Details

Time bar (total: 3.4m)

sample91.0ms

Algorithm
intervals
Results
24.0ms41×body2560valid
19.0ms189×body80valid
12.0ms25×body1280valid
8.0ms91×body80nan
7.0ms11×body640valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify155.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize19.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma b b (* (* a c) -4)))
1.3b
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite34.0ms

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
21.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
8.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
146.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
123.0ms
(sqrt (fma b b (* (* a c) -4)))
80.0ms
(fma b b (* (* a c) -4))

simplify21.3s

Counts
282 → 191
Calls
282 calls:
Slowest
610.0ms
(* (* (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a) (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)) (/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a))
515.0ms
(- (* (sqrt (fma b b (* (* a c) -4))) (sqrt (fma b b (* (* a c) -4)))) (* b b))
436.0ms
(- (pow (sqrt (fma b b (* (* a c) -4))) 3) (pow b 3))
386.0ms
(/ (/ (* (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)))
292.0ms
(* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b))

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize41.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.8b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)

rewrite36.0ms

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
23.0ms
(/ (/ (- (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))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
135.0ms
(sqrt (fma (* a c) -4 (* b b)))
102.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
72.0ms
(fma (* a c) -4 (* b b))

simplify21.7s

Counts
282 → 191
Calls
282 calls:
Slowest
646.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))
602.0ms
(* (* (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a) (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)) (/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a))
443.0ms
(/ (/ (* (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)))
409.0ms
(- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3))
334.0ms
(* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b))

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize47.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma (* a c) -4 (* b b)))
1.3b
(- (sqrt (fma (* a c) -4 (* b b))) b)
0.8b
(fma (* a c) -4 (* b b))
0.2b
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite43.0ms

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
16.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
9.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
7.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series498.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
120.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
119.0ms
(sqrt (fma (* a c) -4 (* b b)))
83.0ms
(fma (* a c) -4 (* b b))

simplify2.2m

Counts
632 → 396
Calls
632 calls:
Slowest
1.6s
(* (* (/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))) (/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))) (/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2))))
846.0ms
(/ (sqrt 1) (/ a (/ (- (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt b)) (cbrt 2))))
840.0ms
(/ (cbrt 1) (/ a (/ (- (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt b)) (sqrt 2))))
766.0ms
(/ (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)))))
707.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))

prune5.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize36.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma (* a c) -4 (* b b)))
21.6b
(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)

rewrite34.0ms

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 (* a c) -4 (* b b))) b)
13.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(sqrt (fma (* a c) -4 (* b b)))
115.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
108.0ms
(- (sqrt (fma (* a c) -4 (* b b))) b)
96.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify9.6s

Counts
174 → 128
Calls
174 calls:
Slowest
813.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))
656.0ms
(- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* b b))
371.0ms
(- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3))
368.0ms
(- (pow (sqrt (fma (* a c) -4 (* b b))) 3) (pow b 3))
344.0ms
(* (* (- (sqrt (fma (* a c) -4 (* b b))) b) (- (sqrt (fma (* a c) -4 (* b b))) b)) (- (sqrt (fma (* a c) -4 (* b b))) b))

prune2.0s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes389.0ms

Accuracy

87.1% (3.5b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 33.1b

bsearch338.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.4s1061×body2560valid
933.0ms5869×body80valid
727.0ms439×body640valid
674.0ms877×body1280valid
421.0ms2830×body80nan
127.0ms103×body5120valid
93.0ms239×body320valid
28.0ms116×body160valid