Details

Time bar (total: 53.1s)

sample228.0ms

Algorithm
intervals
Results
28.0ms199×body80valid
21.0ms25×body2560valid
18.0ms26×body1280valid
14.0ms81×body80nan
8.0ms14×body640valid
4.0ms10×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify121.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
81.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize40.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite214.0ms

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
131.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
48.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(- (* b_2 b_2) (* a c))

series419.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
117.0ms
(sqrt (- (* b_2 b_2) (* a c)))
112.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms
(- (* b_2 b_2) (* a c))

simplify6.0s

Counts
116 → 134
Calls
116 calls:
Slowest
523.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
312.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
310.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
299.0ms
(/ (* (* (- (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))
254.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize35.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite133.0ms

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
58.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
52.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
116.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))
55.0ms
(- (* b_2 b_2) (* a c))

simplify23.3s

Counts
247 → 212
Calls
247 calls:
Slowest
677.0ms
(/ (* (* 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))))
483.0ms
(- 0 (- (log a) (log (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
443.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
403.0ms
(+ (* (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)))
381.0ms
(/ 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))))

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize50.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
18.1b
(/ (- 0 (* a c)) a)
0.9b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))

rewrite86.0ms

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)
21.0ms
(/ (- 0 (* a c)) a)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
14.0ms
(- (* b_2 b_2) (* a c))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(/ (- 0 (* a c)) a)

simplify5.3s

Counts
57 → 102
Calls
57 calls:
Slowest
1.6s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
367.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
290.0ms
(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
271.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
255.0ms
(- (pow 0 3) (pow (* a c) 3))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

localize29.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (- (* b_2 b_2) (* a c)))
0.9b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b
(- (* b_2 b_2) (* a c))
0.2b
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite158.0ms

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
100.0ms
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms
(+ (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))

series468.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(* (- c) (/ 1 (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
91.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))
37.0ms
(- (* b_2 b_2) (* a c))

simplify5.0s

Counts
70 → 120
Calls
70 calls:
Slowest
539.0ms
(+ (* (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)))
468.0ms
(* (* (* (- 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))))
371.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
274.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
254.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

regimes374.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.1b

bsearch308.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s5890×body80valid
959.0ms892×body1280valid
873.0ms1031×body2560valid
326.0ms2856×body80nan
216.0ms426×body640valid
104.0ms227×body320valid
81.0ms101×body5120valid
25.0ms114×body160valid