Details

Time bar (total: 7.8s)

sample42.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
7.0ms178×body80valid
7.0ms37×body1280valid
3.0ms22×body640valid
3.0ms79×body80nan
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify76.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12817
26317
311417
413017
513617
613917
done13917

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in 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 → 77
Calls
4 calls:
38.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify475.0ms

Counts
89 → 89
Iterations

Useful iterations: done (472.0ms)

IterNodesCost
01571750
14051650
213391474
done50011465

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
4.6b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.7b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
54.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
39.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
165.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
203.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify763.0ms

Counts
150 → 150
Iterations

Useful iterations: done (757.0ms)

IterNodesCost
02515108
16364631
222783941
done50013939

prune418.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

7.8b
(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
8.6b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×times-frac
6×pow1 add-exp-log sqrt-prod add-cbrt-cube add-log-exp
5×difference-of-squares
4×flip3-- sqrt-div associate-/r* flip--
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num flip-+ div-inv
Counts
4 → 78
Calls
4 calls:
23.0ms
(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
47.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
209.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify537.0ms

Counts
90 → 90
Iterations

Useful iterations: done (534.0ms)

IterNodesCost
01563091
13852009
212671772
done50001771

prune335.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
4.5b
(* (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.7b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
51×add-exp-log
42×*-un-lft-identity
40×times-frac
28×add-cube-cbrt
27×add-cbrt-cube
24×associate-*l*
20×prod-exp
16×div-exp
14×difference-of-squares
10×sqrt-prod
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r* distribute-lft-out--
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 136
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(* (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
36.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
163.0ms
(* (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
220.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify973.0ms

Counts
148 → 148
Iterations

Useful iterations: done (968.0ms)

IterNodesCost
02564754
17274229
227503426
done50003424

prune368.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes189.0ms

Accuracy

83.1% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 32.0b

bsearch86.0ms

Steps
ItersRangePoint
8
1.5276508475467709e+44
4.1560730947117816e+46
4.1199128263687574e+46
5
-1.2023865605984147e-79
-5.347575839305805e-80
-8.364554704106616e-80

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02941
13641
done3641

end0.0ms

sample1.1s

Algorithm
intervals
Results
255.0ms1073×body2560valid
226.0ms5862×body80valid
170.0ms902×body1280valid
110.0ms2862×body80nan
67.0ms459×body640valid
32.0ms114×body5120valid
25.0ms213×body320valid
9.0ms116×body160valid