Details

Time bar (total: 2.1m)

sample100.0ms

Algorithm
intervals
Results
25.0ms38×body1280valid
19.0ms177×body80valid
18.0ms31×body2560valid
8.0ms79×body80nan
4.0ms11×body640valid
4.0ms11×body320valid
2.0ms2×body5120valid
1.0ms3×body160valid

simplify112.0ms

Calls
1 calls:
Slowest
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize41.0ms

Local error

Found 4 expressions with local error:

21.3b
(sqrt (- (* b b) (* (* 3 a) c)))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.6b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite95.0ms

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-+
Calls
4 calls:
Slowest
32.0ms
(* (* 3 a) c)
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms
(- (* b b) (* (* 3 a) c))

series701.0ms

Calls
4 calls:
Slowest
514.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
97.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
61.0ms
(- (* b b) (* (* 3 a) c))
28.0ms
(* (* 3 a) c)

simplify3.5s

Calls
41 calls:
Slowest
431.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
409.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
388.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
293.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
289.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.9b

localize46.0ms

Local error

Found 4 expressions with local error:

21.3b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.7b
(fma -3 (* c a) (* b b))
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Calls
4 calls:
Slowest
19.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
14.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series416.0ms

Calls
4 calls:
Slowest
118.0ms
(sqrt (fma -3 (* c a) (* b b)))
117.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
107.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
74.0ms
(fma -3 (* c a) (* b b))

simplify4.2s

Calls
87 calls:
Slowest
580.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
356.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
211.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
170.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 3) 3) (* (* a a) a)))
132.0ms
(- (log (- (sqrt (fma -3 (* c a) (* b b))) b)) (+ (log 3) (log a)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.8b

localize26.0ms

Local error

Found 4 expressions with local error:

21.3b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.7b
(fma -3 (* c a) (* b b))
0.1b
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
25.0ms
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
13.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
1.0ms
(fma -3 (* c a) (* b b))

series400.0ms

Calls
4 calls:
Slowest
120.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
98.0ms
(sqrt (fma -3 (* c a) (* b b)))
94.0ms
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
88.0ms
(fma -3 (* c a) (* b b))

simplify14.2s

Calls
225 calls:
Slowest
389.0ms
(/ (/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (* (cbrt 3) (cbrt 3))) (* (cbrt a) (cbrt a)))
200.0ms
(/ (/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (sqrt 3)) (* (cbrt a) (cbrt a)))
195.0ms
(/ (/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (* (cbrt 3) (cbrt 3))) (sqrt a))
182.0ms
(/ (/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* 3 3) 3)) (* (* a a) a))
173.0ms
(/ (* (* (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3)) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3)) (* (* a a) a))

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.8b

localize44.0ms

Local error

Found 4 expressions with local error:

21.3b
(sqrt (fma (* c -3) a (* b b)))
1.1b
(- (sqrt (fma (* c -3) a (* b b))) b)
0.1b
(/ (/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3) a)
0.1b
(/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3)

rewrite381.0ms

Algorithm
rewrite-expression-head
Rules
423×*-un-lft-identity
228×times-frac
160×distribute-lft-out
122×add-sqr-sqrt
117×add-cube-cbrt
49×distribute-lft-out--
40×associate-/l*
32×distribute-rgt-neg-in
18×prod-diff
16×sqrt-prod
11×add-cbrt-cube add-exp-log
7×associate-/l/
6×associate-/r* fma-neg div-sub div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp frac-add associate-+l- insert-posit16 log1p-expm1-u
3×flip3-+ flip3-- flip-+ flip--
2×neg-sub0 clear-num associate-+r- frac-2neg difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Calls
4 calls:
Slowest
188.0ms
(/ (/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3) a)
178.0ms
(/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3)
8.0ms
(- (sqrt (fma (* c -3) a (* b b))) b)
1.0ms
(sqrt (fma (* c -3) a (* b b)))

series462.0ms

Calls
4 calls:
Slowest
128.0ms
(- (sqrt (fma (* c -3) a (* b b))) b)
119.0ms
(/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3)
116.0ms
(/ (/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) 3) a)
99.0ms
(sqrt (fma (* c -3) a (* b b)))

simplify1.4m

Calls
357 calls:
Slowest
1.2s
(/ (/ (* (* (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b))) (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b))) (* (* 3 3) 3)) (* (* a a) a))
928.0ms
(/ (* (* (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b))) (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b))) (* (* 3 3) 3))
907.0ms
(/ (/ (* (cbrt (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b))) (cbrt (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)))) (* (cbrt 3) (cbrt 3))) (sqrt a))
856.0ms
(/ (/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) (sqrt 3)) a)
733.0ms
(/ (+ (- (sqrt (fma (* c -3) a (* b b))) b) (+ (- b) b)) (cbrt 3))

prune3.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

regimes393.0ms

Accuracy

91.6% (1.9b remaining)

Error of 13.1b against oracle of 11.2b and baseline of 33.7b

bsearch353.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.5s1097×body2560valid
994.0ms5800×body80valid
722.0ms910×body1280valid
403.0ms2937×body80nan
221.0ms439×body640valid
131.0ms106×body5120valid
83.0ms223×body320valid
29.0ms117×body160valid