Details

Time bar (total: 4.1s)

sample43.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms184×body80valid
5.0ms30×body1280valid
3.0ms91×body80nan
1.0ms10×body640valid
1.0ms10×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649
done1649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
79.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
33.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Counts
169 → 169
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05903305
121012212
250022128
done50022128

prune319.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
105.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Counts
177 → 177
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06563422
125942238
250012193
done50012193

prune305.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
51.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
32.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Counts
217 → 217
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07184221
130992976
250012863
done50012863

prune331.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify4.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.8b

regimes167.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.5b against oracle of 6.1b and baseline of 34.3b

bsearch120.0ms

Steps
ItersRangePoint
8
1.2146045965263502e+46
6.67231609761305e+48
6.568668442325333e+48
11
-4.915395666956115e-72
-4.878563939054666e-98
-2.763265898390889e-72

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716
done3716

end0.0ms

sample1.2s

Algorithm
intervals
Results
241.0ms1073×body2560valid
236.0ms5844×body80valid
166.0ms898×body1280valid
106.0ms2842×body80nan
61.0ms427×body640valid
28.0ms104×body5120valid
26.0ms243×body320valid
7.0ms92×body160valid