Details

Time bar (total: 21.6s)

sample132.0ms

Algorithm
intervals
Results
32.0ms34×body2560valid
31.0ms198×body80valid
21.0ms29×body1280valid
14.0ms91×body80nan
5.0ms8×body640valid
3.0ms7×body320valid
2.0ms6×body160valid
2.0ms2×body5120valid

simplify138.0ms

Counts
1 → 1
Iterations
IterNodes
8105
7105
6104
5102
494
377
244
125
014

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a -4) c)
1.3b
(- (sqrt (fma b b (* (* a -4) c))) b)
1.5b
(fma b b (* (* a -4) c))
27.8b
(sqrt (fma b b (* (* a -4) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×sqrt-prod
10×pow1
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log associate-*l* *-commutative fma-udef flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
29.0ms
(* (* a -4) c)
16.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(fma b b (* (* a -4) c))
3.0ms
(sqrt (fma b b (* (* a -4) c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (* a -4) c)
146.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
91.0ms
(fma b b (* (* a -4) c))
109.0ms
(sqrt (fma b b (* (* a -4) c)))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
32785
2831
1319
0146

prune861.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
1.3b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b
(fma b b (* -4 (* a c)))
27.8b
(sqrt (fma b b (* -4 (* a c))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
32.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
15.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
2.0ms
(sqrt (fma b b (* -4 (* a c))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (- (sqrt (fma b b (* -4 (* a c)))) b) a)
137.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
64.0ms
(fma b b (* -4 (* a c)))
143.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
32588
2951
1403
0179

prune990.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
1.3b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b
(fma b b (* -4 (* a c)))
27.8b
(sqrt (fma b b (* -4 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
32×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r* add-exp-log
11×times-frac
9×add-cbrt-cube
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip-- unswap-sqr
2×frac-times div-exp associate-*l/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 115
Calls
4 calls:
42.0ms
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
15.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
2.0ms
(sqrt (fma b b (* -4 (* a c))))

series406.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (- (sqrt (fma b b (* -4 (* a c)))) b) (/ 1 a))
100.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
76.0ms
(fma b b (* -4 (* a c)))
100.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify2.6s

Counts
127 → 127
Iterations
IterNodes
33135
21185
1465
0199

prune937.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
1.3b
(- (sqrt (fma b b (* -4 (* a c)))) b)
1.5b
(fma b b (* -4 (* a c)))
27.8b
(sqrt (fma b b (* -4 (* a c))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
18×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
7×div-exp
6×pow1 fma-neg add-log-exp
5×flip3-- div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp 1-exp
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log fma-udef pow-flip inv-pow
Counts
4 → 192
Calls
4 calls:
13.0ms
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
7.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
0.0ms
(fma b b (* -4 (* a c)))
2.0ms
(sqrt (fma b b (* -4 (* a c))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ 1 (/ a (- (sqrt (fma b b (* -4 (* a c)))) b)))
114.0ms
(- (sqrt (fma b b (* -4 (* a c)))) b)
79.0ms
(fma b b (* -4 (* a c)))
113.0ms
(sqrt (fma b b (* -4 (* a c))))

simplify4.5s

Counts
204 → 204
Iterations
IterNodes
33963
21464
1644
0283

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

regimes359.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.5b

bsearch203.0ms

Steps
ItersRangePoint
8
2.764110880089542e-64
2.3245141193625934e-60
2.0617732603635578e-61
9
-229886301330938.94
-710549284.1101115
-227369802444031.66

simplify8.0ms

Iterations
IterNodes
232
132
028

end0.0ms

sample4.5s

Algorithm
intervals
Results
973.0ms908×body1280valid
899.0ms1054×body2560valid
892.0ms5886×body80valid
792.0ms2993×body80nan
282.0ms446×body640valid
204.0ms232×body320valid
117.0ms110×body5120valid
25.0ms113×body160valid