Details

Time bar (total: 45.6s)

sample211.0ms

Algorithm
intervals
Results
47.0ms140×body160valid
46.0ms297×body80nan
40.0ms553×pre80true
19.0ms116×body80valid

simplify141.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize31.0ms

Local error

Found 4 expressions with local error:

29.0b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.3b
(fma c (* -4 a) (* b b))
0.1b
(sqrt (fma c (* -4 a) (* b b)))

rewrite42.0ms

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
22.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
12.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series401.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
104.0ms
(sqrt (fma c (* -4 a) (* b b)))
104.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
63.0ms
(fma c (* -4 a) (* b b))

simplify15.5s

Counts
225 → 191
Calls
225 calls:
Slowest
436.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
374.0ms
(/ (/ (* (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)))
256.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
225.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
186.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.3s

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 26.5b

localize46.0ms

Local error

Found 4 expressions with local error:

29.0b
(- (sqrt (fma b b (* (* a -4) c))) b)
0.4b
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
Slowest
25.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
7.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series484.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1/2 a))
133.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)
110.0ms
(sqrt (fma b b (* (* a -4) c)))
62.0ms
(fma b b (* (* a -4) c))

simplify5.8s

Counts
96 → 123
Calls
96 calls:
Slowest
472.0ms
(* (- (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (* b b)) 1/2)
373.0ms
(* (+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (+ (* b b) (* (sqrt (fma b b (* (* a -4) c))) b))) a)
248.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) (/ 1/2 a))
242.0ms
(- b (* 2 (/ (* a c) b)))
242.0ms
(* (- (pow (sqrt (fma b b (* (* a -4) c))) 3) (pow b 3)) 1/2)

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.2b
(* (/ 1/2 a) (fma a (* c -4) 0))
0.1b
(sqrt (fma b b (* (* a -4) c)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
18×add-cbrt-cube add-exp-log
17×add-cube-cbrt
14×times-frac
13×associate-*l*
7×pow1
6×fma-def sqrt-prod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-*r* distribute-lft-out
2×flip3-+ associate-*l/ associate-/r/ flip-+ fma-udef div-inv unswap-sqr
1×distribute-rgt-in +-commutative rem-sqrt-square clear-num sum-log frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative associate-/l* associate-/l/
Counts
4 → 105
Calls
4 calls:
Slowest
35.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
11.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
9.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))
1.0ms
(sqrt (fma b b (* (* a -4) c)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
322.0ms
(/ (* (/ 1/2 a) (fma a (* c -4) 0)) (+ (sqrt (fma b b (* (* a -4) c))) b))
143.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
117.0ms
(sqrt (fma b b (* (* a -4) c)))
74.0ms
(* (/ 1/2 a) (fma a (* c -4) 0))

simplify7.1s

Counts
72 → 117
Calls
72 calls:
Slowest
1.0s
(* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0)))
553.0ms
(/ (* (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
531.0ms
(/ (* (* (* (/ 1/2 a) (fma a (* c -4) 0)) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (/ 1/2 a) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
424.0ms
(/ (* (* (* (/ 1/2 a) (/ 1/2 a)) (/ 1/2 a)) (* (* (fma a (* c -4) 0) (fma a (* c -4) 0)) (fma a (* c -4) 0))) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
400.0ms
(+ (- (log 1/2) (log a)) (log (fma a (* c -4) 0)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
0.2b
(+ (sqrt (fma b b (* (* a -4) c))) b)
0.1b
(sqrt (fma b b (* (* a -4) c)))
0.0b
(fma b b (* (* a -4) c))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log add-cube-cbrt
6×fma-def sqrt-prod add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* times-frac insert-posit16 log1p-expm1-u
3×distribute-lft-out
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
Slowest
25.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
6.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
1.0ms
(sqrt (fma b b (* (* a -4) c)))
0.0ms
(fma b b (* (* a -4) c))

series579.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
255.0ms
(/ (* -2 c) (+ (sqrt (fma b b (* (* a -4) c))) b))
136.0ms
(sqrt (fma b b (* (* a -4) c)))
130.0ms
(+ (sqrt (fma b b (* (* a -4) c))) b)
58.0ms
(fma b b (* (* a -4) c))

simplify2.8s

Counts
42 → 88
Calls
42 calls:
Slowest
339.0ms
(+ (* (sqrt (fma b b (* (* a -4) c))) (sqrt (fma b b (* (* a -4) c)))) (- (* b b) (* (sqrt (fma b b (* (* a -4) c))) b)))
300.0ms
(/ (* (* (* -2 c) (* -2 c)) (* -2 c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
275.0ms
(/ (* (* (* -2 -2) -2) (* (* c c) c)) (* (* (+ (sqrt (fma b b (* (* a -4) c))) b) (+ (sqrt (fma b b (* (* a -4) c))) b)) (+ (sqrt (fma b b (* (* a -4) c))) b)))
260.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
203.0ms
(- b (* 2 (/ (* a c) b)))

prune911.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes275.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.7s4491×body160valid
1.5s16678×pre80true
1.2s8678×body80nan
506.0ms3509×body80valid