Details

Time bar (total: 10.6s)

sample57.0ms

Algorithm
intervals
Results
12.0ms297×body80nan
11.0ms161×body160valid
10.0ms553×pre80true
4.0ms41×body320valid
2.0ms54×body80valid

simplify56.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12517
24516
38716
410516
511316
done11316

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify755.0ms

Counts
102 → 102
Iterations

Useful iterations: done (753.0ms)

IterNodesCost
01671697
14361584
214821361
done50001351

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series452.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
184.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.1s

Counts
243 → 243
Iterations

Useful iterations: done (1.1s)

IterNodesCost
034110754
18338177
228566648
done50006646

prune572.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma b b (- (* (* 4.0 a) c))))
0.1b
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
0.3b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) (* 2.0 a))

rewrite92.0ms

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
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg 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 → 230
Calls
4 calls:
1.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
11.0ms
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
28.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
42.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) (* 2.0 a))

series513.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma b b (- (* (* 4.0 a) c))))
88.0ms
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
187.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
158.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) (* 2.0 a))

simplify940.0ms

Counts
242 → 242
Iterations

Useful iterations: done (931.0ms)

IterNodesCost
032510721
17778120
224496618
done50006616

prune591.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
0.1b
(/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
0.3b
(/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a)
0.3b
(* (/ (fma (* a c) 4.0 0) 2.0) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
353×times-frac
329×add-sqr-sqrt
303×*-un-lft-identity
197×add-cube-cbrt
85×associate-*r*
60×prod-diff
56×sqrt-prod
52×add-exp-log distribute-lft-out-- difference-of-squares
47×distribute-rgt-neg-in
32×add-cbrt-cube
30×associate-/l*
25×div-exp
21×distribute-lft-neg-in
16×associate-/r/
13×cbrt-undiv associate-*l*
11×div-inv
10×fma-neg prod-exp associate-/r*
9×flip3-- flip--
8×add-log-exp unswap-sqr
7×pow1 neg-mul-1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
2×frac-2neg diff-log clear-num
1×associate--l- neg-sub0 frac-times sub-neg pow-flip associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 407
Calls
4 calls:
12.0ms
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
14.0ms
(/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
28.0ms
(/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a)
70.0ms
(* (/ (fma (* a c) 4.0 0) 2.0) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a))

series555.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))
109.0ms
(/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c))))))
133.0ms
(/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a)
224.0ms
(* (/ (fma (* a c) 4.0 0) 2.0) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* 4.0 a) c)))))) a))

simplify1.7s

Counts
419 → 419
Iterations

Useful iterations: done (1.7s)

IterNodesCost
049915027
1136812212
2372610575
done500110573

prune825.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes135.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02026
12926
23726
done3726

end0.0ms

sample1.4s

Algorithm
intervals
Results
321.0ms4850×body160valid
289.0ms16215×pre80true
267.0ms8215×body80nan
135.0ms1326×body320valid
61.0ms1824×body80valid