Details

Time bar (total: 3.9m)

sample221.0ms

Algorithm
intervals
Results
59.0ms18×body640valid
28.0ms186×body80valid
27.0ms30×body2560valid
22.0ms28×body1280valid
12.0ms96×body80nan
4.0ms10×body320valid
2.0ms6×body160valid

simplify61.0ms

Calls
1 calls:
Slowest
60.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
587×add-sqr-sqrt
380×prod-diff
326×*-un-lft-identity
210×add-cube-cbrt
192×sqrt-prod
132×associate-*l*
130×difference-of-squares
112×unswap-sqr
84×associate-*r*
68×distribute-rgt-neg-in
63×distribute-lft-neg-in swap-sqr
58×distribute-lft-out--
52×*-commutative
25×fma-neg
21×neg-mul-1 times-frac
10×add-log-exp
7×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×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp neg-log div-inv
Calls
4 calls:
Slowest
200.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
47.0ms
(sqrt (- (* b_2 b_2) (* a c)))
34.0ms
(- (* b_2 b_2) (* a c))

series393.0ms

Calls
4 calls:
Slowest
131.0ms
(sqrt (- (* b_2 b_2) (* a c)))
106.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
95.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms
(- (* b_2 b_2) (* a c))

simplify1.1m

Calls
898 calls:
Slowest
447.0ms
(fma (- (* (sqrt a) c)) (sqrt a) (* (* (sqrt a) c) (sqrt a)))
377.0ms
(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
376.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
373.0ms
(/ (* (* (- (- 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))
311.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune6.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite461.0ms

Algorithm
rewrite-expression-head
Rules
587×add-sqr-sqrt
380×prod-diff
326×*-un-lft-identity
210×add-cube-cbrt
192×sqrt-prod
132×associate-*l*
130×difference-of-squares
112×unswap-sqr
84×associate-*r*
68×distribute-rgt-neg-in
63×distribute-lft-neg-in swap-sqr
58×distribute-lft-out--
52×*-commutative
25×fma-neg
21×neg-mul-1 times-frac
10×add-log-exp
7×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×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp neg-log div-inv
Calls
4 calls:
Slowest
286.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
81.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms
(- (* b_2 b_2) (* a c))
37.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series343.0ms

Calls
4 calls:
Slowest
124.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
113.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))
37.0ms
(- (* b_2 b_2) (* a c))

simplify1.2m

Calls
898 calls:
Slowest
475.0ms
(fma (- (sqrt (- (* (sqrt b_2) (sqrt b_2)) (* (sqrt a) (sqrt c))))) (sqrt (+ (* (sqrt b_2) (sqrt b_2)) (* (sqrt a) (sqrt c)))) (* (sqrt (- (* (sqrt b_2) (sqrt b_2)) (* (sqrt a) (sqrt c)))) (sqrt (+ (* (sqrt b_2) (sqrt b_2)) (* (sqrt a) (sqrt c))))))
454.0ms
(/ (* (* (- (- 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))
400.0ms
(- (* (- b_2) (- b_2)) (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))))
383.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
309.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune5.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

25.7b
(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))))))
1.7b
(- (- b_2) (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))
0.6b
(cbrt c)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
70×prod-diff
57×add-sqr-sqrt
50×add-cube-cbrt
45×sqrt-prod
25×distribute-rgt-neg-in
24×distribute-lft-neg-in
11×distribute-lft-out
10×fma-neg
8×neg-mul-1 add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod
2×sqrt-div diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 pow1/3 neg-log flip-+ fma-udef hypot-def flip--
Calls
4 calls:
Slowest
33.0ms
(- (- b_2) (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))
6.0ms
(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))))))

series637.0ms

Calls
4 calls:
Slowest
261.0ms
(cbrt c)
148.0ms
(sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))
132.0ms
(- (- b_2) (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))
96.0ms
(fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c))))))

simplify37.0s

Calls
179 calls:
Slowest
806.0ms
(fma (- (* (cbrt b_2) (cbrt b_2))) (cbrt b_2) (- (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))))))
491.0ms
(sqrt (+ (pow (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 3) (pow 0 3)))
405.0ms
(fma -1 b_2 (- (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))))))
397.0ms
(fma (- 1) b_2 (- (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))))))
390.0ms
(fma (sqrt (- b_2)) (sqrt (- b_2)) (- (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (* (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0))) (cbrt (sqrt (+ (fma b_2 b_2 (- (* (cbrt c) (* a (* (cbrt c) (cbrt c)))))) 0)))))))

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize54.0ms

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)))
1.8b
(- (* b_2 b_2) (* a c))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
276×add-sqr-sqrt
180×prod-diff
149×*-un-lft-identity
117×add-cube-cbrt
100×associate-*l*
84×associate-*r*
56×unswap-sqr
51×sqrt-prod
47×swap-sqr
40×difference-of-squares
36×*-commutative
16×distribute-lft-out--
15×fma-neg
7×pow1
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 diff-log
Calls
4 calls:
Slowest
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))
49.0ms
(- (* b_2 b_2) (* a c))
47.0ms
(sqrt (- (* b_2 b_2) (* a c)))
34.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series288.0ms

Calls
4 calls:
Slowest
97.0ms
(sqrt (- (* b_2 b_2) (* a c)))
78.0ms
(sqrt (- (* b_2 b_2) (* a c)))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))
47.0ms
(- (* b_2 b_2) (* a c))

simplify35.3s

Calls
471 calls:
Slowest
435.0ms
(fma (* (sqrt b_2) (sqrt b_2)) (* (sqrt b_2) (sqrt b_2)) (- (* a c)))
369.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
318.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
307.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
307.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))

prune4.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.5b

regimes460.0ms

Accuracy

84.2% (4.5b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.2b

bsearch380.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s5799×body80valid
955.0ms1077×body2560valid
552.0ms925×body1280valid
278.0ms3024×body80nan
262.0ms471×body640valid
80.0ms252×body320valid
73.0ms99×body5120valid
21.0ms104×body160valid