Details

Time bar (total: 1.7m)

sample139.0ms

Algorithm
intervals
Results
41.0ms39×body2560valid
29.0ms183×body80valid
17.0ms23×body1280valid
13.0ms98×body80nan
10.0ms18×body640valid
4.0ms3×body5120valid
3.0ms7×body320valid
2.0ms5×body160valid

simplify123.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
123.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize20.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (fma c (* -4 a) (* b b)))
1.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
156×times-frac
127×*-un-lft-identity
93×add-cube-cbrt
34×difference-of-squares
32×sqrt-prod
28×associate-/l*
18×prod-diff
17×distribute-lft-out--
11×add-cbrt-cube add-exp-log
6×associate-/r* fma-neg div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×div-sub associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 213
Calls
4 calls:
Slowest
36.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
17.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
103.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
102.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
96.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify14.5s

Counts
272 → 225
Calls
272 calls:
Slowest
415.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
303.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
294.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
213.0ms
(/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2))
169.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.4b

localize51.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (fma c (* -4 a) (* b b)))
1.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
0.2b
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
711×times-frac
479×add-sqr-sqrt
396×*-un-lft-identity
314×add-cube-cbrt
82×difference-of-squares
74×associate-/r*
56×sqrt-prod
41×distribute-lft-out--
27×add-exp-log
18×prod-diff div-inv
16×div-exp
15×add-cbrt-cube
9×associate-/l*
7×cbrt-undiv
6×pow1 fma-neg add-log-exp
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-sub pow-flip inv-pow
Counts
4 → 418
Calls
4 calls:
Slowest
21.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
20.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
98.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
94.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
93.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.2m

Counts
620 → 430
Calls
620 calls:
Slowest
631.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
516.0ms
(/ (cbrt 1) (/ a (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (cbrt 2))))
459.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
437.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
410.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2))))

prune3.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 31.4b

localize26.0ms

Local error

Found 4 expressions with local error:

23.0b
(sqrt (fma c (* -4 a) (* b b)))
23.0b
(sqrt (fma c (* -4 a) (* b b)))
1.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.8b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
Slowest
11.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
77.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
76.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
74.0ms
(sqrt (fma c (* -4 a) (* b b)))
71.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify2.2s

Counts
116 → 128
Calls
116 calls:
Slowest
65.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
64.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
58.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
57.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
53.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 31.4b

localize49.0ms

Local error

Found 4 expressions with local error:

23.8b
(cbrt (fma c (* -4 a) (* b b)))
23.8b
(cbrt (fma c (* -4 a) (* b b)))
23.8b
(cbrt (fma c (* -4 a) (* b b)))
23.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt (fma c (* -4 a) (* b b)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(cbrt (fma c (* -4 a) (* b b)))
168.0ms
(cbrt (fma c (* -4 a) (* b b)))
168.0ms
(cbrt (fma c (* -4 a) (* b b)))
75.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.7s

Counts
26 → 70
Calls
26 calls:
Slowest
208.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
207.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
206.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
174.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
173.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune853.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 31.4b

regimes276.0ms

Accuracy

89.3% (0.5b remaining)

Error of 29.9b against oracle of 29.4b and baseline of 34.0b

bsearch117.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
908.0ms1084×body2560valid
573.0ms5840×body80valid
479.0ms915×body1280valid
330.0ms238×body320valid
283.0ms2882×body80nan
201.0ms442×body640valid
95.0ms124×body5120valid
23.0ms142×body160valid