Details

Time bar (total: 20.9s)

sample109.0ms

Algorithm
intervals
Results
37.0ms36×body2560valid
20.0ms197×body80valid
15.0ms28×body1280valid
10.0ms93×body80nan
8.0ms15×body640valid
2.0ms3×body5120valid
2.0ms6×body320valid
0.0ms2×body160valid

simplify189.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize35.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma (* a c) -4 (* b b)))
1.4b
(fma (* a c) -4 (* b b))
0.4b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
23.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
16.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series344.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
85.0ms
(sqrt (fma (* a c) -4 (* b b)))
82.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
56.0ms
(fma (* a c) -4 (* b b))

simplify1.0s

Counts
252 → 252

prune3.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize45.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma -4 (* a c) (* b b)))
1.4b
(fma -4 (* a c) (* b b))
0.4b
(+ b (sqrt (fma -4 (* a c) (* b b))))
0.1b
(* (- (+ b (sqrt (fma -4 (* a c) (* b b))))) (/ 1/2 a))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
13×associate-*r*
12×associate-*l*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×add-log-exp
4×distribute-lft-neg-in expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u distribute-neg-frac
3×fma-def flip3-+ sqrt-prod flip-+ distribute-lft-out
2×frac-times associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×distribute-lft-neg-out cbrt-undiv +-commutative rem-sqrt-square neg-mul-1 sum-log sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
36.0ms
(* (- (+ b (sqrt (fma -4 (* a c) (* b b))))) (/ 1/2 a))
7.0ms
(sqrt (fma -4 (* a c) (* b b)))
5.0ms
(+ b (sqrt (fma -4 (* a c) (* b b))))
0.0ms
(fma -4 (* a c) (* b b))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (fma -4 (* a c) (* b b)))
128.0ms
(* (- (+ b (sqrt (fma -4 (* a c) (* b b))))) (/ 1/2 a))
108.0ms
(+ b (sqrt (fma -4 (* a c) (* b b))))
78.0ms
(fma -4 (* a c) (* b b))

simplify2.1s

Counts
106 → 106

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

localize28.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma -4 (* c a) (* b b)))
1.4b
(fma -4 (* c a) (* b b))
0.4b
(+ (sqrt (fma -4 (* c a) (* b b))) b)
0.1b
(/ (* (+ (sqrt (fma -4 (* c a) (* b b))) b) -1/2) a)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* times-frac
2×cbrt-undiv flip3-+ div-exp associate-*l/ flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv distribute-lft-out associate-/l*
Counts
4 → 74
Calls
4 calls:
Slowest
25.0ms
(/ (* (+ (sqrt (fma -4 (* c a) (* b b))) b) -1/2) a)
11.0ms
(+ (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(+ (sqrt (fma -4 (* c a) (* b b))) b)
85.0ms
(sqrt (fma -4 (* c a) (* b b)))
85.0ms
(/ (* (+ (sqrt (fma -4 (* c a) (* b b))) b) -1/2) a)
63.0ms
(fma -4 (* c a) (* b b))

simplify1.2s

Counts
86 → 86

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize48.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (fma (* -4 c) a (* b b)))
0.4b
(+ (sqrt (fma (* -4 c) a (* b b))) b)
0.3b
(fma (* -4 c) a (* b b))
0.1b
(/ (* (+ (sqrt (fma (* -4 c) a (* b b))) b) -1/2) a)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* times-frac
2×cbrt-undiv flip3-+ div-exp associate-*l/ flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv distribute-lft-out associate-/l*
Counts
4 → 74
Calls
4 calls:
Slowest
28.0ms
(/ (* (+ (sqrt (fma (* -4 c) a (* b b))) b) -1/2) a)
12.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) b)
3.0ms
(sqrt (fma (* -4 c) a (* b b)))
0.0ms
(fma (* -4 c) a (* b b))

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(sqrt (fma (* -4 c) a (* b b)))
128.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) b)
112.0ms
(/ (* (+ (sqrt (fma (* -4 c) a (* b b))) b) -1/2) a)
81.0ms
(fma (* -4 c) a (* b b))

simplify1.8s

Counts
86 → 86

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

regimes456.0ms

Accuracy

85.1% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.6b

bsearch193.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.6s1077×body2560valid
1.2s895×body1280valid
991.0ms5902×body80valid
401.0ms2917×body80nan
331.0ms465×body640valid
137.0ms106×body5120valid
95.0ms229×body320valid
28.0ms96×body160valid