Details

Time bar (total: 3.4m)

sample213.0ms

Algorithm
intervals
Results
71.0ms179×body80valid
32.0ms41×body2560valid
19.0ms27×body1280valid
12.0ms95×body80nan
7.0ms14×body640valid
4.0ms4×body5120valid
2.0ms6×body320valid
1.0ms3×body160valid

simplify111.0ms

Calls
1 calls:
Slowest
110.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize37.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.8b
(- (* b_2 b_2) (* a c))
0.8b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
381×add-sqr-sqrt
240×prod-diff
212×*-un-lft-identity
154×add-cube-cbrt
108×associate-*l*
90×sqrt-prod
84×associate-*r*
70×difference-of-squares unswap-sqr
51×swap-sqr
40×*-commutative
35×fma-neg
29×distribute-lft-out--
18×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1
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
Calls
4 calls:
Slowest
399.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
187.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
54.0ms
(- (* b_2 b_2) (* a c))

series320.0ms

Calls
4 calls:
Slowest
109.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
90.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms
(sqrt (- (* b_2 b_2) (* a c)))
38.0ms
(- (* b_2 b_2) (* a c))

simplify39.4s

Calls
621 calls:
Slowest
581.0ms
(fma (* b_2 (* (cbrt b_2) (cbrt b_2))) (cbrt b_2) (- (* (* (cbrt a) c) (* (cbrt a) (cbrt a)))))
496.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
328.0ms
(/ (* (* (- (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))
325.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
311.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune4.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize46.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))
2.3b
(fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c))))))
0.8b
(- (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) b_2)
0.6b
(cbrt c)

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
28×add-sqr-sqrt
21×prod-diff add-cube-cbrt sqrt-prod
7×fma-neg
6×add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod
2×sqrt-div difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 pow1/3 diff-log flip-+ fma-udef hypot-def flip-- distribute-lft-out--
Calls
4 calls:
Slowest
66.0ms
(- (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) b_2)
11.0ms
(sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))
1.0ms
(cbrt c)
0.0ms
(fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c))))))

series688.0ms

Calls
4 calls:
Slowest
295.0ms
(cbrt c)
170.0ms
(- (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) b_2)
157.0ms
(sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))
66.0ms
(fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c))))))

simplify8.8s

Calls
78 calls:
Slowest
422.0ms
(sqrt (+ (pow (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 3) (pow 0 3)))
289.0ms
(fma (sqrt (* (cbrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) (cbrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))) (sqrt (cbrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (- (* b_2 1)))
283.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
248.0ms
(fma 1 (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) (- (* (sqrt b_2) (sqrt b_2))))
238.0ms
(sqrt (* (cbrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)) (cbrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

localize45.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (- (* b_2 b_2) (* a c)))
15.9b
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.8b
(- (* b_2 b_2) (* a c))
1.7b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)

rewrite781.0ms

Algorithm
rewrite-expression-head
Rules
548×add-sqr-sqrt
386×*-un-lft-identity
364×times-frac
302×add-cube-cbrt
284×associate-*r*
267×associate-*l*
180×prod-diff
168×distribute-lft-neg-in distribute-rgt-neg-in
106×unswap-sqr
91×*-commutative
45×swap-sqr
34×sqrt-prod
30×distribute-lft-out difference-of-squares
28×associate-/l*
20×fma-def
15×fma-neg
14×neg-mul-1
13×associate-/r*
12×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp associate-*r/ associate-/r/ flip-+ flip--
1×neg-sub0 +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp distribute-frac-neg cbrt-unprod div-inv
Calls
4 calls:
Slowest
483.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
163.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))
42.0ms
(- (* b_2 b_2) (* a c))

series453.0ms

Calls
4 calls:
Slowest
237.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
88.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms
(sqrt (- (* b_2 b_2) (* a c)))
45.0ms
(- (* b_2 b_2) (* a c))

simplify1.6m

Calls
1220 calls:
Slowest
1.9s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.4s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* 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))))
568.0ms
(/ (- (* (sqrt a) (sqrt c))) (* (sqrt a) (sqrt (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
567.0ms
(/ (- (* (sqrt a) (sqrt c))) (* (sqrt a) (sqrt (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
553.0ms
(/ (- (* (sqrt a) (sqrt c))) (* (sqrt a) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))

prune7.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (- (* b_2 b_2) (* a c)))
1.8b
(- (* b_2 b_2) (* a c))
1.7b
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.1b
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
232×add-sqr-sqrt
180×prod-diff
151×*-un-lft-identity
125×add-cube-cbrt
92×associate-*l*
84×associate-*r*
43×swap-sqr
42×unswap-sqr
32×*-commutative
20×difference-of-squares
17×sqrt-prod
15×fma-neg
12×times-frac
8×distribute-lft-out-- add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×fma-def associate-/l*
2×flip3-+ flip3-- sqrt-div associate-/r/ flip-+ flip--
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-exp div-inv
Calls
4 calls:
Slowest
144.0ms
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
45.0ms
(- (* b_2 b_2) (* a c))
35.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series474.0ms

Calls
4 calls:
Slowest
221.0ms
(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
101.0ms
(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
101.0ms
(sqrt (- (* b_2 b_2) (* a c)))
51.0ms
(- (* b_2 b_2) (* a c))

simplify34.9s

Calls
467 calls:
Slowest
624.0ms
(- (* 2 b_2) (* 1/2 (/ (* a c) b_2)))
356.0ms
(/ (* (* c c) c) (* (* (+ 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))))))
317.0ms
(+ (* b_2 b_2) (- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 (sqrt (- (* b_2 b_2) (* a c))))))
311.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
282.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune3.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.3b

regimes495.0ms

Accuracy

94.1% (1.4b remaining)

Error of 7.1b against oracle of 5.7b and baseline of 30.1b

bsearch322.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
999.0ms888×body1280valid
862.0ms1073×body2560valid
689.0ms5853×body80valid
359.0ms3021×body80nan
223.0ms454×body640valid
77.0ms101×body5120valid
71.0ms244×body320valid
48.0ms107×body160valid