0ms	(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
92.0ms	(+ (- g) (sqrt (- (* g g) (* h h))))
67.0ms	(sqrt (- (* g g) (* h h)))
64.0ms	(sqrt (- (* g g) (* h h)))

simplify4.7s

Counts

45 → 95

Calls

45 calls:

Slowest

421.0ms	(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
326.0ms	(cbrt (* 1 (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
302.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
285.0ms	(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
261.0ms	(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.6s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 26.6b

regimes1.7s

Accuracy

-2.5% (2.3b remaining)

Error of 31.7b against oracle of 29.4b and baseline of 31.6b

bsearch362.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

3.3s	3731×	body	320	valid
2.1s	7991×	body	80	nan
1.9s	4127×	body	160	valid
92.0ms	142×	body	80	valid