Details

Time bar (total: 17.8s)

sample367.0ms

Algorithm
intervals
Results
163.0ms23×body1280valid
57.0ms34×body2560valid
31.0ms189×body80valid
12.0ms80×body80nan
6.0ms12×body640valid
3.0ms3×body5120valid
3.0ms9×body320valid
1.0ms4×body160valid

simplify73.0ms

Counts
1 → 1

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize19.0ms

Local error

Found 4 expressions with local error:

21.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (* b_2 b_2) (* a c))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
92.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
52.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(- (* b_2 b_2) (* a c))
147.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
134.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
130.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts
100 → 100

prune986.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize31.0ms

Local error

Found 4 expressions with local error:

21.4b
(sqrt (- (* b_2 b_2) (* a c)))
6.1b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
1.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
Slowest
42.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
14.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
113.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))
50.0ms
(- (* b_2 b_2) (* a c))

simplify1.0s

Counts
109 → 109

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize27.0ms

Local error

Found 4 expressions with local error:

21.4b
(sqrt (- (* b_2 b_2) (* a c)))
9.7b
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
1.0b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
132×add-sqr-sqrt
95×*-un-lft-identity
82×add-cube-cbrt
43×sqrt-prod
24×associate-/r*
15×add-exp-log
14×difference-of-squares
10×sqrt-div
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1 div-inv
4×insert-posit16
3×cbrt-undiv associate-/l* distribute-lft-out--
2×rec-exp sub-neg diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub pow-flip inv-pow
Counts
4 → 181
Calls
4 calls:
Slowest
89.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
21.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(- (* b_2 b_2) (* a c))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
98.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
96.0ms
(sqrt (- (* b_2 b_2) (* a c)))
50.0ms
(- (* b_2 b_2) (* a c))

simplify889.0ms

Counts
193 → 193

prune2.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

21.4b
(sqrt (- (* b_2 b_2) (* a c)))
9.9b
(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
1.0b
(- (* b_2 b_2) (* a c))
0.3b
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac associate-*r* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×associate-*l* frac-sub unswap-sqr
4×frac-times associate-*l/ prod-exp insert-posit16
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod div-inv sub-div
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 distribute-rgt-out-- pow1/2 1-exp pow-prod-down *-commutative
Counts
4 → 98
Calls
4 calls:
Slowest
37.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
34.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(- (* b_2 b_2) (* a c))

series449.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
137.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)) (/ b_2 a))
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))
65.0ms
(- (* b_2 b_2) (* a c))

simplify1.8s

Counts
110 → 110

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.5b

regimes397.0ms

Accuracy

83.8% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.6b

bsearch210.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.4s1095×body2560valid
780.0ms5798×body80valid
598.0ms860×body1280valid
348.0ms485×body640valid
312.0ms2810×body80nan
89.0ms106×body5120valid
82.0ms247×body320valid
28.0ms129×body160valid