Details

Time bar (total: 13.3s)

sample116.0ms

Algorithm
intervals
Results
30.0ms510×pre80true
20.0ms138×body160valid
19.0ms254×body80nan
9.0ms118×body80valid

simplify138.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))
27.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite215.0ms

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:
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
60.0ms
(- (* b b) (* (* 4.0 a) c))
135.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
107.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01671697
14521588
221181361
done50011352

prune396.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite239.0ms

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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series635.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
266.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
95.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
216.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify500.0ms

Counts
243 → 243
Iterations

Useful iterations: done (489.0ms)

IterNodesCost
033910026
18627622
done50006606

prune896.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c)))
0.4b
(/ (- (* 0 0) (* (* c (* 4.0 a)) (* c (* 4.0 a)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c))))
0.5b
(* (* c (* 4.0 a)) (* c (* 4.0 a)))

rewrite458.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
67×pow-prod-down
60×prod-diff
59×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
47×add-exp-log add-cbrt-cube
32×sqrt-prod
29×prod-exp cbrt-unprod
24×distribute-rgt-neg-in
22×distribute-lft-neg-in
10×fma-neg
9×pow-sqr pow-prod-up
8×neg-mul-1 associate-*l* add-log-exp
7×associate-*r*
6×difference-of-squares
4×expm1-log1p-u flip3-- times-frac associate-*l/ flip-- log1p-expm1-u associate-/l* distribute-lft-out--
3×pow-plus
2×cbrt-undiv diff-log div-exp associate-/r/ *-commutative associate-/l/
1×associate--l- pow2 neg-sub0 sub-neg frac-2neg div-sub swap-sqr neg-log clear-num associate-/r* distribute-rgt-neg-out div-inv unswap-sqr
Counts
4 → 212
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c)))
101.0ms
(/ (- (* 0 0) (* (* c (* 4.0 a)) (* c (* 4.0 a)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c))))
147.0ms
(* (* c (* 4.0 a)) (* c (* 4.0 a)))

series558.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c)))
268.0ms
(/ (- (* 0 0) (* (* c (* 4.0 a)) (* c (* 4.0 a)))) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* (* 4.0 a) c))))
54.0ms
(* (* c (* 4.0 a)) (* c (* 4.0 a)))

simplify551.0ms

Counts
224 → 224
Iterations

Useful iterations: done (541.0ms)

IterNodesCost
02988289
18466140
done50004921

prune792.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
135×add-sqr-sqrt
133×*-un-lft-identity
125×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
15×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
7×associate-*r*
6×pow1 associate-*r/
4×expm1-log1p-u sub-neg flip3-- prod-exp flip-- cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp associate-*l* associate-/l*
2×associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ pow-prod-down neg-log clear-num associate-/r* *-commutative flip-+ div-inv unswap-sqr
Counts
4 → 285
Calls
4 calls:
132.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
126.0ms
(/ (+ 0 (* c (* 4.0 a))) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
82.0ms
(- (* b b) (* (* 4.0 a) c))
89.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
246.0ms
(/ (+ 0 (* c (* 4.0 a))) (* 2.0 (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify577.0ms

Counts
297 → 297
Iterations

Useful iterations: done (552.0ms)

IterNodesCost
037417014
193411245
done50008973

prune789.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes216.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
02844
14040
25340
35740
done5740

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s4473×body160valid
698.0ms8395×body80nan
561.0ms16395×pre80true
230.0ms3527×body80valid