Details

Time bar (total: 24.6s)

sample80.0ms

Algorithm
intervals
Results
45.0ms282×body80valid
14.0ms96×body80nan

simplify271.0ms

Counts
1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize191.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.8b
(- (* b b) (* (* 4 a) c))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 144
Calls
4 calls:
Slowest
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
16.0ms
(- (* b b) (* (* 4 a) c))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
91.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
66.0ms
(- (* b b) (* (* 4 a) c))

simplify2.1s

Counts
156 → 156

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize167.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
13.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative neg-mul-1 flip3-+ neg-log associate-+l- flip-+
Counts
4 → 80
Calls
4 calls:
Slowest
21.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
92 → 92

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize179.0ms

Local error

Found 4 expressions with local error:

23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
10.6b
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4 a) c))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×fma-def *-un-lft-identity add-cube-cbrt
8×add-log-exp
6×cbrt-prod
5×pow1
4×expm1-log1p-u cbrt-div add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-- sqrt-prod flip--
2×sum-log pow1/3 sqrt-div
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ pow1/2 neg-log associate-+l- flip-+
Counts
4 → 76
Calls
4 calls:
Slowest
14.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4 a) c))))))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
109.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
100.0ms
(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4 a) c))))))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
88 → 88

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

localize202.0ms

Local error

Found 4 expressions with local error:

22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
5.0b
(/ (* 2 (- (* c (/ a b)) b)) (* 2 a))
3.0b
(* c (/ a b))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
60×prod-diff
58×*-un-lft-identity
54×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in add-cbrt-cube add-exp-log
13×associate-*r*
11×times-frac
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- associate-*l* associate-*r/ flip--
2×sqrt-div diff-log div-inv distribute-lft-out-- difference-of-squares unswap-sqr associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log *-commutative associate-/l*
Counts
4 → 170
Calls
4 calls:
Slowest
37.0ms
(/ (* 2 (- (* c (/ a b)) b)) (* 2 a))
20.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(* c (/ a b))

series359.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
73.0ms
(/ (* 2 (- (* c (/ a b)) b)) (* 2 a))
25.0ms
(* c (/ a b))

simplify970.0ms

Counts
182 → 182

prune4.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

regimes437.0ms

Accuracy

86.4% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 19.2b

bsearch273.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.4s8744×body80valid
552.0ms2799×body80nan