Details

Time bar (total: 27.7s)

sample80.0ms

Algorithm
intervals
Results
18.0ms181×body80valid
16.0ms27×body2560valid
14.0ms29×body1280valid
9.0ms106×body80nan
8.0ms21×body640valid
3.0ms10×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify178.0ms

Calls
1 calls:
Slowest
178.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize47.0ms

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)

rewrite22.0ms

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
13.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
7.0ms
(- (- 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))

series248.0ms

Calls
4 calls:
Slowest
80.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
66.0ms
(sqrt (fma (* a c) -4 (* b b)))
55.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
47.0ms
(fma (* a c) -4 (* b b))

simplify5.0s

Calls
77 calls:
Slowest
141.0ms
(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))))))))
126.0ms
(fma -1 b (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))
123.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
119.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
115.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize8.0ms

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))

rewrite20.0ms

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
12.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
6.0ms
(- (- 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))

series200.0ms

Calls
4 calls:
Slowest
65.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
51.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
42.0ms
(fma (* a c) -4 (* b b))
41.0ms
(sqrt (fma (* a c) -4 (* b b)))

simplify5.2s

Calls
85 calls:
Slowest
281.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
221.0ms
(+ (log (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (log (/ 1 a)))
209.0ms
(* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ 1 a))
171.0ms
(* (* (* (/ (- (- 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)))
107.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize27.0ms

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)

rewrite10.0ms

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
7.0ms
(/ (+ b (sqrt (fma a (* c -4) (* b b)))) a)
1.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
1.0ms
(sqrt (fma a (* c -4) (* b b)))

series167.0ms

Calls
3 calls:
Slowest
60.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
60.0ms
(/ (+ b (sqrt (fma a (* c -4) (* b b)))) a)
47.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify1.1s

Calls
17 calls:
Slowest
339.0ms
(- (* b b) (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))))
249.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
128.0ms
(+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))
95.0ms
(- (* 2 (/ b a)) (* 2 (/ c b)))
89.0ms
(* 2 (/ (* a c) b))

prune720.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize12.0ms

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)))

rewrite18.0ms

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
13.0ms
(- (- 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))

series232.0ms

Calls
4 calls:
Slowest
80.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
72.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
46.0ms
(sqrt (fma (* a c) -4 (* b b)))
34.0ms
(fma (* a c) -4 (* b b))

simplify5.4s

Calls
78 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))))))))
121.0ms
(fma 1 (- b) (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))
116.0ms
(cbrt (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
115.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
115.0ms
(fma 1 (- b) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))

prune1.4s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.7b

regimes489.0ms

Accuracy

83.4% (4.6b remaining)

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

bsearch190.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s1023×body2560valid
866.0ms5813×body80valid
751.0ms944×body1280valid
614.0ms467×body640valid
446.0ms2870×body80nan
101.0ms106×body5120valid
91.0ms230×body320valid
52.0ms115×body160valid