Details

Time bar (total: 25.4s)

sample111.0ms

Algorithm
intervals
Results
74.0ms279×body80valid
16.0ms91×body80nan

simplify140.0ms

Counts
1 → 1
Iterations
IterNodes
8160
7160
6159
5152
4140
3108
263
136
020

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize147.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.3b
(- (sqrt (fma -4 (* c a) (* b b))) b)
21.9b
(sqrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))

rewrite26.0ms

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:
11.0ms
(- (- b) (sqrt (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)))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
110.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
109.0ms
(sqrt (fma -4 (* c a) (* b b)))
122.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts
177 → 177
Iterations
IterNodes
32192
2837
1415
0194

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize183.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* 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 -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))

series870.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(sqrt (fma -4 (* c a) (* b b)))
287.0ms
(cbrt (fma -4 (* c a) (* b b)))
247.0ms
(cbrt (fma -4 (* c a) (* b b)))
234.0ms
(cbrt (fma -4 (* c a) (* b b)))

simplify3.4s

Counts
70 → 70
Iterations
IterNodes
56385
41989
3676
2257
1121
068

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.5b

localize225.0ms

Local error

Found 4 expressions with local error:

22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.8b
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
0.0ms
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
242.0ms
(cbrt (fma -4 (* c a) (* b b)))
201.0ms
(cbrt (fma -4 (* c a) (* b b)))
223.0ms
(cbrt (fma -4 (* c a) (* b b)))
642.0ms
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (cbrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

simplify1.8s

Counts
65 → 65
Iterations
IterNodes
43693
31023
2342
1154
080

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.5b

localize208.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.7b
(cbrt (fma -4 (* c a) (* b b)))
22.8b
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×cbrt-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 55
Calls
4 calls:
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
0.0ms
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (fma -4 (* c a) (* b b)))
271.0ms
(cbrt (fma -4 (* c a) (* b b)))
286.0ms
(cbrt (fma -4 (* c a) (* b b)))
590.0ms
(fma (sqrt (* (cbrt (fma -4 (* c a) (* b b))) (cbrt (fma -4 (* c a) (* b b))))) (sqrt (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b)))))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

simplify1.7s

Counts
67 → 67
Iterations
IterNodes
43818
31075
2368
1173
095

prune1.8s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.5b

regimes639.0ms

Accuracy

90.8% (0.7b remaining)

Error of 12.9b against oracle of 12.2b and baseline of 19.4b

bsearch185.0ms

Steps
ItersRangePoint
9
1.7155709022758137e+74
7.648947555279674e+80
2.8082964050636793e+75

simplify7.0ms

Iterations
IterNodes
238
138
033

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.1s8775×body80valid
569.0ms2919×body80nan