Details

Time bar (total: 44.1s)

sample129.0ms

Algorithm
intervals
Results
27.0ms34×body2560valid
26.0ms185×body80valid
26.0ms32×body1280valid
13.0ms100×body80nan
9.0ms16×body640valid
5.0ms5×body5120valid
2.0ms4×body320valid
1.0ms3×body160valid

simplify131.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
131.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.1b

localize40.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(fma -3 (* c a) (* b b))
0.9b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))

rewrite32.0ms

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
Counts
4 → 102
Calls
4 calls:
Slowest
18.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
11.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series423.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
103.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
99.0ms
(sqrt (fma -3 (* c a) (* b b)))
93.0ms
(fma -3 (* c a) (* b b))

simplify4.4s

Counts
87 → 114
Calls
87 calls:
Slowest
556.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
318.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
213.0ms
(/ (* (* (- (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)))
212.0ms
(/ (* (* (- (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)))
122.0ms
(fma (* (cbrt (sqrt (fma -3 (* c a) (* b b)))) (cbrt (sqrt (fma -3 (* c a) (* b b))))) (cbrt (sqrt (fma -3 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.8b

localize42.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(fma -3 (* c a) (* b b))
0.9b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)

rewrite37.0ms

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/
Counts
4 → 179
Calls
4 calls:
Slowest
22.0ms
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
7.0ms
(- (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))

series460.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
126.0ms
(sqrt (fma -3 (* c a) (* b b)))
117.0ms
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) a)
82.0ms
(fma -3 (* c a) (* b b))

simplify15.3s

Counts
225 → 191
Calls
225 calls:
Slowest
475.0ms
(/ (/ (- (sqrt (fma -3 (* c a) (* b b))) b) 3) (sqrt a))
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)))
236.0ms
(/ (/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (sqrt 3)) (* (cbrt a) (cbrt a)))
213.0ms
(/ (/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (* (cbrt 3) (cbrt 3))) (sqrt a))
198.0ms
(/ (* (* (/ (- (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))

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 30.8b

localize20.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(fma -3 (* c a) (* b b))
0.9b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.2b
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
38×*-un-lft-identity
30×add-cube-cbrt
22×associate-*r*
19×times-frac sqrt-prod
18×prod-diff
9×add-cbrt-cube add-exp-log
8×difference-of-squares
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out--
3×associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv flip--
Counts
4 → 113
Calls
4 calls:
Slowest
24.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
8.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
1.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
105.0ms
(sqrt (fma -3 (* c a) (* b b)))
104.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
75.0ms
(fma -3 (* c a) (* b b))

simplify4.0s

Counts
97 → 125
Calls
97 calls:
Slowest
170.0ms
(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* a a) a)))
142.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
141.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
131.0ms
(+ (log 1/3) (log (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
131.0ms
(* (sqrt 1/3) (/ (sqrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (sqrt a)))

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 30.8b

localize45.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (fma -3 (* c a) (* b b)))
1.1b
(fma -3 (* c a) (* b b))
0.9b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.3b
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
54×prod-diff
49×*-un-lft-identity
45×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
7×pow1
6×add-cbrt-cube fma-neg associate-*r* add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×sub-neg associate-*l*
2×flip3-- associate-*r/ flip-- distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 135
Calls
4 calls:
Slowest
39.0ms
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
22.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series377.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
114.0ms
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
91.0ms
(sqrt (fma -3 (* c a) (* b b)))
55.0ms
(fma -3 (* c a) (* b b))

simplify5.8s

Counts
119 → 147
Calls
119 calls:
Slowest
459.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)))
145.0ms
(+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))
111.0ms
(* 1/3 (fma (- (cbrt b)) (* (cbrt b) (cbrt b)) (* (cbrt b) (* (cbrt b) (cbrt b)))))
107.0ms
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
102.0ms
(* (fma (- (cbrt b)) (* (cbrt b) (cbrt b)) (* (cbrt b) (* (cbrt b) (cbrt b)))) 1/3)

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 30.8b

regimes476.0ms

Accuracy

90.7% (0.4b remaining)

Error of 29.7b against oracle of 29.3b and baseline of 33.8b

bsearch200.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.4s1049×body2560valid
945.0ms5850×body80valid
696.0ms910×body1280valid
501.0ms2774×body80nan
223.0ms442×body640valid
179.0ms120×body5120valid
95.0ms241×body320valid
28.0ms108×body160valid