Details

Time bar (total: 7.4m)

sample73.0ms

Algorithm
intervals
Results
18.0ms203×body80valid
13.0ms25×body2560valid
13.0ms30×body1280valid
8.0ms103×body80nan
2.0ms10×body320valid
2.0ms3×body5120valid
1.0ms5×body640valid
0.0ms2×body160valid

simplify114.0ms

Calls
1 calls:
Slowest
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.2b

localize31.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(- (* b b) (* (* 3 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite631.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
330×associate-*l* prod-diff
309×*-un-lft-identity
229×add-cube-cbrt
177×associate-*r*
125×unswap-sqr
75×swap-sqr
65×*-commutative
60×times-frac
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
17×distribute-rgt-neg-in
15×fma-neg
12×associate-/r* distribute-lft-out--
10×fma-def add-log-exp
9×add-cbrt-cube add-exp-log
5×pow1 associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
325.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
128.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
113.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
42.0ms
(- (* b b) (* (* 3 a) c))

series445.0ms

Calls
4 calls:
Slowest
163.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
127.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
102.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
53.0ms
(- (* b b) (* (* 3 a) c))

simplify2.4m

Calls
897 calls:
Slowest
793.0ms
(fma (* (* (cbrt b) (cbrt b)) (* (cbrt b) (cbrt b))) (* (cbrt b) (cbrt b)) (- (* (* (* (sqrt 3) (sqrt a)) c) (* (sqrt 3) (sqrt a)))))
763.0ms
(fma (* b (sqrt b)) (sqrt b) (- (* (* (* (sqrt 3) (sqrt a)) (sqrt c)) (* (* (sqrt 3) (sqrt a)) (sqrt c)))))
573.0ms
(fma b b (- (* (cbrt (* (* 3 a) c)) (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))))))
548.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
547.0ms
(fma (sqrt (* b b)) (sqrt (* b b)) (- (* (* (* (cbrt 3) a) c) (* (cbrt 3) (cbrt 3)))))

prune6.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(- (* b b) (* (* 3 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(* (* 3 a) c)

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
451×add-sqr-sqrt
330×prod-diff
327×associate-*l*
230×*-un-lft-identity
202×add-cube-cbrt
165×associate-*r*
123×unswap-sqr
75×swap-sqr
61×*-commutative
30×difference-of-squares
24×sqrt-prod
15×fma-neg
12×distribute-lft-out--
10×pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down prod-exp cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log neg-log associate-+l- flip-+
Calls
4 calls:
Slowest
105.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
57.0ms
(- (* b b) (* (* 3 a) c))
28.0ms
(* (* 3 a) c)

series291.0ms

Calls
4 calls:
Slowest
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
97.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
61.0ms
(- (* b b) (* (* 3 a) c))
24.0ms
(* (* 3 a) c)

simplify2.2m

Calls
779 calls:
Slowest
677.0ms
(fma (* 1 1) (* b b) (- (* (cbrt (* (* 3 a) c)) (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))))))
616.0ms
(fma (- (* (cbrt (* 3 a)) c)) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (* (cbrt (* 3 a)) c) (* (cbrt (* 3 a)) (cbrt (* 3 a)))))
562.0ms
(fma (* b 1) b (- (* (* (* 3 a) c) 1)))
514.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
507.0ms
(fma (- (* (* (sqrt 3) (sqrt a)) (sqrt c))) (* (* (sqrt 3) (sqrt a)) (sqrt c)) (* (* (* (sqrt 3) (sqrt a)) (sqrt c)) (* (* (sqrt 3) (sqrt a)) (sqrt c))))

prune6.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize33.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b b) (* a (* 3 c))))
1.2b
(- (* b b) (* a (* 3 c)))
0.7b
(+ (- b) (sqrt (- (* b b) (* a (* 3 c)))))
0.2b
(* a (* 3 c))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
451×add-sqr-sqrt
330×prod-diff
309×associate-*r*
222×*-un-lft-identity
202×add-cube-cbrt
173×associate-*l*
123×unswap-sqr
75×swap-sqr
61×*-commutative
30×difference-of-squares
22×sqrt-prod
15×fma-neg
10×pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log
8×distribute-lft-out--
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down prod-exp cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log neg-log associate-+l- flip-+
Calls
4 calls:
Slowest
98.0ms
(sqrt (- (* b b) (* a (* 3 c))))
84.0ms
(+ (- b) (sqrt (- (* b b) (* a (* 3 c)))))
50.0ms
(- (* b b) (* a (* 3 c)))
29.0ms
(* a (* 3 c))

series307.0ms

Calls
4 calls:
Slowest
112.0ms
(+ (- b) (sqrt (- (* b b) (* a (* 3 c)))))
98.0ms
(sqrt (- (* b b) (* a (* 3 c))))
62.0ms
(- (* b b) (* a (* 3 c)))
34.0ms
(* a (* 3 c))

simplify2.2m

Calls
776 calls:
Slowest
816.0ms
(fma (- (cbrt c)) (* a (* 3 (* (cbrt c) (cbrt c)))) (* (cbrt c) (* a (* 3 (* (cbrt c) (cbrt c))))))
803.0ms
(fma b b (- (* (* (sqrt 3) (sqrt c)) (* a (* (sqrt 3) (sqrt c))))))
750.0ms
(fma (* (* (cbrt b) (cbrt b)) (* (cbrt b) (cbrt b))) (* (cbrt b) (cbrt b)) (- (* (cbrt c) (* a (* 3 (* (cbrt c) (cbrt c)))))))
492.0ms
(fma (sqrt (* b b)) (sqrt (* b b)) (- (* (* (cbrt a) (* 3 c)) (* (cbrt a) (cbrt a)))))
474.0ms
(fma b b (- (* (* (cbrt a) (* 3 c)) (* (cbrt a) (cbrt a)))))

prune5.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize34.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (fma (* a c) -3 (* b b)))
1.3b
(fma (* a c) -3 (* b b))
0.7b
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
0.2b
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
60×times-frac
52×add-sqr-sqrt
39×add-cube-cbrt
28×distribute-lft-out
18×associate-*r* associate-*l*
17×distribute-rgt-neg-in
12×associate-/r*
10×fma-def
9×add-cbrt-cube add-exp-log
8×add-log-exp
6×*-commutative unswap-sqr
5×pow1 associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ div-exp associate-+l- flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num neg-mul-1 frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod fma-udef div-inv
Calls
4 calls:
Slowest
30.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
8.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
2.0ms
(sqrt (fma (* a c) -3 (* b b)))
0.0ms
(fma (* a c) -3 (* b b))

series476.0ms

Calls
4 calls:
Slowest
153.0ms
(/ (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (* 3 a))
119.0ms
(+ (- b) (sqrt (fma (* a c) -3 (* b b))))
118.0ms
(sqrt (fma (* a c) -3 (* b b)))
86.0ms
(fma (* a c) -3 (* b b))

simplify10.2s

Calls
166 calls:
Slowest
362.0ms
(+ (pow (- b) 3) (pow (sqrt (fma (* a c) -3 (* b b))) 3))
356.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -3 (* b b))) (sqrt (fma (* a c) -3 (* b b)))))
287.0ms
(/ (* (* (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
240.0ms
(/ (* (* (+ (- b) (sqrt (fma (* a c) -3 (* b b)))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (* (* (* 3 3) 3) (* (* a a) a)))
201.0ms
(/ (* (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b))))) (cbrt (+ (- b) (sqrt (fma (* a c) -3 (* b b)))))) (* 3 (* (cbrt a) (cbrt a))))

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes523.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.4b against oracle of 5.5b and baseline of 33.0b

bsearch545.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.4s1019×body2560valid
1.0s5985×body80valid
712.0ms906×body1280valid
476.0ms2872×body80nan
231.0ms434×body640valid
104.0ms114×body5120valid
72.0ms214×body320valid
27.0ms115×body160valid