Details

Time bar (total: 4.5m)

sample206.0ms

Algorithm
intervals
Results
91.0ms121×body320valid
49.0ms132×body160valid
44.0ms237×body80nan
0.0ms3×body80valid

simplify352.0ms

Calls
1 calls:
Slowest
352.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.8b

localize75.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (- (* g g) (* h h)))
30.3b
(sqrt (- (* g g) (* h h)))
8.6b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
7.2b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))

rewrite536.0ms

Algorithm
rewrite-expression-head
Rules
229×add-sqr-sqrt
108×*-un-lft-identity
100×cbrt-prod
82×times-frac
79×sqrt-prod
76×difference-of-squares
56×add-cube-cbrt
52×cbrt-div
42×associate-*l*
29×unswap-sqr
28×*-commutative
25×associate-*r*
24×swap-sqr
23×distribute-lft-out--
21×associate-/r*
18×frac-times
15×associate-/l*
10×flip3-+ flip-+
9×associate-*l/
6×pow1
4×expm1-log1p-u clear-num frac-2neg add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 associate-*r/ div-inv associate-/l/
1×distribute-lft-out
Calls
4 calls:
Slowest
246.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
161.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
69.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(sqrt (- (* g g) (* h h)))

series905.0ms

Calls
4 calls:
Slowest
397.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
381.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
65.0ms
(sqrt (- (* g g) (* h h)))
62.0ms
(sqrt (- (* g g) (* h h)))

simplify28.2s

Calls
238 calls:
Slowest
697.0ms
(cbrt (/ (sqrt (- (sqrt (- (* g g) (* h h))) g)) (* (cbrt (* a 2)) (cbrt (* a 2)))))
643.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
600.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
504.0ms
(cbrt (* (/ -1/2 (* (cbrt a) (cbrt a))) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
427.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))

prune4.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.1b

localize35.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (- (* g g) (* h h)))
30.3b
(sqrt (- (* g g) (* h h)))
7.2b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
2.6b
(- (* g g) (* h h))

rewrite439.0ms

Algorithm
rewrite-expression-head
Rules
395×add-sqr-sqrt
225×prod-diff
214×*-un-lft-identity
176×add-cube-cbrt
129×swap-sqr
118×associate-*l*
97×associate-*r*
75×difference-of-squares
66×sqrt-prod
63×unswap-sqr
62×*-commutative
29×cbrt-div
24×cbrt-prod
18×frac-times
15×fma-neg distribute-lft-out--
10×flip3-+ times-frac flip-+
9×associate-/r* associate-*l/ associate-/l*
6×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×clear-num frac-2neg flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×sub-neg pow1/3 diff-log div-inv distribute-lft-out
Calls
4 calls:
Slowest
254.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
71.0ms
(sqrt (- (* g g) (* h h)))
58.0ms
(sqrt (- (* g g) (* h h)))
44.0ms
(- (* g g) (* h h))

series599.0ms

Calls
4 calls:
Slowest
416.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
79.0ms
(sqrt (- (* g g) (* h h)))
66.0ms
(sqrt (- (* g g) (* h h)))
39.0ms
(- (* g g) (* h h))

simplify55.3s

Calls
657 calls:
Slowest
767.0ms
(cbrt (* (/ -1/2 (* (cbrt a) (cbrt a))) (+ g (sqrt (- (* g g) (* h h))))))
583.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
560.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
421.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
387.0ms
(fma (sqrt (* g g)) (sqrt (* g g)) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))

prune8.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.7b

localize25.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (- (* g g) (* h h)))
30.3b
(sqrt (- (* g g) (* h h)))
7.2b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
2.6b
(- (* g g) (* h h))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
395×add-sqr-sqrt
225×prod-diff
214×*-un-lft-identity
176×add-cube-cbrt
129×swap-sqr
118×associate-*l*
97×associate-*r*
75×difference-of-squares
66×sqrt-prod
63×unswap-sqr
62×*-commutative
29×cbrt-div
24×cbrt-prod
18×frac-times
15×fma-neg distribute-lft-out--
10×flip3-+ times-frac flip-+
9×associate-/r* associate-*l/ associate-/l*
6×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×clear-num frac-2neg flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×sub-neg pow1/3 diff-log div-inv distribute-lft-out
Calls
4 calls:
Slowest
235.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
54.0ms
(sqrt (- (* g g) (* h h)))
51.0ms
(sqrt (- (* g g) (* h h)))
31.0ms
(- (* g g) (* h h))

series605.0ms

Calls
4 calls:
Slowest
414.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
75.0ms
(sqrt (- (* g g) (* h h)))
74.0ms
(sqrt (- (* g g) (* h h)))
42.0ms
(- (* g g) (* h h))

simplify54.4s

Calls
657 calls:
Slowest
667.0ms
(fma (* (cbrt g) (cbrt g)) (* (cbrt g) g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
601.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
537.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
462.0ms
(cbrt (* (/ -1/2 (* (cbrt a) (cbrt a))) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
410.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))

prune8.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 30.7b

localize23.0ms

Local error

Found 4 expressions with local error:

30.3b
(sqrt (- (* g g) (* h h)))
30.3b
(sqrt (- (* g g) (* h h)))
2.6b
(- (* g g) (* h h))
2.6b
(- (* g g) (* h h))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
642×add-sqr-sqrt
450×prod-diff
364×*-un-lft-identity
316×add-cube-cbrt
234×swap-sqr
202×associate-*l*
186×associate-*r*
102×*-commutative unswap-sqr
100×difference-of-squares
66×sqrt-prod
30×fma-neg
20×distribute-lft-out--
8×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
Calls
4 calls:
Slowest
78.0ms
(sqrt (- (* g g) (* h h)))
68.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(- (* g g) (* h h))
35.0ms
(- (* g g) (* h h))

series236.0ms

Calls
4 calls:
Slowest
76.0ms
(sqrt (- (* g g) (* h h)))
62.0ms
(- (* g g) (* h h))
50.0ms
(sqrt (- (* g g) (* h h)))
47.0ms
(- (* g g) (* h h))

simplify1.5m

Calls
1122 calls:
Slowest
471.0ms
(fma (* g (sqrt g)) (sqrt g) (- (* (sqrt h) (* h (sqrt h)))))
421.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
420.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
396.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
385.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))

prune12.9s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 30.7b

regimes900.0ms

Accuracy

0% (2.0b remaining)

Error of 31.0b against oracle of 29.0b and baseline of 31.0b

bsearch8.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.0s3774×body320valid
2.0s4077×body160valid
1.9s8134×body80nan
28.0ms149×body80valid