Details

Time bar (total: 6.7m)

sample120.0ms

Algorithm
intervals
Results
30.0ms35×body2560valid
27.0ms182×body80valid
21.0ms29×body1280valid
13.0ms97×body80nan
8.0ms13×body640valid
2.0ms2×body5120valid
2.0ms5×body320valid
1.0ms2×body160valid

simplify104.0ms

Calls
1 calls:
Slowest
103.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize33.0ms

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)

rewrite161.0ms

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
84.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(- (* b_2 b_2) (* a c))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Calls
4 calls:
Slowest
106.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
104.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))
64.0ms
(- (* b_2 b_2) (* a c))

simplify16.2s

Calls
210 calls:
Slowest
433.0ms
(/ (* (* (- (- 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))
405.0ms
(fma (* (cbrt b_2) (cbrt b_2)) (- (cbrt b_2)) (- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
372.0ms
(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
363.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
292.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize31.0ms

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))

rewrite56.0ms

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
20.0ms
(sqrt (- (* b_2 b_2) (* a c)))
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
9.0ms
(- (* b_2 b_2) (* a c))

series318.0ms

Calls
4 calls:
Slowest
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))
85.0ms
(sqrt (- (* b_2 b_2) (* a c)))
79.0ms
(sqrt (- (* b_2 b_2) (* a c)))
49.0ms
(- (* b_2 b_2) (* a c))

simplify3.5s

Calls
36 calls:
Slowest
362.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
309.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
305.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
292.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
283.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize36.0ms

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)

rewrite138.0ms

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
49.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series409.0ms

Calls
4 calls:
Slowest
141.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
107.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
99.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(- (* b_2 b_2) (* a c))

simplify5.8m

Calls
1630 calls:
Slowest
777.0ms
(fma (/ (* (cbrt (- b_2)) (cbrt (- b_2))) 1) (/ (cbrt (- b_2)) a) (- (* (/ (sqrt (- (* b_2 b_2) (* a c))) (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
764.0ms
(fma (/ -1 (* (cbrt a) (cbrt a))) (/ b_2 (cbrt 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)))))
733.0ms
(fma (/ (- 1) (* (cbrt a) (cbrt a))) (/ b_2 (cbrt a)) (- (* (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (/ (sqrt (* (cbrt (- (* b_2 b_2) (* a c))) (cbrt (- (* b_2 b_2) (* a c))))) (* (cbrt a) (cbrt a))))))
688.0ms
(fma (/ (sqrt b_2) (* (cbrt a) (cbrt a))) (/ (- (sqrt b_2)) (cbrt a)) (- (* (cbrt (/ (sqrt (- (* b_2 b_2) (* a c))) a)) (* (cbrt (/ (sqrt (- (* b_2 b_2) (* a c))) a)) (cbrt (/ (sqrt (- (* b_2 b_2) (* a c))) a))))))
688.0ms
(fma (/ (- (sqrt b_2)) (* (cbrt a) (cbrt a))) (/ (sqrt b_2) (cbrt a)) (- (* (/ (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) (/ (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c))))) (* (cbrt a) (cbrt a))))))

prune8.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

localize24.0ms

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))

rewrite86.0ms

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
37.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
28.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series320.0ms

Calls
4 calls:
Slowest
113.0ms
(* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))
95.0ms
(- (/ (- b_2) a) (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a)))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))
40.0ms
(- (* b_2 b_2) (* a c))

simplify15.1s

Calls
184 calls:
Slowest
567.0ms
(fma (/ (- (* (cbrt b_2) (cbrt b_2))) 1) (/ (cbrt b_2) a) (- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))))
394.0ms
(* (* (* (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)))
336.0ms
(/ (exp (/ (- b_2) a)) (exp (* (sqrt (- (* b_2 b_2) (* a c))) (/ 1 a))))
278.0ms
(fma (/ (- 1) (* (cbrt a) (cbrt a))) (/ b_2 (cbrt a)) (- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))))
260.0ms
(fma (/ (* (cbrt b_2) (cbrt b_2)) (* (cbrt a) (cbrt a))) (/ (- (cbrt b_2)) (cbrt a)) (- (* (/ 1 a) (sqrt (- (* b_2 b_2) (* a c))))))

prune1.5s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

regimes382.0ms

Accuracy

82.6% (5.0b remaining)

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

bsearch121.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
940.0ms1092×body2560valid
574.0ms5836×body80valid
462.0ms925×body1280valid
225.0ms2941×body80nan
127.0ms424×body640valid
82.0ms105×body5120valid
54.0ms233×body320valid
41.0ms120×body160valid