Details

Time bar (total: 4.3m)

sample104.0ms

Algorithm
intervals
Results
32.0ms139×body160valid
24.0ms277×body80nan
21.0ms533×pre80true
11.0ms117×body80valid

simplify142.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.3b

localize41.0ms

Local error

Found 4 expressions with local error:

27.1b
(- (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)))

rewrite63.0ms

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
33.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms
(- (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))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
121.0ms
(sqrt (fma c (* -4 a) (* b b)))
110.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
99.0ms
(fma c (* -4 a) (* b b))

simplify13.7s

Counts
225 → 191
Calls
225 calls:
Slowest
395.0ms
(/ (/ (* (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)))
233.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
198.0ms
(/ (* (* (/ (- (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))
191.0ms
(/ (/ (* (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)

prune2.2s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 24.6b

localize54.0ms

Local error

Found 4 expressions with local error:

26.3b
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
0.4b
(* (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
(/ (/ (/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
682×times-frac
399×*-un-lft-identity
305×add-sqr-sqrt
293×add-cube-cbrt
74×associate-/l*
54×difference-of-squares
53×distribute-lft-out
26×associate-/r/
19×pow1
18×sqrt-prod div-inv
17×add-cbrt-cube add-exp-log
13×flip3-+ flip-+
8×sqrt-pow1 pow1/2 swap-sqr
7×cbrt-undiv associate-/r* div-exp
6×associate-*r* associate-*l* add-log-exp
5×pow-prod-up
4×expm1-log1p-u div-sub insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log prod-diff prod-exp *-commutative cbrt-unprod
Counts
4 → 418
Calls
4 calls:
Slowest
53.0ms
(/ (/ (/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)
44.0ms
(/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
24.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
15.0ms
(* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b))))

series743.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(/ (/ (/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b)) 2) a)
288.0ms
(/ (- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b)) (+ (sqrt (fma c (* -4 a) (* b b))) b))
83.0ms
(- (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (* b b))
65.0ms
(* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b))))

simplify2.8m

Counts
623 → 430
Calls
623 calls:
Slowest
1.2s
(/ (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)))
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)))
1.1s
(/ (cbrt (- (* (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)))

prune5.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* c a) -4) (/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a))
0.3b
(/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a)
0.3b
(fma c (* -4 a) (* b b))
0.2b
(/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
157×*-un-lft-identity
107×add-sqr-sqrt add-cube-cbrt
58×associate-*r*
47×add-cbrt-cube add-exp-log
25×distribute-lft-out
21×associate-/l*
18×prod-exp cbrt-unprod
16×associate-/r/
13×pow1 cbrt-undiv div-exp
10×div-inv
8×flip3-+ flip-+
7×associate-/r*
6×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×associate-*l* associate-*r/ *-commutative fma-udef associate-/l/
Counts
4 → 232
Calls
4 calls:
Slowest
79.0ms
(* (* (* c a) -4) (/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a))
31.0ms
(/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a)
9.0ms
(/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))
0.0ms
(fma c (* -4 a) (* b b))

series581.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(* (* (* c a) -4) (/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a))
127.0ms
(/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))
120.0ms
(/ (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) a)
70.0ms
(fma c (* -4 a) (* b b))

simplify26.5s

Counts
256 → 244
Calls
256 calls:
Slowest
997.0ms
(* (* (* (* (* c c) c) (* (* a a) a)) (* (* -4 -4) -4)) (/ (* (* (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))) (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))) (* (* a a) a)))
836.0ms
(* (* (* (* (* c a) (* c a)) (* c a)) (* (* -4 -4) -4)) (/ (/ (* (* 1/2 1/2) 1/2) (* (* (+ b (sqrt (fma c (* -4 a) (* b b)))) (+ b (sqrt (fma c (* -4 a) (* b b))))) (+ b (sqrt (fma c (* -4 a) (* b b)))))) (* (* a a) a)))
797.0ms
(* (* (* (* (* c a) -4) (* (* c a) -4)) (* (* c a) -4)) (/ (/ (* (* 1/2 1/2) 1/2) (* (* (+ b (sqrt (fma c (* -4 a) (* b b)))) (+ b (sqrt (fma c (* -4 a) (* b b))))) (+ b (sqrt (fma c (* -4 a) (* b b)))))) (* (* a a) a)))
755.0ms
(* (* (* (* (* c a) -4) (* (* c a) -4)) (* (* c a) -4)) (/ (* (* (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b))))) (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))) (/ 1/2 (+ b (sqrt (fma c (* -4 a) (* b b)))))) (* (* a a) a)))
735.0ms
(* (* (* (* (* c c) c) (* (* a a) a)) (* (* -4 -4) -4)) (/ (/ (* (* 1/2 1/2) 1/2) (* (* (+ b (sqrt (fma c (* -4 a) (* b b)))) (+ b (sqrt (fma c (* -4 a) (* b b))))) (+ b (sqrt (fma c (* -4 a) (* b b)))))) (* (* a a) a)))

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
119×*-un-lft-identity
79×add-sqr-sqrt add-cube-cbrt
34×add-cbrt-cube add-exp-log
20×distribute-lft-out
19×associate-/l*
17×cbrt-undiv associate-/r* div-exp
14×div-inv
8×associate-/r/
6×fma-def add-log-exp
4×expm1-log1p-u pow1 prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sqrt-prod
2×clear-num frac-2neg flip3-+ flip-+
1×+-commutative sum-log fma-udef associate-/l/
Counts
4 → 201
Calls
4 calls:
Slowest
34.0ms
(/ (/ (* c a) (/ a -2)) (+ (sqrt (fma (* c a) -4 (* b b))) b))
21.0ms
(/ (* c a) (/ a -2))
6.0ms
(+ (sqrt (fma (* c a) -4 (* b b))) b)
0.0ms
(fma (* c a) -4 (* b b))

series499.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(/ (/ (* c a) (/ a -2)) (+ (sqrt (fma (* c a) -4 (* b b))) b))
112.0ms
(+ (sqrt (fma (* c a) -4 (* b b))) b)
96.0ms
(fma (* c a) -4 (* b b))
15.0ms
(/ (* c a) (/ a -2))

simplify31.5s

Counts
244 → 213
Calls
244 calls:
Slowest
839.0ms
(/ (/ c (/ (* (cbrt a) (cbrt a)) (* (cbrt -2) (cbrt -2)))) 1)
818.0ms
(/ (/ (* (* (* c a) (* c a)) (* c a)) (* (* (/ a -2) (/ a -2)) (/ a -2))) (* (* (+ (sqrt (fma (* c a) -4 (* b b))) b) (+ (sqrt (fma (* c a) -4 (* b b))) b)) (+ (sqrt (fma (* c a) -4 (* b b))) b)))
799.0ms
(- (- (+ (log c) (log a)) (log (/ a -2))) (log (+ (sqrt (fma (* c a) -4 (* b b))) b)))
768.0ms
(/ (/ (* (* (* c c) c) (* (* a a) a)) (* (* (/ a -2) (/ a -2)) (/ a -2))) (* (* (+ (sqrt (fma (* c a) -4 (* b b))) b) (+ (sqrt (fma (* c a) -4 (* b b))) b)) (+ (sqrt (fma (* c a) -4 (* b b))) b)))
758.0ms
(/ (/ (* (* (* c a) (* c a)) (* c a)) (/ (* (* a a) a) (* (* -2 -2) -2))) (* (* (+ (sqrt (fma (* c a) -4 (* b b))) b) (+ (sqrt (fma (* c a) -4 (* b b))) b)) (+ (sqrt (fma (* c a) -4 (* b b))) b)))

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes198.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.3s16552×pre80true
1.3s4471×body160valid
1.2s8552×body80nan
470.0ms3529×body80valid