Details

Time bar (total: 31.3s)

sample172.0ms

Algorithm
intervals
Results
72.0ms318×body80nan
48.0ms132×body320valid
32.0ms120×body160valid
0.0ms4×body80valid

simplify305.0ms

Calls
1 calls:
Slowest
305.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize43.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (- (* g g) (* h h)))
29.7b
(sqrt (- (* g g) (* h h)))
7.7b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
6.8b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×cbrt-prod *-un-lft-identity add-cube-cbrt sqrt-prod
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×times-frac
2×frac-times rem-sqrt-square flip3-+ flip3-- pow1/2 pow1/3 associate-*r/ flip-+ flip-- difference-of-squares
1×associate-*l/ div-inv
Calls
4 calls:
Slowest
12.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
5.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
3.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(sqrt (- (* g g) (* h h)))

series852.0ms

Calls
4 calls:
Slowest
433.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
277.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
83.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(sqrt (- (* g g) (* h h)))

simplify5.3s

Calls
40 calls:
Slowest
347.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
328.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))
276.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
275.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
266.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))

prune1.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 30.1b

localize13.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (- (* g g) (* h h)))
29.7b
(sqrt (- (* g g) (* h h)))
6.8b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
3.2b
(- (* g g) (* h h))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt sqrt-prod
7×cbrt-prod
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×times-frac flip3-- flip-- difference-of-squares
2×rem-sqrt-square pow1/2
1×cbrt-div sub-neg fma-neg pow1/3 diff-log prod-diff div-inv
Calls
4 calls:
Slowest
11.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
8.0ms
(- (* g g) (* h h))
7.0ms
(sqrt (- (* g g) (* h h)))
4.0ms
(sqrt (- (* g g) (* h h)))

series504.0ms

Calls
4 calls:
Slowest
341.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
62.0ms
(sqrt (- (* g g) (* h h)))
57.0ms
(sqrt (- (* g g) (* h h)))
44.0ms
(- (* g g) (* h h))

simplify3.8s

Calls
39 calls:
Slowest
311.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
279.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
262.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
257.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
254.0ms
(- (+ (* 1/18 (* (cbrt 1/2) (* (exp (* 1/3 (- (log (/ 1 (sqrt -1))) (+ (* 5 (log h)) (log a))))) (pow g 2)))) (* (cbrt 1/2) (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))))) (* 1/3 (* (cbrt 1/2) (* g (exp (* 1/3 (- (log -1) (+ (* 2 (log h)) (log a)))))))))

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 28.9b

localize27.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (- (* g g) (* h h)))
29.7b
(sqrt (- (* g g) (* h h)))
3.2b
(- (* g g) (* h h))
3.2b
(- (* g g) (* h h))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg pow1/2 fma-neg diff-log prod-diff
Calls
4 calls:
Slowest
7.0ms
(sqrt (- (* g g) (* h h)))
6.0ms
(sqrt (- (* g g) (* h h)))
5.0ms
(- (* g g) (* h h))
5.0ms
(- (* g g) (* h h))

series233.0ms

Calls
4 calls:
Slowest
80.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(- (* g g) (* h h))
39.0ms
(- (* g g) (* h h))

simplify2.2s

Calls
36 calls:
Slowest
286.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
278.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
269.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
237.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
181.0ms
(sqrt (* (cbrt (- (* g g) (* h h))) (cbrt (- (* g g) (* h h)))))

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 28.9b

localize18.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (- (* g g) (* h h)))
29.7b
(sqrt (- (* g g) (* h h)))
3.2b
(- (* g g) (* h h))
3.2b
(- (* g g) (* h h))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg pow1/2 fma-neg diff-log prod-diff
Calls
4 calls:
Slowest
8.0ms
(sqrt (- (* g g) (* h h)))
8.0ms
(- (* g g) (* h h))
6.0ms
(- (* g g) (* h h))
5.0ms
(sqrt (- (* g g) (* h h)))

series199.0ms

Calls
4 calls:
Slowest
65.0ms
(sqrt (- (* g g) (* h h)))
58.0ms
(sqrt (- (* g g) (* h h)))
43.0ms
(- (* g g) (* h h))
33.0ms
(- (* g g) (* h h))

simplify2.2s

Calls
36 calls:
Slowest
325.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
301.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
281.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
203.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
165.0ms
(sqrt (* (cbrt (- (* g g) (* h h))) (cbrt (- (* g g) (* h h)))))

prune1.8s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 28.9b

regimes890.0ms

Accuracy

32.8% (1.3b remaining)

Error of 30.4b against oracle of 29.2b and baseline of 31.1b

bsearch682.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
2.6s3662×body320valid
2.3s4161×body160valid
2.1s8100×body80nan
35.0ms177×body80valid