Details

Time bar (total: 44.0s)

sample159.0ms

Algorithm
intervals
Results
39.0ms106×body80nan
31.0ms191×body80valid
29.0ms35×body2560valid
27.0ms37×body1280valid
9.0ms16×body640valid
2.0ms4×body320valid
1.0ms1×body5120valid
1.0ms4×body160valid

simplify155.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize28.0ms

Local error

Found 3 expressions with local error:

20.3b
(sqrt (fma c (* -4 a) (* b b)))
0.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
134×add-sqr-sqrt
107×*-un-lft-identity
81×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
8×add-cbrt-cube add-exp-log
6×fma-neg
5×div-inv add-log-exp
4×pow1
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- associate-/l/
Counts
3 → 168
Calls
3 calls:
Slowest
17.0ms
(/ (/ (- (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)))

series327.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
103.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
89.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify14.2s

Counts
222 → 177
Calls
222 calls:
Slowest
425.0ms
(/ (/ (* (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)))
240.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
197.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
177.0ms
(/ (/ (* (* (- (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)) (* (* a a) a))
172.0ms
(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.6b

localize32.0ms

Local error

Found 3 expressions with local error:

20.3b
(sqrt (fma c (* -4 a) (* b b)))
0.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
34×times-frac
25×add-exp-log
22×associate-*l*
19×sqrt-prod
18×prod-diff
15×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp difference-of-squares
6×pow1 fma-neg unswap-sqr
5×add-log-exp
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rec-exp 1-exp div-inv
1×frac-times rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative flip--
Counts
3 → 127
Calls
3 calls:
Slowest
39.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series371.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
142.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
118.0ms
(sqrt (fma c (* -4 a) (* b b)))
111.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

simplify7.9s

Counts
123 → 136
Calls
123 calls:
Slowest
469.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- (log a)))
334.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
319.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
266.0ms
(* (/ (* (* (- (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)) (/ (* (* 1 1) 1) (* (* a a) a)))
262.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- 0 (log a)))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.6b

localize54.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma c (* -4 a) (* b b)))
20.3b
(sqrt (fma c (* -4 a) (* b b)))
0.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite26.0ms

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)
8.0ms
(- (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
116.0ms
(sqrt (fma c (* -4 a) (* b b)))
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
101.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
89.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify4.1s

Counts
116 → 128
Calls
116 calls:
Slowest
135.0ms
(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)))))
126.0ms
(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)))
119.0ms
(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)))))
112.0ms
(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)))) (- (* (sqrt b) (sqrt b))))

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.6b

localize44.0ms

Local error

Found 4 expressions with local error:

20.3b
(sqrt (fma c (* -4 a) (* b b)))
0.9b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.6b
(cbrt a)
0.6b
(cbrt a)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff
16×sqrt-prod
6×cbrt-prod fma-neg add-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×pow1/3 difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 86
Calls
4 calls:
Slowest
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(cbrt a)
1.0ms
(cbrt a)

series728.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
261.0ms
(cbrt a)
253.0ms
(cbrt a)
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
101.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify2.2s

Counts
70 → 98
Calls
70 calls:
Slowest
140.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
121.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
103.0ms
(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))))
100.0ms
(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)))))
96.0ms
(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)))

prune1.5s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 28.6b

regimes441.0ms

Accuracy

81.5% (1.0b remaining)

Error of 30.1b against oracle of 29.1b and baseline of 34.5b

bsearch116.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s5821×body80valid
1.1s1072×body2560valid
841.0ms935×body1280valid
413.0ms2839×body80nan
301.0ms428×body640valid
90.0ms233×body320valid
86.0ms92×body5120valid
67.0ms127×body160valid