Details

Time bar (total: 28.9s)

sample146.0ms

Algorithm
intervals
Results
48.0ms181×body80valid
26.0ms27×body2560valid
20.0ms29×body1280valid
13.0ms106×body80nan
13.0ms21×body640valid
5.0ms10×body320valid
1.0ms1×body5120valid
1.0ms2×body160valid

simplify218.0ms

Calls
1 calls:
Slowest
218.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize30.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* a c) -4 (* b b)))
0.6b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate-/l*
2×div-sub div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef flip-- distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
12.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
5.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series236.0ms

Calls
4 calls:
Slowest
83.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
67.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
44.0ms
(sqrt (fma (* a c) -4 (* b b)))
42.0ms
(fma (* a c) -4 (* b b))

simplify4.7s

Calls
77 calls:
Slowest
133.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
119.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
105.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
103.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
100.0ms
(fma -1 b (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* a c) -4 (* b b)))
0.6b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity prod-diff
22×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u fma-neg associate-*r* associate-*l* insert-posit16 log1p-expm1-u
2×div-inv difference-of-squares
1×associate--l- neg-sub0 frac-times rem-sqrt-square sub-neg flip3-- pow1/2 diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ un-div-inv *-commutative cbrt-unprod fma-udef flip-- distribute-lft-out--
Calls
4 calls:
Slowest
22.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
11.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series215.0ms

Calls
4 calls:
Slowest
69.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
56.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
52.0ms
(sqrt (fma (* a c) -4 (* b b)))
38.0ms
(fma (* a c) -4 (* b b))

simplify6.1s

Calls
85 calls:
Slowest
301.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
251.0ms
(* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ 1 a))
227.0ms
(* (* (* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
169.0ms
(+ (log (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (log (/ 1 a)))
130.0ms
(fma 1 (- b) (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize42.0ms

Local error

Found 3 expressions with local error:

26.1b
(sqrt (fma a (* c -4) (* b b)))
0.5b
(+ b (sqrt (fma a (* c -4) (* b b))))
0.1b
(/ (+ b (sqrt (fma a (* c -4) (* b b)))) a)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u pow1 add-cbrt-cube add-exp-log sqrt-prod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×flip3-+ flip-+ associate-/l/
1×+-commutative rem-sqrt-square clear-num frac-2neg pow1/2 div-inv
Calls
3 calls:
Slowest
12.0ms
(/ (+ b (sqrt (fma a (* c -4) (* b b)))) a)
2.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
2.0ms
(sqrt (fma a (* c -4) (* b b)))

series179.0ms

Calls
3 calls:
Slowest
66.0ms
(/ (+ b (sqrt (fma a (* c -4) (* b b)))) a)
60.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
53.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify1.2s

Calls
17 calls:
Slowest
410.0ms
(- (* b b) (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))))
211.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
165.0ms
(+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))
117.0ms
(* 2 (/ (* a c) b))
104.0ms
(- (* 2 (/ b a)) (* 2 (/ c b)))

prune753.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

26.1b
(sqrt (fma (* a c) -4 (* b b)))
0.6b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
5×pow1 associate-/r* add-exp-log
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u
2×associate-/r/ div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef pow-flip flip-- distribute-lft-out-- inv-pow
Calls
4 calls:
Slowest
12.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
0.0ms
(fma (* a c) -4 (* b b))

series247.0ms

Calls
4 calls:
Slowest
83.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
65.0ms
(sqrt (fma (* a c) -4 (* b b)))
52.0ms
(fma (* a c) -4 (* b b))
46.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))

simplify5.2s

Calls
78 calls:
Slowest
131.0ms
(fma 1 (- b) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
119.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))
117.0ms
(cbrt (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
113.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
111.0ms
(fma -1 b (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune1.3s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.7b

regimes476.0ms

Accuracy

83.4% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 33.4b

bsearch205.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.2s944×body1280valid
1.1s5813×body80valid
1.1s1023×body2560valid
516.0ms106×body5120valid
408.0ms2870×body80nan
293.0ms467×body640valid
103.0ms230×body320valid
32.0ms115×body160valid