Details

Time bar (total: 6.1s)

sample41.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
7.0ms191×body80valid
4.0ms20×body1280valid
3.0ms77×body80nan
2.0ms17×body640valid
1.0ms10×body320valid
1.0ms3×body5120valid
0.0ms4×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735
done5001735

prune281.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.5b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify215.0ms

Counts
244 → 244
Iterations

Useful iterations: 2 (158.0ms)

IterNodesCost
08295119
137633863
250013860
done50013860

prune553.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×*-un-lft-identity
14×add-sqr-sqrt
13×add-cbrt-cube
11×add-cube-cbrt
10×fma-def prod-exp add-log-exp
7×pow1 associate-*r*
5×distribute-rgt-neg-in associate-*l*
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 100
Calls
4 calls:
96.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05141011
12322856
25001843
done5001843

prune293.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

5.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
10.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
18.6b
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
146×*-un-lft-identity
102×add-cube-cbrt times-frac
90×prod-diff
82×log-prod exp-sum
44×sqrt-prod
41×distribute-rgt-neg-in
33×associate-/l* difference-of-squares
30×distribute-lft-neg-in
22×distribute-lft-out--
18×add-exp-log add-cbrt-cube
10×neg-mul-1 fma-neg
9×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 273
Calls
4 calls:
97.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
66.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
35.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))))
81.0ms
(- (- b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify150.0ms

Counts
285 → 285
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
09787738
139644917
250014916
done50014916

prune603.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes219.0ms

Accuracy

83.8% (4.3b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 32.6b

bsearch85.0ms

Steps
ItersRangePoint
5
3.8896208850456714e-71
9.054856756550336e-71
6.485606601696406e-71
8
-3.9507459177053075e+109
-4.2638646006519825e+105
-1.2447742914077108e+109

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03816
13816
done3816

end0.0ms

sample1.2s

Algorithm
intervals
Results
243.0ms1119×body2560valid
216.0ms5759×body80valid
164.0ms900×body1280valid
105.0ms2850×body80nan
71.0ms476×body640valid
35.0ms129×body5120valid
22.0ms216×body320valid
10.0ms108×body160valid