Details

Time bar (total: 23.1s)

sample83.0ms

Algorithm
intervals
Results
42.0ms282×body80valid
11.0ms107×body80nan

simplify200.0ms

Counts
1 → 1
Iterations
IterNodes
done170
7170
6168
5164
4157
3134
275
139
020

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize159.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 151
Calls
4 calls:
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
163 → 163
Iterations
IterNodes
done5000
34518
21209
1431
0179

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize201.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
13×add-sqr-sqrt
10×fma-def add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube add-exp-log log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log distribute-lft-out
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 78
Calls
4 calls:
24.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts
90 → 90
Iterations
IterNodes
done5001
32991
2749
1233
087

prune945.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize375.0ms

Local error

Found 4 expressions with local error:

21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
62.1b
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
1.0ms
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
141.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
237.0ms
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

simplify2.2s

Counts
67 → 67
Iterations
IterNodes
done5001
32177
2590
1203
089

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize356.0ms

Local error

Found 4 expressions with local error:

21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.4b
(cbrt (- (* b b) (* (* 4.0 a) c)))
61.9b
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (* (cbrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
1×fma-udef
Counts
4 → 55
Calls
4 calls:
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
0.0ms
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (* (cbrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
125.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
283.0ms
(fma (- (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (sqrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (* (* (cbrt (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (cbrt (- (* b b) (* (* 4.0 a) c)))))))

simplify2.1s

Counts
67 → 67
Iterations
IterNodes
done5001
32184
2604
1211
092

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

regimes452.0ms

Accuracy

92.1% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 19.9b

bsearch283.0ms

Steps
ItersRangePoint
6
4.2942163002471454e+116
2.920461936675284e+117
2.4732339682798126e+117
10
-8.897020078895062e+156
-1.101416214509623e+146
-4.073691083157782e+153

simplify31.0ms

Iterations
IterNodes
done75
275
173
057

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s8756×body80valid
296.0ms2911×body80nan