Details

Time bar (total: 1.9m)

sample113.0ms

Algorithm
intervals
Results
61.0ms268×body80valid
19.0ms97×body80nan

simplify309.0ms

Calls
1 calls:
Slowest
309.0ms
(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize145.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* -4 a) c (* b b)))
25.7b
(sqrt (fma (* -4 a) c (* b b)))
1.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.5b
(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Calls
4 calls:
Slowest
27.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
15.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms
(sqrt (fma (* -4 a) c (* b b)))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series450.0ms

Calls
4 calls:
Slowest
127.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
115.0ms
(sqrt (fma (* -4 a) c (* b b)))
107.0ms
(sqrt (fma (* -4 a) c (* b b)))
101.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)

simplify15.7s

Calls
204 calls:
Slowest
249.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
248.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
246.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
237.0ms
(fma (- 1) b (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))
235.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize139.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* -4 a) c (* b b)))
3.9b
(* (/ c b) a)
3.6b
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
1.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
21×add-cbrt-cube add-exp-log
18×prod-diff
16×sqrt-prod
13×associate-*l*
11×times-frac
7×pow1
6×fma-neg prod-exp cbrt-unprod add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l/
2×flip3-- div-inv flip-- difference-of-squares unswap-sqr associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down *-commutative associate-/l* distribute-lft-out--
Calls
4 calls:
Slowest
27.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
10.0ms
(* (/ c b) a)
8.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms
(sqrt (fma (* -4 a) c (* b b)))

series298.0ms

Calls
4 calls:
Slowest
130.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
88.0ms
(sqrt (fma (* -4 a) c (* b b)))
48.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
32.0ms
(* (/ c b) a)

simplify11.4s

Calls
100 calls:
Slowest
2.4s
(/ (* (* (* (- (* (/ c b) a) b) (- (* (/ c b) a) b)) (- (* (/ c b) a) b)) (* (* 2 2) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.7s
(/ (* (* (* (- (* (/ c b) a) b) (- (* (/ c b) a) b)) (- (* (/ c b) a) b)) (* (* 2 2) 2)) (* (* (* 2 2) 2) (* (* a a) a)))
911.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 2) 2) (* (* a a) a)))
844.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
801.0ms
(- (log (* (- (* (/ c b) a) b) 2)) (log (* 2 a)))

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.8b

localize133.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* -4 a) c (* b b)))
1.5b
(- (sqrt (fma (* -4 a) c (* b b))) b)
0.3b
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
0.0b
(- (/ c b) (/ b a))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
267×times-frac
252×add-sqr-sqrt
235×*-un-lft-identity
219×add-cube-cbrt
187×prod-diff
28×div-inv
20×sqrt-prod
19×fma-neg
14×difference-of-squares
8×add-log-exp
7×distribute-lft-out--
6×associate-/r* add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-- flip-- associate-/l*
2×sub-neg diff-log associate-/r/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp frac-sub
Calls
4 calls:
Slowest
33.0ms
(- (/ c b) (/ b a))
17.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
8.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series534.0ms

Calls
4 calls:
Slowest
273.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
123.0ms
(sqrt (fma (* -4 a) c (* b b)))
106.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
32.0ms
(- (/ c b) (/ b a))

simplify1.1m

Calls
475 calls:
Slowest
911.0ms
(fma 1 (/ c b) (- (* (/ b (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
654.0ms
(fma (- (/ (cbrt b) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (* (/ (cbrt b) (cbrt a)) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a)))))
631.0ms
(fma (/ (sqrt c) 1) (/ (sqrt c) b) (- (* (/ b (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
596.0ms
(fma (/ 1 1) (/ c b) (- (* (/ b (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))
534.0ms
(fma (/ (sqrt c) (sqrt b)) (/ (sqrt c) (sqrt b)) (- (* (/ b (cbrt a)) (/ 1 (* (cbrt a) (cbrt a))))))

prune4.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

localize147.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* -4 a) c (* b b)))
13.7b
(cbrt (/ c b))
13.7b
(cbrt (/ c b))
13.7b
(cbrt (/ c b))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
1.0ms
(cbrt (/ c b))
1.0ms
(cbrt (/ c b))
1.0ms
(cbrt (/ c b))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series374.0ms

Calls
4 calls:
Slowest
105.0ms
(sqrt (fma (* -4 a) c (* b b)))
92.0ms
(cbrt (/ c b))
91.0ms
(cbrt (/ c b))
86.0ms
(cbrt (/ c b))

simplify2.9s

Calls
59 calls:
Slowest
352.0ms
(exp (* 1/3 (- (log (/ -1 b)) (log (/ -1 c)))))
340.0ms
(exp (* 1/3 (- (log (/ -1 b)) (log (/ -1 c)))))
333.0ms
(exp (* 1/3 (- (log (/ -1 b)) (log (/ -1 c)))))
232.0ms
(exp (* 1/3 (- (log c) (log b))))
219.0ms
(exp (* 1/3 (- (log (/ 1 b)) (log (/ 1 c)))))

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

regimes503.0ms

Accuracy

83.2% (1.4b remaining)

Error of 13.7b against oracle of 12.3b and baseline of 20.5b

bsearch149.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.4s8735×body80valid
546.0ms2942×body80nan