Details

Time bar (total: 18.3s)

sample92.0ms

Algorithm
intervals
Results
27.0ms555×pre80true
17.0ms299×body80nan
17.0ms142×body160valid
7.0ms114×body80valid

simplify92.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize13.0ms

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))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite149.0ms

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:
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
52.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.1s

Counts
102 → 102
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01671697
14331584
214811361
done50001347

prune346.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

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

rewrite312.0ms

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:
49.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(- (* b b) (* (* 4.0 a) c))
119.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
120.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
176.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
257.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.9s

Counts
243 → 243
Iterations

Useful iterations: done (1.9s)

IterNodesCost
034010026
18127598
232366483
done50016397

prune695.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

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:
14.0ms
(- (* b b) (* 4.0 (* a c)))
0.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
55.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
35.0ms
(/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c)))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
209.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
338.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
416.0ms
(/ (+ 0 (* (* a c) 4.0)) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* 4.0 (* a c)))))))

simplify1.2s

Counts
117 → 117
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02233857
15733551
222812698
done50012695

prune732.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize22.0ms

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
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
317×times-frac
280×add-sqr-sqrt
269×*-un-lft-identity
180×add-cube-cbrt
103×add-exp-log
85×associate-*r*
63×add-cbrt-cube
61×prod-diff
52×sqrt-prod
45×div-exp
44×distribute-lft-out-- difference-of-squares
43×distribute-rgt-neg-in
35×prod-exp
27×associate-/l*
24×cbrt-undiv
21×distribute-lft-neg-in cbrt-unprod
14×associate-/r/
11×fma-neg
10×div-inv add-log-exp
9×flip3-- flip--
7×neg-mul-1 associate-*l*
6×pow1
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×diff-log associate-/r*
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 378
Calls
4 calls:
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
227.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series506.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
183.0ms
(* (/ (* 4.0 (* a c)) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify2.8s

Counts
390 → 390
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
052514301
1140511489
246089771
done50009771

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes277.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02029
12327
done2327

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.2s16495×pre80true
1.2s4493×body160valid
843.0ms8495×body80nan
397.0ms3507×body80valid