Details

Time bar (total: 2.8m)

sample123.0ms

Algorithm
intervals
Results
37.0ms189×body80valid
24.0ms30×body2560valid
21.0ms32×body1280valid
12.0ms99×body80nan
8.0ms15×body640valid
2.0ms4×body320valid
1.0ms5×body160valid
1.0ms1×body5120valid

simplify168.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
168.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize39.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma b b (* (* a c) -4)))
1.3b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
25.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
15.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
3.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series450.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
114.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
112.0ms
(sqrt (fma b b (* (* a c) -4)))
62.0ms
(fma b b (* (* a c) -4))

simplify16.1s

Counts
225 → 191
Calls
225 calls:
Slowest
427.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
263.0ms
(- b (* 2 (/ (* a c) b)))
234.0ms
(/ (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* a a) a))
224.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
211.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
32.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
8.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
102.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
99.0ms
(sqrt (fma (* a c) -4 (* b b)))
91.0ms
(fma (* a c) -4 (* b b))

simplify16.8s

Counts
225 → 191
Calls
225 calls:
Slowest
494.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) (cbrt a))
423.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
249.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
242.0ms
(/ (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
186.0ms
(/ (* (* (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)) (* (* a a) a))

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize44.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.6b
(fma (* a c) -4 (* b b))
0.2b
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
18×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
6×pow1 cbrt-undiv fma-neg add-log-exp
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 384
Calls
4 calls:
Slowest
30.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
17.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
114.0ms
(sqrt (fma (* a c) -4 (* b b)))
100.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
78.0ms
(fma (* a c) -4 (* b b))

simplify1.9m

Counts
573 → 396
Calls
573 calls:
Slowest
998.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
812.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2)))))
590.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* a c) -4 (* b b))) b))) 1)))
582.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (+ (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt b)) (sqrt 2))))
544.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (/ (sqrt (- (sqrt (fma (* a c) -4 (* b b))) b)) (sqrt 2))))

prune5.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (fma (* a c) -4 (* b b)))
20.7b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)

rewrite29.0ms

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
9.0ms
(sqrt (fma (* a c) -4 (* b b)))
8.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
8.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms
(sqrt (fma (* a c) -4 (* b b)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(sqrt (fma (* a c) -4 (* b b)))
113.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
111.0ms
(sqrt (fma (* a c) -4 (* b b)))
110.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)

simplify4.6s

Counts
116 → 128
Calls
116 calls:
Slowest
129.0ms
(fma (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (fma (* a c) -4 (* b b)))) (- (* b 1)))
124.0ms
(fma (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (fma (* a c) -4 (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
110.0ms
(fma (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (fma (* a c) -4 (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
98.0ms
(fma (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
97.0ms
(fma (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (fma (* a c) -4 (* b b)))) (- (* b 1)))

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.1b

regimes304.0ms

Accuracy

83.4% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.2b

bsearch225.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.3s5831×body80valid
1.1s1118×body2560valid
684.0ms879×body1280valid
394.0ms2896×body80nan
356.0ms462×body640valid
133.0ms109×body5120valid
124.0ms207×body320valid
32.0ms121×body160valid