Details

Time bar (total: 18.8s)

sample90.0ms

Algorithm
intervals
Results
29.0ms36×body2560valid
17.0ms197×body80valid
11.0ms28×body1280valid
8.0ms93×body80nan
6.0ms15×body640valid
2.0ms3×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify40.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize51.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Counts
4 → 175
Calls
4 calls:
Slowest
95.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
109.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms
(sqrt (- (* b_2 b_2) (* a c)))
48.0ms
(- (* b_2 b_2) (* a c))

simplify669.0ms

Counts
187 → 187

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×associate-*r* add-exp-log
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg sqrt-div div-exp associate-*l/ cbrt-unprod
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 173
Calls
4 calls:
Slowest
90.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
114.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms
(sqrt (- (* b_2 b_2) (* a c)))
39.0ms
(- (* b_2 b_2) (* a c))

simplify764.0ms

Counts
185 → 185

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize45.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (* b_2 b_2) (* a c))
0.4b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b
(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
36×times-frac
33×add-sqr-sqrt
32×add-cube-cbrt
16×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/l*
9×distribute-lft-out
8×add-log-exp
6×fma-def add-cbrt-cube add-exp-log sqrt-prod
5×pow1
4×expm1-log1p-u neg-mul-1 insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-+ flip3-- sqrt-div flip-+ flip-- distribute-neg-frac associate-/l/
1×neg-sub0 cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff distribute-frac-neg div-inv
Counts
4 → 126
Calls
4 calls:
Slowest
102.0ms
(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
52.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
108.0ms
(/ (- (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
92.0ms
(sqrt (- (* b_2 b_2) (* a c)))
73.0ms
(- (* b_2 b_2) (* a c))

simplify1.6s

Counts
138 → 138

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

localize65.0ms

Local error

Found 4 expressions with local error:

24.8b
(sqrt (- (* b_2 b_2) (* a c)))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))
24.8b
(sqrt (- (* b_2 b_2) (* a c)))
1.4b
(- (* b_2 b_2) (* a c))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 71
Calls
4 calls:
Slowest
23.0ms
(- (* b_2 b_2) (* a c))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(sqrt (- (* b_2 b_2) (* a c)))
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
44.0ms
(- (* b_2 b_2) (* a c))

simplify1.4s

Counts
83 → 83

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.7b

regimes519.0ms

Accuracy

85.1% (4.2b remaining)

Error of 9.8b against oracle of 5.7b and baseline of 33.6b

bsearch178.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.3s1080×body2560valid
1.2s5905×body80valid
671.0ms894×body1280valid
396.0ms2917×body80nan
215.0ms465×body640valid
90.0ms106×body5120valid
80.0ms228×body320valid
21.0ms96×body160valid