Details

Time bar (total: 2.6m)

sample149.0ms

Algorithm
intervals
Results
40.0ms39×body2560valid
32.0ms183×body80valid
19.0ms23×body1280valid
16.0ms98×body80nan
12.0ms18×body640valid
4.0ms7×body320valid
3.0ms3×body5120valid
2.0ms5×body160valid

simplify194.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
193.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize23.0ms

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)

rewrite50.0ms

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
22.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
16.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
107.0ms
(sqrt (fma c (* -4 a) (* b b)))
105.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
99.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify17.5s

Counts
272 → 225
Calls
272 calls:
Slowest
521.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
448.0ms
(/ (/ (* (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)))
305.0ms
(- (pow (sqrt (fma c (* -4 a) (* b b))) 3) (pow b 3))
235.0ms
(/ (* (* (- (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))
228.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.4b

localize28.0ms

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)))

rewrite58.0ms

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
20.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
19.0ms
(/ (- (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)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(/ 1 (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
128.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
122.0ms
(/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)
103.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify1.9m

Counts
620 → 430
Calls
620 calls:
Slowest
817.0ms
(/ (sqrt 1) (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (cbrt 2))))
796.0ms
(/ (cbrt 1) (/ a (/ (- (sqrt (fma c (* -4 a) (* b b))) b) (cbrt 2))))
792.0ms
(/ (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)))))
775.0ms
(/ 1 (/ a (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (cbrt 2))))
628.0ms
(/ (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))))

prune5.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 31.4b

localize56.0ms

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)

rewrite32.0ms

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
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
10.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
105.0ms
(sqrt (fma c (* -4 a) (* b b)))
103.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
92.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify3.9s

Counts
116 → 128
Calls
116 calls:
Slowest
117.0ms
(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)))
108.0ms
(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)))
105.0ms
(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))))
104.0ms
(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)))))
94.0ms
(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)))))

prune2.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 31.4b

localize79.0ms

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)))

rewrite8.0ms

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
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(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)))

series873.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
278.0ms
(cbrt (fma c (* -4 a) (* b b)))
246.0ms
(cbrt (fma c (* -4 a) (* b b)))
239.0ms
(cbrt (fma c (* -4 a) (* b b)))
110.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify2.8s

Counts
26 → 70
Calls
26 calls:
Slowest
389.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
342.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
320.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
296.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
295.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.4s

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 31.4b

regimes459.0ms

Accuracy

89.3% (0.5b remaining)

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

bsearch189.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.4s5840×body80valid
1.2s1084×body2560valid
787.0ms915×body1280valid
598.0ms238×body320valid
455.0ms2882×body80nan
234.0ms442×body640valid
116.0ms124×body5120valid
37.0ms142×body160valid