Details

Time bar (total: 55.2s)

sample151.0ms

Algorithm
intervals
Results
39.0ms80×body80nan
19.0ms192×body80valid
17.0ms30×body2560valid
15.0ms33×body1280valid
5.0ms15×body640valid
1.0ms6×body320valid
1.0ms1×body5120valid

simplify474.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
474.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize18.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (- (* b_2 b_2) (* a c)))
0.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
Slowest
116.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
72.0ms
(- (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)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
113.0ms
(sqrt (- (* b_2 b_2) (* a c)))
105.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms
(- (* b_2 b_2) (* a c))

simplify6.1s

Counts
116 → 134
Calls
116 calls:
Slowest
528.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
385.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
353.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
284.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
283.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize33.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (- (* b_2 b_2) (* a c)))
0.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 200
Calls
4 calls:
Slowest
48.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series389.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
87.0ms
(sqrt (- (* b_2 b_2) (* a c)))
39.0ms
(- (* b_2 b_2) (* a c))

simplify24.9s

Counts
247 → 212
Calls
247 calls:
Slowest
673.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
450.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
445.0ms
(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
438.0ms
(/ (sqrt 1) (+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2))))
423.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))

prune2.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (- (* b_2 b_2) (* a c)))
12.1b
(/ (- 0 (* a c)) a)
1.2b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(- (* b_2 b_2) (* a c))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt
9×times-frac
8×add-log-exp
6×fma-def add-cbrt-cube add-exp-log sqrt-prod
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- flip-- associate-/l*
2×sqrt-div associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log div-sub div-exp prod-diff distribute-frac-neg flip-+ div-inv distribute-lft-out sub0-neg
Counts
4 → 90
Calls
4 calls:
Slowest
30.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
26.0ms
(/ (- 0 (* a c)) a)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
43.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(/ (- 0 (* a c)) a)

simplify5.4s

Counts
57 → 102
Calls
57 calls:
Slowest
1.5s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
363.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
310.0ms
(- (pow 0 3) (pow (* a c) 3))
269.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
267.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize25.0ms

Local error

Found 4 expressions with local error:

22.3b
(sqrt (- (* b_2 b_2) (* a c)))
1.2b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(- (* b_2 b_2) (* a c))
0.2b
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
26×add-sqr-sqrt
18×associate-*r* add-cube-cbrt
14×times-frac
13×add-exp-log
10×associate-*l*
9×add-cbrt-cube
8×add-log-exp
7×pow1
6×fma-def sqrt-prod
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u distribute-lft-out
3×distribute-lft-neg-in distribute-rgt-neg-in unswap-sqr
2×flip3-+ flip3-- sqrt-div div-exp associate-/r/ cbrt-unprod flip-+ flip--
1×distribute-lft-neg-out cbrt-undiv +-commutative rem-sqrt-square rec-exp neg-mul-1 sum-log sub-neg sqrt-pow1 pow1/2 fma-neg diff-log 1-exp prod-diff pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
Slowest
96.0ms
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
29.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series874.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
624.0ms
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
110.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms
(sqrt (- (* b_2 b_2) (* a c)))
51.0ms
(- (* b_2 b_2) (* a c))

simplify5.2s

Counts
70 → 120
Calls
70 calls:
Slowest
571.0ms
(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (- (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
446.0ms
(* (* (* (- c) (- c)) (- c)) (* (* (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
372.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
290.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
272.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes315.0ms

Accuracy

96.5% (0.8b remaining)

Error of 6.2b against oracle of 5.4b and baseline of 28.9b

bsearch282.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s5865×body80valid
829.0ms1034×body2560valid
618.0ms891×body1280valid
347.0ms2867×body80nan
260.0ms452×body640valid
150.0ms97×body5120valid
86.0ms272×body320valid
24.0ms113×body160valid