Details

Time bar (total: 15.1s)

sample104.0ms

Algorithm
intervals
Results
36.0ms190×body80valid
19.0ms31×body2560valid
15.0ms31×body1280valid
8.0ms84×body80nan
5.0ms13×body640valid
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms5×body160valid

simplify140.0ms

Counts
1 → 1
Iterations
IterNodes
done142
7142
6140
5135
4130
3110
263
129
014

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* -4 a) c (* b b))
0.1b
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
1.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.4b
(sqrt (fma (* -4 a) c (* b b)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
60×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
10×fma-neg distribute-lft-out-- difference-of-squares
8×add-log-exp
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- diff-log flip-- associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log fma-udef div-inv
Counts
4 → 167
Calls
4 calls:
0.0ms
(fma (* -4 a) c (* b b))
45.0ms
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
21.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
4.0ms
(sqrt (fma (* -4 a) c (* b b)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma (* -4 a) c (* b b))
130.0ms
(/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) a)
97.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
111.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify895.0ms

Counts
179 → 179
Iterations
IterNodes
done2000
21190
1497
0222

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* -4 a) c (* b b))
0.2b
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
1.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.4b
(sqrt (fma (* -4 a) c (* b b)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
60×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×associate-*r* add-exp-log
11×times-frac
10×fma-neg
9×add-cbrt-cube
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
3×flip3-- flip-- unswap-sqr
2×frac-times diff-log div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 165
Calls
4 calls:
0.0ms
(fma (* -4 a) c (* b b))
42.0ms
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
11.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
5.0ms
(sqrt (fma (* -4 a) c (* b b)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(fma (* -4 a) c (* b b))
117.0ms
(* (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (/ 1 a))
88.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
90.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify981.0ms

Counts
177 → 177
Iterations
IterNodes
done2001
21365
1559
0241

prune895.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize86.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.4b
(sqrt (fma (* -4 a) c (* b b)))
23.4b
(sqrt (fma (* -4 a) c (* b b)))
23.4b
(sqrt (fma (* -4 a) c (* b b)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip--
Counts
4 → 139
Calls
4 calls:
10.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))
3.0ms
(sqrt (fma (* -4 a) c (* b b)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
99.0ms
(sqrt (fma (* -4 a) c (* b b)))
109.0ms
(sqrt (fma (* -4 a) c (* b b)))
107.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts
151 → 151
Iterations
IterNodes
done2000
31874
2671
1317
0146

prune738.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize47.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
23.4b
(sqrt (fma (* -4 a) c (* b b)))
23.4b
(sqrt (fma (* -4 a) c (* b b)))
23.4b
(sqrt (fma (* -4 a) c (* b b)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log flip--
Counts
4 → 139
Calls
4 calls:
10.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
86.0ms
(sqrt (fma (* -4 a) c (* b b)))
97.0ms
(sqrt (fma (* -4 a) c (* b b)))
102.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts
151 → 151
Iterations
IterNodes
done2000
31874
2671
1317
0146

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

regimes457.0ms

Accuracy

83% (4.9b remaining)

Error of 10.1b against oracle of 5.3b and baseline of 34.0b

bsearch255.0ms

Steps
ItersRangePoint
7
1.9723660647371773e+81
3.4101289177416236e+83
1.7665622931893247e+83
7
-8.865960730997555e-39
-3.628908962658003e-41
-5.7874989996849275e-40

simplify32.0ms

Iterations
IterNodes
done55
255
153
044

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.2s1051×body2560valid
1.0s5928×body80valid
822.0ms2986×body80nan
694.0ms917×body1280valid
249.0ms423×body640valid
118.0ms116×body5120valid
93.0ms224×body320valid
67.0ms122×body160valid