Details

Time bar (total: 2.9m)

sample139.0ms

Algorithm
intervals
Results
52.0ms116×body320valid
36.0ms137×body160valid
34.0ms273×body80nan
0.0ms3×body80valid

simplify346.0ms

Calls
1 calls:
Slowest
346.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize76.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
9.3b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
6.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))

rewrite625.0ms

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
289.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
182.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
76.0ms
(sqrt (- (* g g) (* h h)))
70.0ms
(sqrt (- (* g g) (* h h)))

series924.0ms

Calls
4 calls:
Slowest
464.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
333.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
71.0ms
(sqrt (- (* g g) (* h h)))
57.0ms
(sqrt (- (* g g) (* h h)))

simplify27.6s

Calls
238 calls:
Slowest
631.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
609.0ms
(cbrt (/ (+ (sqrt (sqrt (- (* g g) (* h h)))) (sqrt g)) (sqrt a)))
538.0ms
(cbrt (* 1 (- (* g g) (* (sqrt (- (* g g) (* h h))) (sqrt (- (* g g) (* h h)))))))
520.0ms
(cbrt (* (/ -1/2 (* (cbrt a) (cbrt a))) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
423.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))

prune4.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 29.3b

localize37.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
6.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
1.4b
(+ g (sqrt (- (* g g) (* h h))))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
210×add-sqr-sqrt
94×*-un-lft-identity
79×sqrt-prod
76×cbrt-prod difference-of-squares
72×times-frac
42×add-cube-cbrt
29×associate-*l*
27×*-commutative unswap-sqr
24×swap-sqr
23×cbrt-div distribute-lft-out--
21×associate-*r*
12×associate-/r*
6×pow1 associate-/l* add-log-exp
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×fma-def flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×+-commutative clear-num sum-log frac-2neg flip3-+ pow1/3 flip-+ div-inv distribute-lft-out
Calls
4 calls:
Slowest
141.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
77.0ms
(+ g (sqrt (- (* g g) (* h h))))
60.0ms
(sqrt (- (* g g) (* h h)))
42.0ms
(sqrt (- (* g g) (* h h)))

series539.0ms

Calls
4 calls:
Slowest
314.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
99.0ms
(+ g (sqrt (- (* g g) (* h h))))
71.0ms
(sqrt (- (* g g) (* h h)))
53.0ms
(sqrt (- (* g g) (* h h)))

simplify17.6s

Calls
189 calls:
Slowest
399.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
345.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
343.0ms
(cbrt (/ (* (cbrt (- (sqrt (- (* g g) (* h h))) g)) (cbrt (- (sqrt (- (* g g) (* h h))) g))) (* a (* (cbrt 2) (cbrt 2)))))
340.0ms
(cbrt (- (pow (sqrt (- (* g g) (* h h))) 3) (pow g 3)))
340.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune4.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.5b

localize52.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
1.4b
(+ g (sqrt (- (* g g) (* h h))))
1.4b
(- (* g g) (* h h))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
376×add-sqr-sqrt
225×prod-diff
200×*-un-lft-identity
162×add-cube-cbrt
129×swap-sqr
105×associate-*l*
93×associate-*r*
75×difference-of-squares
66×sqrt-prod
61×*-commutative unswap-sqr
15×fma-neg distribute-lft-out--
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×fma-def flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sub-neg flip3-+ diff-log flip-+ distribute-lft-out
Calls
4 calls:
Slowest
77.0ms
(+ g (sqrt (- (* g g) (* h h))))
65.0ms
(sqrt (- (* g g) (* h h)))
56.0ms
(- (* g g) (* h h))
50.0ms
(sqrt (- (* g g) (* h h)))

series278.0ms

Calls
4 calls:
Slowest
86.0ms
(sqrt (- (* g g) (* h h)))
73.0ms
(+ g (sqrt (- (* g g) (* h h))))
64.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(- (* g g) (* h h))

simplify44.6s

Calls
608 calls:
Slowest
699.0ms
(fma (* (* (cbrt g) (cbrt g)) (* (cbrt g) (cbrt g))) (* (cbrt g) (cbrt g)) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
417.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
367.0ms
(fma (* g 1) g (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
348.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
336.0ms
(fma (sqrt (* g g)) (sqrt (* g g)) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))

prune7.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.5b

localize59.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
1.4b
(+ g (sqrt (- (* g g) (* h h))))
1.4b
(- (* g g) (* h h))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
376×add-sqr-sqrt
225×prod-diff
200×*-un-lft-identity
162×add-cube-cbrt
129×swap-sqr
105×associate-*l*
93×associate-*r*
75×difference-of-squares
66×sqrt-prod
61×*-commutative unswap-sqr
15×fma-neg distribute-lft-out--
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×fma-def flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log sub-neg flip3-+ diff-log flip-+ distribute-lft-out
Calls
4 calls:
Slowest
79.0ms
(+ g (sqrt (- (* g g) (* h h))))
56.0ms
(sqrt (- (* g g) (* h h)))
46.0ms
(sqrt (- (* g g) (* h h)))
32.0ms
(- (* g g) (* h h))

series267.0ms

Calls
4 calls:
Slowest
80.0ms
(+ g (sqrt (- (* g g) (* h h))))
70.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(- (* g g) (* h h))
58.0ms
(sqrt (- (* g g) (* h h)))

simplify46.4s

Calls
608 calls:
Slowest
698.0ms
(fma (* (sqrt g) (sqrt g)) (* (sqrt g) (sqrt g)) (- (* (cbrt (* h h)) (* (cbrt (* h h)) (cbrt (* h h))))))
398.0ms
(fma 1 (* g g) (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))
391.0ms
(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))))))
363.0ms
(fma (* g 1) g (- (* (* (cbrt h) (cbrt h)) (* (* (cbrt h) (cbrt h)) (* (cbrt h) (cbrt h))))))

prune7.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.5b

regimes774.0ms

Accuracy

45.3% (1.4b remaining)

Error of 31.2b against oracle of 29.8b and baseline of 32.3b

bsearch323.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
2.7s3690×body320valid
2.5s4142×body160valid
2.0s7864×body80nan
33.0ms168×body80valid