Details

Time bar (total: 23.5s)

sample107.0ms

Algorithm
intervals
Results
49.0ms283×body80valid
16.0ms108×body80nan

simplify191.0ms

Counts
1 → 1
Iterations
IterNodes
8170
7170
6168
5164
4157
3132
276
139
020

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.0b

localize148.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (fma c (* a -4) (* b b))) b)
1.1b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
23.2b
(sqrt (fma c (* a -4) (* b b)))
23.2b
(sqrt (fma c (* a -4) (* b b)))

rewrite48.0ms

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 c (* a -4) (* b b))) b)
21.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
3.0ms
(sqrt (fma c (* a -4) (* b b)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series499.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
130.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
111.0ms
(sqrt (fma c (* a -4) (* b b)))
134.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts
177 → 177
Iterations
IterNodes
32234
2875
1417
0194

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.2b

localize175.0ms

Local error

Found 4 expressions with local error:

13.8b
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
23.2b
(sqrt (fma c (* a -4) (* b b)))
23.2b
(sqrt (fma c (* a -4) (* b b)))
23.2b
(sqrt (fma c (* a -4) (* b b)))

rewrite9.0ms

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))
2.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series712.0ms

Counts
4 → 12
Calls
4 calls:
401.0ms
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
91.0ms
(sqrt (fma c (* a -4) (* b b)))
106.0ms
(sqrt (fma c (* a -4) (* b b)))
113.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Counts
71 → 71
Iterations
IterNodes
42376
3684
2236
1111
065

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.2b

localize128.0ms

Local error

Found 4 expressions with local error:

11.3b
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
23.2b
(sqrt (fma c (* a -4) (* b b)))
23.2b
(sqrt (fma c (* a -4) (* b b)))
23.2b
(sqrt (fma c (* a -4) (* b b)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
10.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (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)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
129.0ms
(sqrt (fma c (* a -4) (* b b)))
126.0ms
(sqrt (fma c (* a -4) (* b b)))
83.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.8s

Counts
98 → 98
Iterations
IterNodes
44031
31361
2481
1207
097

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.2b

localize138.0ms

Local error

Found 4 expressions with local error:

23.2b
(sqrt (fma c (* a -4) (* b b)))
23.9b
(cbrt (fma c (* a -4) (* b b)))
23.9b
(cbrt (fma c (* a -4) (* b b)))
23.9b
(cbrt (fma c (* a -4) (* b b)))

rewrite8.0ms

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:
2.0ms
(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)))
2.0ms
(cbrt (fma c (* a -4) (* b b)))

series821.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (fma c (* a -4) (* b b)))
243.0ms
(cbrt (fma c (* a -4) (* b b)))
244.0ms
(cbrt (fma c (* a -4) (* b b)))
229.0ms
(cbrt (fma c (* a -4) (* b b)))

simplify3.2s

Counts
70 → 70
Iterations
IterNodes
56476
41995
3662
2255
1123
068

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 14.2b

regimes463.0ms

Accuracy

85.4% (0.9b remaining)

Error of 13.6b against oracle of 12.6b and baseline of 19.0b

bsearch227.0ms

Steps
ItersRangePoint
9
1.9710174875302874e+32
1.945305249879839e+37
1.9280516389664611e+37

simplify13.0ms

Iterations
IterNodes
235
135
032

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.4s8739×body80valid
521.0ms2881×body80nan