Details

Time bar (total: 25.6s)

sample110.0ms

Algorithm
intervals
Results
65.0ms273×body80valid
17.0ms81×body80nan

simplify230.0ms

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize179.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (fma c (* a -4) (* b b))))
2.7b
(- (sqrt (fma c (* a -4) (* b b))) b)
23.5b
(sqrt (fma c (* a -4) (* b b)))
23.5b
(sqrt (fma c (* a -4) (* b b)))

rewrite60.0ms

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:
21.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
17.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms
(sqrt (fma c (* a -4) (* b b)))
14.0ms
(sqrt (fma c (* a -4) (* b b)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (- b) (sqrt (fma c (* a -4) (* b b))))
111.0ms
(- (sqrt (fma c (* a -4) (* b b))) b)
107.0ms
(sqrt (fma c (* a -4) (* b b)))
151.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify1.0s

Counts
177 → 177
Iterations
IterNodes
32244
2813
1418
0194

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize145.0ms

Local error

Found 4 expressions with local error:

12.3b
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
23.5b
(sqrt (fma c (* a -4) (* b b)))
23.5b
(sqrt (fma c (* a -4) (* b b)))
23.5b
(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:
9.0ms
(- (- 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)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (* (sqrt (sqrt (fma c (* a -4) (* b b)))) (sqrt (sqrt (fma c (* a -4) (* b b))))))
128.0ms
(sqrt (fma c (* a -4) (* b b)))
109.0ms
(sqrt (fma c (* a -4) (* b b)))
102.0ms
(sqrt (fma c (* a -4) (* b b)))

simplify2.4s

Counts
98 → 98
Iterations
IterNodes
44259
31384
2489
1209
097

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize199.0ms

Local error

Found 4 expressions with local error:

23.5b
(sqrt (fma c (* a -4) (* b b)))
24.3b
(cbrt (fma c (* a -4) (* b b)))
24.3b
(cbrt (fma c (* a -4) (* b b)))
24.3b
(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)))

series807.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (fma c (* a -4) (* b b)))
245.0ms
(cbrt (fma c (* a -4) (* b b)))
201.0ms
(cbrt (fma c (* a -4) (* b b)))
266.0ms
(cbrt (fma c (* a -4) (* b b)))

simplify3.3s

Counts
70 → 70
Iterations
IterNodes
56441
41992
3663
2256
1124
068

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.5b

localize195.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×pow3 rem-cbrt-cube
Counts
4 → 55
Calls
4 calls:
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)))
36.0ms
(cbrt (* (* (cbrt (fma c (* a -4) (* b b))) (cbrt (fma c (* a -4) (* b b)))) (cbrt (fma c (* a -4) (* b b)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
296.0ms
(cbrt (fma c (* a -4) (* b b)))
256.0ms
(cbrt (fma c (* a -4) (* b b)))
259.0ms
(cbrt (fma c (* a -4) (* b b)))
236.0ms
(cbrt (* (* (cbrt (fma c (* a -4) (* b b))) (cbrt (fma c (* a -4) (* b b)))) (cbrt (fma c (* a -4) (* b b)))))

simplify3.0s

Counts
67 → 67
Iterations
IterNodes
56503
41901
3627
2242
1117
064

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.5b

regimes432.0ms

Accuracy

92% (0.5b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 19.9b

bsearch109.0ms

Steps
ItersRangePoint
6
1.890398075878753e+149
8.723340275486535e+149
1.9081232567651569e+149

simplify23.0ms

Iterations
IterNodes
244
144
038

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.9s8740×body80valid
893.0ms2863×body80nan