Details

Time bar (total: 6.2s)

sample52.0ms

Algorithm
intervals
Results
9.0ms142×body160valid
8.0ms509×pre80true
8.0ms253×body80nan
4.0ms45×body320valid
2.0ms69×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219
done1219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
35.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite110.0ms

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:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735
done5001735

prune248.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite189.0ms

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:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify145.0ms

Counts
243 → 243
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
08325099
139673830
250013828
done50013828

prune554.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
0.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
30.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series735.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
172.0ms
(fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
239.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
278.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (sqrt b) (- (sqrt b)) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify111.0ms

Counts
117 → 117
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
05982143
130141804
250021754
done50021754

prune418.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
91×*-un-lft-identity
57×add-sqr-sqrt add-cube-cbrt
32×distribute-lft-neg-in distribute-rgt-neg-in
27×add-exp-log add-cbrt-cube
17×distribute-lft-out
15×associate-/r* div-inv
10×cbrt-undiv div-exp
8×neg-mul-1 associate-/l* add-log-exp
6×prod-exp cbrt-unprod
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ distribute-neg-frac
1×+-commutative sub-neg flip3-- fma-neg diff-log prod-diff sum-log flip-- associate-/l/
Counts
4 → 184
Calls
4 calls:
70.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms
(/ (* 4.0 (* a c)) a)
18.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))

series298.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms
(/ (* 4.0 (* a c)) a)
84.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))

simplify119.0ms

Counts
196 → 196
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08392756
145542476
250022473
done50022473

prune507.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03013
13113
23113
done3113

end0.0ms

sample1.5s

Algorithm
intervals
Results
320.0ms4823×body160valid
278.0ms16463×pre80true
266.0ms8463×body80nan
129.0ms1346×body320valid
60.0ms1831×body80valid