Details

Time bar (total: 50.4s)

sample105.0ms

Algorithm
intervals
Results
62.0ms284×body80valid
19.0ms91×body80nan

simplify222.0ms

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: 24.0b

localize165.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.6b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
27.8b
(sqrt (fma -4 (* c a) (* b b)))
27.8b
(sqrt (fma -4 (* c a) (* b b)))

rewrite47.0ms

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:
16.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
22.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
141.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
135.0ms
(sqrt (fma -4 (* c a) (* b b)))
157.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts
177 → 177
Iterations
IterNodes
32261
2875
1415
0194

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.2b

localize161.0ms

Local error

Found 4 expressions with local error:

20.8b
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
27.8b
(sqrt (fma -4 (* c a) (* b b)))
27.8b
(sqrt (fma -4 (* c a) (* b b)))
27.8b
(sqrt (fma -4 (* c a) (* b b)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×fma-udef
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))

series789.0ms

Counts
4 → 12
Calls
4 calls:
459.0ms
(fma (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
114.0ms
(sqrt (fma -4 (* c a) (* b b)))
118.0ms
(sqrt (fma -4 (* c a) (* b b)))
98.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts
71 → 71
Iterations
IterNodes
42649
3738
2247
1122
068

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.2b

localize148.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
1.2b
(fma -4 (* c a) (* b b))
1.3b
(- (sqrt (fma -4 (* c a) (* b b))) b)
27.8b
(sqrt (fma -4 (* c a) (* b b)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
31.0ms
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
0.0ms
(fma -4 (* c a) (* b b))
8.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
66.0ms
(fma -4 (* c a) (* b b))
109.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
91.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify2.1s

Counts
191 → 191
Iterations
IterNodes
34330
21409
1599
0278

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 17.2b

localize171.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2)))
1.2b
(fma -4 (* c a) (* b b))
1.3b
(- (sqrt (fma -4 (* c a) (* b b))) b)
27.8b
(sqrt (fma -4 (* c a) (* b b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
18×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
6×pow1 cbrt-undiv fma-neg add-log-exp
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 384
Calls
4 calls:
16.0ms
(/ 1 (/ a (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2)))
0.0ms
(fma -4 (* c a) (* b b))
8.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ 1 (/ a (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2)))
66.0ms
(fma -4 (* c a) (* b b))
112.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
128.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify28.1s

Counts
396 → 396
Iterations
IterNodes
24337
11521
0579

prune4.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 17.2b

regimes499.0ms

Accuracy

85.8% (1.0b remaining)

Error of 13.6b against oracle of 12.6b and baseline of 19.5b

bsearch213.0ms

Steps
ItersRangePoint
9
2.662790715355376e+61
3.00977400694497e+66
4.965076354638055e+62

simplify25.0ms

Iterations
IterNodes
348
248
146
038

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.0s8749×body80valid
556.0ms2993×body80nan