Details

Time bar (total: 20.6s)

sample112.0ms

Algorithm
intervals
Results
67.0ms288×body80valid
19.0ms87×body80nan

simplify199.0ms

Counts
1 → 1
Iterations
IterNodes
done170
7170
6168
5164
4157
3132
276
139
020

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize129.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (fma c (* a -4) (* b b))) b)
1.0b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
24.3b
(sqrt (fma c (* a -4) (* b b)))
24.3b
(sqrt (fma c (* a -4) (* b b)))

rewrite25.0ms

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:
8.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
12.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
125.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
121.0ms
(sqrt (fma c (* a -4) (* b b)))
97.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.8s

Counts
177 → 177
Iterations
IterNodes
done5014
33014
2995
1426
0194

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize181.0ms

Local error

Found 4 expressions with local error:

15.7b
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
24.3b
(sqrt (fma c (* a -4) (* b b)))
24.3b
(sqrt (fma c (* a -4) (* b b)))
24.3b
(sqrt (fma c (* a -4) (* b b)))

rewrite5.0ms

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 c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series750.0ms

Counts
4 → 12
Calls
4 calls:
419.0ms
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
98.0ms
(sqrt (fma c (* a -4) (* b b)))
129.0ms
(sqrt (fma c (* a -4) (* b b)))
104.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.9s

Counts
71 → 71
Iterations
IterNodes
done5002
42885
3715
2243
1112
065

prune710.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.8b

localize183.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
11.4b
(fma 1 (sqrt (fma c (* a -4) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
24.3b
(sqrt (fma c (* a -4) (* b b)))
24.3b
(sqrt (fma c (* a -4) (* b b)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Counts
4 → 134
Calls
4 calls:
11.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
0.0ms
(fma 1 (sqrt (fma c (* a -4) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
118.0ms
(fma 1 (sqrt (fma c (* a -4) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
114.0ms
(sqrt (fma c (* a -4) (* b b)))
124.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.6s

Counts
146 → 146
Iterations
IterNodes
done5001
32024
2707
1342
0163

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

localize176.0ms

Local error

Found 4 expressions with local error:

24.3b
(sqrt (fma c (* a -4) (* b b)))
25.1b
(cbrt (fma c (* a -4) (* b b)))
25.1b
(cbrt (fma c (* a -4) (* b b)))
25.1b
(cbrt (fma c (* a -4) (* b b)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))
1.0ms
(cbrt (fma c (* a -4) (* b b)))

series927.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(sqrt (fma c (* a -4) (* b b)))
245.0ms
(cbrt (fma c (* a -4) (* b b)))
273.0ms
(cbrt (fma c (* a -4) (* b b)))
272.0ms
(cbrt (fma c (* a -4) (* b b)))

simplify2.1s

Counts
70 → 70
Iterations
IterNodes
done5019
43363
3861
2279
1124
068

prune643.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.7b

regimes445.0ms

Accuracy

85.4% (1.1b remaining)

Error of 13.4b against oracle of 12.3b and baseline of 19.8b

bsearch118.0ms

Steps
ItersRangePoint
9
6.2301214455520334e+75
1.9082112581546424e+85
1.6691257204922504e+85

simplify7.0ms

Iterations
IterNodes
done31
131
029

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.1s8705×body80valid
490.0ms2845×body80nan