Details

Time bar (total: 1.9m)

sample173.0ms

Algorithm
intervals
Results
45.0ms143×body160valid
44.0ms304×body80nan
38.0ms560×pre80true
18.0ms113×body80valid

simplify146.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
145.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize19.0ms

Local error

Found 4 expressions with local error:

28.1b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(fma c (* -4 a) (* b b))
0.2b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite33.0ms

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 c (* -4 a) (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series425.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(sqrt (fma c (* -4 a) (* b b)))
127.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
114.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
56.0ms
(fma c (* -4 a) (* b b))

simplify14.6s

Counts
225 → 191
Calls
225 calls:
Slowest
429.0ms
(/ (/ (* (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)))
243.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
231.0ms
(/ (* (* (/ (- (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))
182.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)
170.0ms
(/ (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (cbrt 2)) (cbrt a))

prune2.2s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 25.8b

localize31.0ms

Local error

Found 4 expressions with local error:

27.3b
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
0.5b
(* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b))))
0.3b
(/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
0.3b
(fma c (* -4 a) (* b b))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×*-un-lft-identity
22×add-cube-cbrt
19×pow1
18×sqrt-prod
16×times-frac
8×sqrt-pow1 add-cbrt-cube pow1/2 swap-sqr add-exp-log
6×associate-*r* associate-*l* add-log-exp difference-of-squares
5×pow-prod-up distribute-lft-out
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u associate-/l* unswap-sqr
3×pow-prod-down pow-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow2 cbrt-undiv clear-num sub-neg rem-square-sqrt frac-2neg flip3-+ pow-plus fma-neg sqrt-unprod diff-log div-sub div-exp prod-diff prod-exp *-commutative cbrt-unprod flip-+ fma-udef div-inv
Counts
4 → 125
Calls
4 calls:
Slowest
29.0ms
(/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
27.0ms
(* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b))))
11.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
0.0ms
(fma c (* -4 a) (* b b))

series530.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
315.0ms
(/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
84.0ms
(fma c (* -4 a) (* b b))
69.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
62.0ms
(* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b))))

simplify23.6s

Counts
124 → 137
Calls
124 calls:
Slowest
1.2s
(/ (sqrt (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))) (cbrt (+ (sqrt (fma c (* -4 a) (* b b))) b)))
1.1s
(/ (sqrt (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))) (sqrt (+ (sqrt (fma c (* -4 a) (* b b))) b)))
1.1s
(/ (sqrt (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))) (sqrt (+ (sqrt (fma c (* -4 a) (* b b))) b)))
1.0s
(sqrt (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)))
1.0s
(/ (cbrt (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))) (sqrt (+ (sqrt (fma c (* -4 a) (* b b))) b)))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
0.3b
(fma c (* -4 a) (* b b))
0.2b
(+ (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (/ (/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
141×*-un-lft-identity
111×add-sqr-sqrt add-cube-cbrt
35×associate-/l*
33×add-cbrt-cube add-exp-log
26×associate-/r/
18×div-inv
15×cbrt-undiv div-exp distribute-lft-out
14×flip3-+ flip-+
7×associate-/r*
6×fma-def prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×sqrt-prod
2×clear-num frac-2neg
1×+-commutative sum-log fma-udef associate-/l/
Counts
4 → 225
Calls
4 calls:
Slowest
48.0ms
(/ (/ (/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)
23.0ms
(/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
9.0ms
(+ (sqrt (fma c (* -4 a) (* b b))) b)
0.0ms
(fma c (* -4 a) (* b b))

series697.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
252.0ms
(/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
227.0ms
(/ (/ (/ (* -4 (* a c)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)
134.0ms
(+ (sqrt (fma c (* -4 a) (* b b))) b)
84.0ms
(fma c (* -4 a) (* b b))

simplify59.5s

Counts
289 → 237
Calls
289 calls:
Slowest
1.1s
(/ (/ (/ (* (* (* -4 (* a c)) (* -4 (* a c))) (* -4 (* a c))) (* (* (+ (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))
1.0s
(/ (/ (/ (* (* (* -4 -4) -4) (* (* (* a c) (* a c)) (* a c))) (* (* (+ (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))
876.0ms
(/ (/ (/ (* (* (* -4 -4) -4) (* (* (* a a) a) (* (* c c) c))) (* (* (+ (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))
785.0ms
(/ (/ (/ (* a c) (+ (sqrt (fma c (* -4 a) (* b b))) b)) (sqrt 2)) a)
658.0ms
(/ (* (* (* -4 (* a c)) (* -4 (* a c))) (* -4 (* a c))) (* (* (+ (sqrt (fma c (* -4 a) (* b b))) b) (+ (sqrt (fma c (* -4 a) (* b b))) b)) (+ (sqrt (fma c (* -4 a) (* b b))) b)))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ c (+ b (sqrt (fma b b (* (* c a) -4)))))
0.2b
(+ b (sqrt (fma b b (* (* c a) -4))))
0.1b
(sqrt (fma b b (* (* c a) -4)))
0.0b
(fma b b (* (* c a) -4))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
16×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
3×fma-def sqrt-prod associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 div-exp fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
Slowest
10.0ms
(/ c (+ b (sqrt (fma b b (* (* c a) -4)))))
5.0ms
(+ b (sqrt (fma b b (* (* c a) -4))))
1.0ms
(sqrt (fma b b (* (* c a) -4)))
0.0ms
(fma b b (* (* c a) -4))

series525.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ c (+ b (sqrt (fma b b (* (* c a) -4)))))
128.0ms
(sqrt (fma b b (* (* c a) -4)))
125.0ms
(+ b (sqrt (fma b b (* (* c a) -4))))
65.0ms
(fma b b (* (* c a) -4))

simplify3.0s

Counts
55 → 93
Calls
55 calls:
Slowest
452.0ms
(/ (* (* c c) c) (* (* (+ b (sqrt (fma b b (* (* c a) -4)))) (+ b (sqrt (fma b b (* (* c a) -4))))) (+ b (sqrt (fma b b (* (* c a) -4))))))
309.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
287.0ms
(- b (* 2 (/ (* a c) b)))
282.0ms
(+ (* b b) (- (* (sqrt (fma b b (* (* c a) -4))) (sqrt (fma b b (* (* c a) -4)))) (* b (sqrt (fma b b (* (* c a) -4))))))
98.0ms
(- (pow b 2) (* 4 (* a c)))

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes221.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.6s8486×body80nan
1.4s4522×body160valid
1.1s16486×pre80true
497.0ms3478×body80valid