Details

Time bar (total: 2.0m)

sample100.0ms

Algorithm
intervals
Results
46.0ms279×body80valid
31.0ms86×body80nan

simplify173.0ms

Counts
1 → 1
Iterations
IterNodes
8160
7160
6159
5152
4140
3108
263
136
020

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize127.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.7b
(- (sqrt (fma -4 (* c a) (* b b))) b)
24.6b
(sqrt (fma -4 (* c a) (* b b)))
24.6b
(sqrt (fma -4 (* c a) (* b b)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
10.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
7.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
5.0ms
(sqrt (fma -4 (* c a) (* b b)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
108.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
132.0ms
(sqrt (fma -4 (* c a) (* b b)))
145.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.0s

Counts
177 → 177
Iterations
IterNodes
32192
2837
1415
0194

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize198.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma -4 (* c a) (* b b))) b)
3.3b
(/ (* 2 c) (* 2 (- (* c (/ a b)) b)))
4.3b
(* c (/ a b))
24.6b
(sqrt (fma -4 (* c a) (* b b)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
21×add-cbrt-cube add-exp-log
18×prod-diff
16×sqrt-prod
13×associate-*r*
11×times-frac
7×pow1
6×fma-neg prod-exp cbrt-unprod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*l* associate-*r/
2×flip3-- associate-/r/ div-inv flip-- difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative associate-/l* distribute-lft-out--
Counts
4 → 119
Calls
4 calls:
15.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
41.0ms
(/ (* 2 c) (* 2 (- (* c (/ a b)) b)))
24.0ms
(* c (/ a b))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
59.0ms
(/ (* 2 c) (* 2 (- (* c (/ a b)) b)))
20.0ms
(* c (/ a b))
124.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify55.9s

Counts
131 → 131
Iterations
IterNodes
310772
21795
1486
0202

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize154.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.8b
(* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b)))
3.3b
(/ (* 2 c) (* 2 (- (* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b))) b)))
24.6b
(sqrt (fma -4 (* c a) (* b b)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
303×times-frac
246×add-sqr-sqrt
157×*-un-lft-identity
155×add-cube-cbrt
151×cbrt-prod
136×associate-*l*
37×add-exp-log
28×add-cbrt-cube
22×associate-*r*
21×unswap-sqr
18×prod-diff
16×sqrt-prod
13×cbrt-undiv div-exp
10×prod-exp cbrt-unprod
9×div-inv
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r/
2×flip3-- associate-/r/ flip-- difference-of-squares
1×frac-times rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*l/ *-commutative associate-/l* distribute-lft-out--
Counts
4 → 290
Calls
4 calls:
15.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
30.0ms
(* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b)))
30.0ms
(/ (* 2 c) (* 2 (- (* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b))) b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series580.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
81.0ms
(* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b)))
255.0ms
(/ (* 2 c) (* 2 (- (* (/ (/ c (cbrt b)) (cbrt b)) (/ a (cbrt b))) b)))
119.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.8s

Counts
302 → 302
Iterations
IterNodes
24232
11213
0404

prune5.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize162.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
1.2b
(/ (* 2 c) (* 2 (- (* (* c (/ (* (cbrt a) (cbrt a)) (sqrt b))) (/ (cbrt a) (sqrt b))) b)))
1.7b
(- (sqrt (fma -4 (* c a) (* b b))) b)
24.6b
(sqrt (fma -4 (* c a) (* b b)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×add-cbrt-cube add-exp-log sqrt-prod
6×fma-neg add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×cbrt-prod
2×flip3-- associate-*r/ associate-/r/ flip-- difference-of-squares
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 times-frac pow1/2 pow1/3 diff-log div-inv associate-/l* distribute-lft-out--
Counts
4 → 98
Calls
4 calls:
1.0ms
(cbrt a)
68.0ms
(/ (* 2 c) (* 2 (- (* (* c (/ (* (cbrt a) (cbrt a)) (sqrt b))) (/ (cbrt a) (sqrt b))) b)))
7.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(cbrt a)
195.0ms
(/ (* 2 c) (* 2 (- (* (* c (/ (* (cbrt a) (cbrt a)) (sqrt b))) (/ (cbrt a) (sqrt b))) b)))
102.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
118.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify42.6s

Counts
110 → 110
Iterations
IterNodes
39993
21691
1460
0188

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

regimes390.0ms

Accuracy

92% (0.7b remaining)

Error of 12.6b against oracle of 12.0b and baseline of 20.3b

bsearch169.0ms

Steps
ItersRangePoint
8
6.45623811977989e+97
1.5556153764929518e+101
3.0416169482605103e+99

simplify20.0ms

Iterations
IterNodes
254
154
045

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.3s8764×body80valid
531.0ms2976×body80nan