Details

Time bar (total: 27.5s)

sample115.0ms

Algorithm
intervals
Results
66.0ms279×body80valid
21.0ms89×body80nan

simplify240.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize143.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (sqrt (fma c (* a -4) (* b b))) b)
1.4b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))

rewrite36.0ms

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:
15.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
13.0ms
(- (- 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)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
104.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
109.0ms
(sqrt (fma c (* a -4) (* b b)))
141.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.0s

Counts
177 → 177
Iterations
IterNodes
32234
2875
1417
0194

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize189.0ms

Local error

Found 4 expressions with local error:

14.1b
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))

rewrite26.0ms

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:
17.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (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)))
3.0ms
(sqrt (fma c (* a -4) (* b b)))

series481.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
132.0ms
(sqrt (fma c (* a -4) (* b b)))
131.0ms
(sqrt (fma c (* a -4) (* b b)))
120.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.5s

Counts
98 → 98
Iterations
IterNodes
44031
31361
2481
1207
097

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.5b

localize210.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
10.4b
(fma 1 (sqrt (fma c (* a -4) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))

rewrite24.0ms

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:
20.0ms
(- (- 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)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
170.0ms
(fma 1 (sqrt (fma c (* a -4) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
115.0ms
(sqrt (fma c (* a -4) (* b b)))
105.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify4.1s

Counts
146 → 146
Iterations
IterNodes
46090
31735
2661
1341
0163

prune2.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 16.3b

localize175.0ms

Local error

Found 4 expressions with local error:

26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))
26.8b
(sqrt (fma c (* a -4) (* b b)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 64
Calls
4 calls:
1.0ms
(sqrt (fma c (* a -4) (* b b)))
1.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))
2.0ms
(sqrt (fma c (* a -4) (* b b)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(sqrt (fma c (* a -4) (* b b)))
125.0ms
(sqrt (fma c (* a -4) (* b b)))
110.0ms
(sqrt (fma c (* a -4) (* b b)))
91.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify5.9s

Counts
76 → 76
Iterations
IterNodes
106396
91432
8579
7291
6197
5159
4132
387
251
136
028

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 16.2b

regimes394.0ms

Accuracy

84.9% (1.1b remaining)

Error of 13.5b against oracle of 12.4b and baseline of 19.5b

bsearch167.0ms

Steps
ItersRangePoint
9
2.662790715355376e+61
3.00977400694497e+66
8.748494799376129e+63

simplify9.0ms

Iterations
IterNodes
229
129
027

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.7s8711×body80valid
457.0ms2970×body80nan