Details

Time bar (total: 7.1m)

sample131.0ms

Algorithm
intervals
Results
48.0ms35×body2560valid
15.0ms182×body80valid
11.0ms29×body1280valid
6.0ms97×body80nan
4.0ms13×body640valid
1.0ms2×body5120valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify61.0ms

Calls
1 calls:
Slowest
61.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize19.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (- (* b_2 b_2) (* a c)))
0.8b
(- (* b_2 b_2) (* a c))
0.5b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×associate-/r* diff-log
2×sub-neg sqrt-div associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log div-inv
Calls
4 calls:
Slowest
98.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series433.0ms

Calls
4 calls:
Slowest
131.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
126.0ms
(sqrt (- (* b_2 b_2) (* a c)))
124.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
52.0ms
(- (* b_2 b_2) (* a c))

simplify16.2s

Calls
210 calls:
Slowest
464.0ms
(/ (* (* (- (- b_2) (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))))) (* (* a a) a))
377.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
310.0ms
(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
268.0ms
(fma (sqrt (- b_2)) (sqrt (- b_2)) (- (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))))))
244.0ms
(fma 1 (- b_2) (- (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))))))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize38.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (- (* b_2 b_2) (* a c)))
25.7b
(sqrt (- (* b_2 b_2) (* a c)))
25.7b
(sqrt (- (* b_2 b_2) (* a c)))
0.8b
(- (* b_2 b_2) (* a c))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div add-log-exp
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg fma-neg diff-log prod-diff
Calls
4 calls:
Slowest
14.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Calls
4 calls:
Slowest
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))
44.0ms
(- (* b_2 b_2) (* a c))

simplify3.5s

Calls
36 calls:
Slowest
434.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
410.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
379.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
271.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
214.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize31.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (- (* b_2 b_2) (* a c)))
5.7b
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
0.8b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
1339×times-frac
946×add-sqr-sqrt
940×*-un-lft-identity
926×add-cube-cbrt
749×prod-diff
323×sqrt-prod
210×distribute-rgt-neg-in
207×distribute-lft-neg-in
69×neg-mul-1
60×div-inv
35×fma-neg
8×add-log-exp
7×distribute-lft-out--
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- sqrt-div insert-posit16 log1p-expm1-u flip--
3×associate-/r*
2×sub-neg diff-log associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-sub div-exp frac-sub sub-div
Calls
4 calls:
Slowest
36.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
30.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
16.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series463.0ms

Calls
4 calls:
Slowest
152.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
145.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
104.0ms
(sqrt (- (* b_2 b_2) (* a c)))
62.0ms
(- (* b_2 b_2) (* a c))

simplify6.1m

Calls
1630 calls:
Slowest
781.0ms
(fma (/ (- (sqrt b_2)) (sqrt a)) (/ (sqrt b_2) (sqrt a)) (- (* (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
733.0ms
(fma (/ (- 1) (sqrt a)) (/ b_2 (sqrt a)) (- (* (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
730.0ms
(fma (/ 1 (sqrt a)) (/ (- b_2) (sqrt a)) (- (* (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (* (cbrt a) (cbrt a))))))
692.0ms
(fma (/ -1 1) (/ b_2 a) (- (* (/ (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt a)) (/ (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (sqrt a)))))
687.0ms
(fma (/ 1 (sqrt a)) (/ (- b_2) (sqrt a)) (- (* (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (* (cbrt a) (cbrt a))))))

prune10.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize31.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (- (* b_2 b_2) (* a c)))
9.6b
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
0.8b
(- (* b_2 b_2) (* a c))
0.3b
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
73×times-frac
69×add-sqr-sqrt
56×*-un-lft-identity
54×add-cube-cbrt
35×fma-neg prod-diff
18×distribute-lft-neg-in distribute-rgt-neg-in
13×associate-*r* add-exp-log
10×sqrt-div
9×add-cbrt-cube sqrt-prod
8×add-log-exp
7×pow1 flip3-- flip--
6×neg-mul-1 associate-*l* frac-sub unswap-sqr
4×expm1-log1p-u frac-times associate-*l/ prod-exp insert-posit16 log1p-expm1-u div-inv
3×associate-*r/ un-div-inv
2×sub-neg diff-log div-exp cbrt-unprod sub-div
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 distribute-rgt-out-- pow1/2 1-exp div-sub pow-prod-down *-commutative
Calls
4 calls:
Slowest
47.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
28.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
19.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Calls
4 calls:
Slowest
147.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
145.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))
63.0ms
(- (* b_2 b_2) (* a c))

simplify21.5s

Calls
184 calls:
Slowest
586.0ms
(* (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c)))) (/ (* (* 1 1) 1) (* (* a a) a)))
534.0ms
(/ (exp (/ (- b_2) a)) (exp (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))))
431.0ms
(fma (/ (- (* (cbrt b_2) (cbrt b_2))) 1) (/ (cbrt b_2) a) (- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))))
395.0ms
(* (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) 1)
391.0ms
(* (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3))) (/ 1 a))

prune2.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

regimes564.0ms

Accuracy

82.6% (5.0b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 34.2b

bsearch150.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s5836×body80valid
956.0ms1092×body2560valid
614.0ms424×body640valid
603.0ms925×body1280valid
310.0ms2941×body80nan
80.0ms105×body5120valid
72.0ms233×body320valid
26.0ms120×body160valid