Details

Time bar (total: 20.1s)

sample79.0ms

Algorithm
intervals
Results
36.0ms273×body80valid
13.0ms97×body80nan

simplify213.0ms

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.0b

localize146.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
1.6b
(- (sqrt (fma c (* a -4) (* b b))) b)
23.1b
(sqrt (fma c (* a -4) (* b b)))
23.1b
(sqrt (fma c (* a -4) (* b b)))

rewrite40.0ms

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:
18.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
13.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
111.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
112.0ms
(sqrt (fma c (* a -4) (* b b)))
102.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.5s

Counts
177 → 177
Iterations
IterNodes
done5000
33147
2965
1427
0194

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.7b

localize169.0ms

Local error

Found 4 expressions with local error:

17.9b
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
23.1b
(sqrt (fma c (* a -4) (* b b)))
23.1b
(sqrt (fma c (* a -4) (* b b)))
23.1b
(sqrt (fma c (* a -4) (* b b)))

rewrite12.0ms

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

series1.2s

Counts
4 → 12
Calls
4 calls:
834.0ms
(fma (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b)))) (- b))
112.0ms
(sqrt (fma c (* a -4) (* b b)))
136.0ms
(sqrt (fma c (* a -4) (* b b)))
126.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.0s

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

prune503.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

localize181.0ms

Local error

Found 4 expressions with local error:

9.2b
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
23.1b
(sqrt (fma c (* a -4) (* b b)))
23.1b
(sqrt (fma c (* a -4) (* b b)))
23.1b
(sqrt (fma c (* a -4) (* b b)))

rewrite49.0ms

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:
37.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (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)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
82.0ms
(sqrt (fma c (* a -4) (* b b)))
99.0ms
(sqrt (fma c (* a -4) (* b b)))
112.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify3.6s

Counts
98 → 98
Iterations
IterNodes
done5000
44877
31417
2512
1209
097

prune863.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.4b

localize170.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (fma c (* a -4) (* b b)))
23.8b
(cbrt (fma c (* a -4) (* b b)))
23.8b
(cbrt (fma c (* a -4) (* b b)))
23.8b
(cbrt (fma c (* a -4) (* b b)))

rewrite9.0ms

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

series905.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(sqrt (fma c (* a -4) (* b b)))
276.0ms
(cbrt (fma c (* a -4) (* b b)))
245.0ms
(cbrt (fma c (* a -4) (* b b)))
249.0ms
(cbrt (fma c (* a -4) (* b b)))

simplify2.0s

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

prune594.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.4b

regimes351.0ms

Accuracy

82.5% (1.2b remaining)

Error of 13.3b against oracle of 12.0b and baseline of 19.1b

bsearch135.0ms

Steps
ItersRangePoint
8
2.5230591910300896e+45
6.095379443414697e+48
4.7476977383731215e+48

simplify13.0ms

Iterations
IterNodes
done35
135
032

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.5s8736×body80valid
283.0ms3069×body80nan