Details

Time bar (total: 19.9s)

sample118.0ms

Algorithm
intervals
Results
34.0ms37×body2560valid
25.0ms185×body80valid
22.0ms32×body1280valid
10.0ms85×body80nan
4.0ms9×body640valid
1.0ms4×body320valid
1.0ms3×body160valid

simplify152.0ms

Counts
1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize32.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.8b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
16.0ms
(* (* 3 a) c)
12.0ms
(- (* b b) (* (* 3 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
78.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
51.0ms
(- (* b b) (* (* 3 a) c))
20.0ms
(* (* 3 a) c)

simplify1.5s

Counts
96 → 96

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.6b

localize40.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
9.5b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
0.8b
(- (* b b) (* (* 3 a) c))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×fma-def add-log-exp
9×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2
1×neg-sub0 +-commutative neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log associate-+l- flip-+
Counts
4 → 79
Calls
4 calls:
Slowest
19.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
13.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
13.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms
(- (* b b) (* (* 3 a) c))

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
103.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
99.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
75.0ms
(- (* b b) (* (* 3 a) c))

simplify1.2s

Counts
91 → 91

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.6b

localize68.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
22.8b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
Counts
4 → 72
Calls
4 calls:
Slowest
18.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
119.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
98.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.2s

Counts
84 → 84

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.6b

localize38.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
22.8b
(sqrt (- (* b b) (* (* 3 a) c)))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
20×fma-def *-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt add-log-exp
8×distribute-rgt-neg-in
6×distribute-lft-neg-in pow1 sqrt-prod
4×expm1-log1p-u sum-log add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out
2×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ flip3-- pow1/2 neg-log associate-+l- flip-+ flip--
Counts
4 → 92
Calls
4 calls:
Slowest
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
17.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
103.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
95.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify992.0ms

Counts
104 → 104

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.5b

regimes695.0ms

Accuracy

86.1% (3.2b remaining)

Error of 14.6b against oracle of 11.4b and baseline of 34.7b

bsearch142.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.2s5830×body80valid
1.1s1086×body2560valid
827.0ms935×body1280valid
450.0ms2952×body80nan
228.0ms454×body640valid
137.0ms215×body320valid
104.0ms112×body5120valid
25.0ms100×body160valid