Details

Time bar (total: 2.0m)

sample148.0ms

Algorithm
intervals
Results
44.0ms33×body1280valid
32.0ms192×body80valid
29.0ms30×body2560valid
12.0ms80×body80nan
10.0ms15×body640valid
3.0ms6×body320valid
1.0ms1×body5120valid

simplify164.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
164.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize46.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma b b (* (* a c) -4)))
0.3b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.3b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite32.0ms

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
16.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
10.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series398.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
103.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
99.0ms
(sqrt (fma b b (* (* a c) -4)))
76.0ms
(fma b b (* (* a c) -4))

simplify15.7s

Counts
225 → 191
Calls
225 calls:
Slowest
439.0ms
(- (pow b 2) (* 4 (* a c)))
356.0ms
(/ (/ (* (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)))
238.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
209.0ms
(- b (* 2 (/ (* a c) b)))
176.0ms
(/ (/ (* (* (- (sqrt (fma b b (* (* a c) -4))) b) (- (sqrt (fma b b (* (* a c) -4))) b)) (- (sqrt (fma b b (* (* a c) -4))) b)) (* (* 2 2) 2)) (* (* a a) a))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize32.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma (* -4 c) a (* b b)))
0.3b
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
0.1b
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) a)
0.0b
(fma (* -4 c) a (* b b))

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
476×*-un-lft-identity
264×times-frac
254×distribute-lft-out
113×add-sqr-sqrt
112×add-cube-cbrt
73×distribute-rgt-neg-in
40×associate-/l*
9×add-cbrt-cube add-exp-log
8×div-sub add-log-exp
6×fma-def sqrt-prod
5×pow1 div-inv
4×expm1-log1p-u associate-+l- insert-posit16 log1p-expm1-u
3×neg-sub0 cbrt-undiv associate-+r- associate-/r* div-exp
2×sum-log unsub-neg
1×+-commutative rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+ fma-udef associate-/l/
Counts
4 → 238
Calls
4 calls:
Slowest
260.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) a)
8.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))
0.0ms
(fma (* -4 c) a (* b b))

series427.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
115.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) a)
106.0ms
(sqrt (fma (* -4 c) a (* b b)))
64.0ms
(fma (* -4 c) a (* b b))

simplify1.4m

Counts
316 → 250
Calls
316 calls:
Slowest
1.5s
(/ (/ (* (* (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b))) (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b))) (* (* 2 2) 2)) (* (* a a) a))
860.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) (sqrt a))
809.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) 2) (cbrt a))
636.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) (sqrt 2)) (cbrt a))
629.0ms
(/ (/ (+ (+ (sqrt (fma (* -4 c) a (* b b))) (- b)) (+ (- b) b)) (cbrt 2)) (cbrt a))

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma (* -4 c) a (* b b)))
22.2b
(sqrt (fma (* -4 c) a (* b b)))
0.3b
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
0.3b
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
12×add-sqr-sqrt fma-def sqrt-prod add-log-exp
10×add-cube-cbrt
6×pow1
4×expm1-log1p-u sum-log add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out
2×neg-sub0 +-commutative rem-sqrt-square associate-+r- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 unsub-neg neg-log flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
15.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
12.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))
1.0ms
(sqrt (fma (* -4 c) a (* b b)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
123.0ms
(sqrt (fma (* -4 c) a (* b b)))
123.0ms
(+ (sqrt (fma (* -4 c) a (* b b))) (- b))
118.0ms
(sqrt (fma (* -4 c) a (* b b)))

simplify1.3s

Counts
40 → 96
Calls
40 calls:
Slowest
115.0ms
(* (exp (sqrt (fma (* -4 c) a (* b b)))) (exp (- b)))
100.0ms
(* (exp (sqrt (fma (* -4 c) a (* b b)))) (exp (- b)))
82.0ms
(* (exp (sqrt (fma (* -4 c) a (* b b)))) (/ 1 (exp b)))
78.0ms
(* (exp (sqrt (fma (* -4 c) a (* b b)))) (/ 1 (exp b)))
62.0ms
(* (cbrt (sqrt (fma (* -4 c) a (* b b)))) (cbrt (sqrt (fma (* -4 c) a (* b b)))))

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize48.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma b b (* (* a c) -4)))
22.2b
(sqrt (fma b b (* (* a c) -4)))
0.3b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.3b
(- (sqrt (fma b b (* (* a c) -4))) 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
10.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
7.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
1.0ms
(sqrt (fma b b (* (* a c) -4)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(sqrt (fma b b (* (* a c) -4)))
110.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
100.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
98.0ms
(sqrt (fma b b (* (* a c) -4)))

simplify5.6s

Counts
116 → 128
Calls
116 calls:
Slowest
388.0ms
(fma b b (* (* a c) -4))
283.0ms
(- b (* 2 (/ (* a c) b)))
220.0ms
(- b (* 2 (/ (* a c) b)))
141.0ms
(- (* 2 (/ (* a c) b)) b)
120.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

regimes413.0ms

Accuracy

85.4% (4.0b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 33.0b

bsearch241.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
866.0ms1032×body2560valid
793.0ms5872×body80valid
579.0ms891×body1280valid
562.0ms454×body640valid
410.0ms2868×body80nan
245.0ms272×body320valid
127.0ms96×body5120valid
26.0ms107×body160valid