Details

Time bar (total: 25.6s)

sample92.0ms

Algorithm
intervals
Results
55.0ms268×body80valid
17.0ms97×body80nan

simplify273.0ms

Calls
1 calls:
Slowest
272.0ms
(if (>= b 0) (/ (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)) (/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize120.0ms

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))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×*-un-lft-identity
24×prod-diff
23×add-cube-cbrt
22×sqrt-prod
10×fma-neg
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square sub-neg flip3-- pow1/2 flip-- difference-of-squares
1×associate--l- neg-sub0 diff-log distribute-lft-out--
Calls
4 calls:
Slowest
11.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
11.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms
(sqrt (fma (* -4 a) c (* b b)))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series444.0ms

Calls
4 calls:
Slowest
137.0ms
(sqrt (fma (* -4 a) c (* b b)))
106.0ms
(sqrt (fma (* -4 a) c (* b b)))
105.0ms
(- (- b) (sqrt (fma (* -4 a) c (* b b))))
95.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)

simplify5.0s

Calls
81 calls:
Slowest
128.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* -4 a) c (* b b))) 1)))
128.0ms
(fma -1 b (- (* (sqrt (fma (* -4 a) c (* b b))) (sqrt 1))))
125.0ms
(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))))))))
122.0ms
(fma 1 (- b) (- (* (sqrt (cbrt (fma (* -4 a) c (* b b)))) (sqrt (* (cbrt (fma (* -4 a) c (* b b))) (cbrt (fma (* -4 a) c (* b b))))))))
115.0ms
(fma 1 (- b) (- (* (sqrt (fma (* -4 a) c (* b b))) (sqrt 1))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize107.0ms

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)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube fma-neg add-exp-log sqrt-prod
4×expm1-log1p-u pow1 associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/
2×flip3-- div-inv flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg times-frac pow1/2 div-exp *-commutative associate-/l*
Calls
4 calls:
Slowest
22.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
12.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms
(* (/ c b) a)
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series326.0ms

Calls
4 calls:
Slowest
127.0ms
(sqrt (fma (* -4 a) c (* b b)))
110.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
68.0ms
(/ (* (- (* (/ c b) a) b) 2) (* 2 a))
21.0ms
(* (/ c b) a)

simplify2.6s

Calls
31 calls:
Slowest
737.0ms
(- (log (* (- (* (/ c b) a) b) 2)) (log (* 2 a)))
716.0ms
(/ (* (* (* (- (* (/ c b) a) b) 2) (* (- (* (/ c b) a) b) 2)) (* (- (* (/ c b) a) b) 2)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
353.0ms
(* (- (pow (* (/ c b) a) 3) (pow b 3)) 2)
206.0ms
(* (- (* (* (/ c b) a) (* (/ c b) a)) (* b b)) 2)
105.0ms
(/ (- (* (/ c b) a) b) 2)

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.8b

localize107.0ms

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))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
17×add-cube-cbrt
16×prod-diff
10×fma-neg div-inv
6×sqrt-prod add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×associate-/r* flip3-- flip--
2×sub-neg associate-/r/
1×rem-sqrt-square clear-num frac-2neg pow1/2 diff-log frac-sub distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
12.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
10.0ms
(- (/ c b) (/ b a))
6.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
2.0ms
(sqrt (fma (* -4 a) c (* b b)))

series488.0ms

Calls
4 calls:
Slowest
257.0ms
(/ c (- (sqrt (fma (* -4 a) c (* b b))) b))
99.0ms
(- (sqrt (fma (* -4 a) c (* b b))) b)
90.0ms
(sqrt (fma (* -4 a) c (* b b)))
42.0ms
(- (/ c b) (/ b a))

simplify2.8s

Calls
66 calls:
Slowest
157.0ms
(+ (* (sqrt (fma (* -4 a) c (* b b))) (sqrt (fma (* -4 a) c (* b b)))) (+ (* b b) (* (sqrt (fma (* -4 a) c (* b b))) b)))
115.0ms
(fma (* (cbrt (/ c b)) (cbrt (/ c b))) (cbrt (/ c b)) (- (* (/ 1 a) b)))
101.0ms
(fma c (/ 1 b) (- (* (/ b a) 1)))
101.0ms
(fma 1 (/ c b) (- (* (/ 1 a) b)))
95.0ms
(fma (sqrt (/ c b)) (sqrt (/ c b)) (- (* (/ b a) 1)))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

localize104.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* -4 a) c (* b b)))
20.2b
(cbrt (* (/ c b) a))
20.2b
(cbrt (* (/ c b) a))
20.2b
(cbrt (* (/ c b) a))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*l/ sqrt-prod
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
2.0ms
(cbrt (* (/ c b) a))
2.0ms
(cbrt (* (/ c b) a))
2.0ms
(cbrt (* (/ c b) a))
1.0ms
(sqrt (fma (* -4 a) c (* b b)))

series474.0ms

Calls
4 calls:
Slowest
138.0ms
(cbrt (* (/ c b) a))
114.0ms
(cbrt (* (/ c b) a))
112.0ms
(cbrt (* (/ c b) a))
110.0ms
(sqrt (fma (* -4 a) c (* b b)))

simplify2.5s

Calls
22 calls:
Slowest
324.0ms
(* (exp (* 1/3 (- (log (/ -1 b)) (+ (log (/ -1 c)) (log (/ -1 a)))))) (cbrt -1))
312.0ms
(exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c))))))
286.0ms
(exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c))))))
283.0ms
(* (exp (* 1/3 (- (log (/ -1 b)) (+ (log (/ -1 c)) (log (/ -1 a)))))) (cbrt -1))
278.0ms
(exp (* 1/3 (- (log (/ 1 b)) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.7b

regimes546.0ms

Accuracy

83.1% (1.4b remaining)

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

bsearch229.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.3s8735×body80valid
624.0ms2942×body80nan