Details

Time bar (total: 3.9m)

sample102.0ms

Algorithm
intervals
Results
37.0ms186×body80valid
19.0ms30×body2560valid
14.0ms28×body1280valid
9.0ms96×body80nan
7.0ms18×body640valid
3.0ms8×body320valid
1.0ms8×body160valid

simplify180.0ms

Calls
1 calls:
Slowest
180.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize48.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma (* a c) -4 (* b b)))
1.8b
(fma (* a c) -4 (* b b))
1.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
174×*-un-lft-identity
159×times-frac
118×add-cube-cbrt
60×prod-diff
47×sqrt-prod
35×distribute-rgt-neg-in
32×associate-/l*
28×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
17×associate-/l/
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1 div-inv
4×expm1-log1p-u div-sub insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp
2×associate--l- neg-sub0 clear-num frac-2neg flip3-- diff-log flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 neg-log fma-udef
Calls
4 calls:
Slowest
37.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
19.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series420.0ms

Calls
4 calls:
Slowest
135.0ms
(sqrt (fma (* a c) -4 (* b b)))
116.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
94.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
74.0ms
(fma (* a c) -4 (* b b))

simplify32.0s

Calls
345 calls:
Slowest
457.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
353.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
277.0ms
(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))))))))
263.0ms
(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))))))))
244.0ms
(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))))))))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize37.0ms

Local error

Found 3 expressions with local error:

25.6b
(sqrt (fma a (* c -4) (* b b)))
1.7b
(+ b (sqrt (fma a (* c -4) (* b b))))
0.2b
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
27×add-sqr-sqrt
21×add-cube-cbrt
20×distribute-neg-frac
18×frac-times
13×associate-*r*
12×associate-*l*
11×flip3-+ flip-+
10×times-frac associate-/l*
9×associate-/r* associate-*r/
8×add-cbrt-cube add-exp-log
6×pow1
5×add-log-exp
4×distribute-lft-neg-in clear-num distribute-rgt-neg-in
3×expm1-log1p-u fma-def frac-2neg sqrt-prod insert-posit16 log1p-expm1-u distribute-lft-out
2×associate-*l/ prod-exp un-div-inv cbrt-unprod unswap-sqr
1×distribute-lft-neg-out cbrt-undiv +-commutative rem-sqrt-square neg-mul-1 sum-log sqrt-pow1 pow1/2 div-exp pow-prod-down *-commutative div-inv
Calls
3 calls:
Slowest
51.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
5.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
1.0ms
(sqrt (fma a (* c -4) (* b b)))

series344.0ms

Calls
3 calls:
Slowest
128.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
125.0ms
(* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (/ 1/2 a))
90.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify11.5s

Calls
96 calls:
Slowest
542.0ms
(* (+ (* b b) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b (sqrt (fma a (* c -4) (* b b)))))) (- a))
424.0ms
(* (* (* (- (+ b (sqrt (fma a (* c -4) (* b b))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (- (+ b (sqrt (fma a (* c -4) (* b b)))))) (/ (* (* 1/2 1/2) 1/2) (* (* a a) a)))
408.0ms
(* (- (+ (pow b 3) (pow (sqrt (fma a (* c -4) (* b b))) 3))) (/ 1/2 (* (cbrt a) (cbrt a))))
363.0ms
(* (+ (* b b) (- (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))) (* b (sqrt (fma a (* c -4) (* b b)))))) (sqrt a))
341.0ms
(* (- (- (* b b) (* (sqrt (fma a (* c -4) (* b b))) (sqrt (fma a (* c -4) (* b b)))))) (/ 1/2 (* (cbrt a) (cbrt a))))

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize41.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma (* a c) -4 (* b b)))
25.6b
(sqrt (fma (* a c) -4 (* b b)))
11.7b
(- (- b) (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b))))))
1.8b
(fma (* a c) -4 (* b b))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
702×sqrt-prod
640×add-sqr-sqrt
470×prod-diff
288×*-un-lft-identity
280×add-cube-cbrt
159×swap-sqr
146×distribute-rgt-neg-in
144×distribute-lft-neg-in
99×unswap-sqr
92×associate-*l*
90×associate-*r*
48×neg-mul-1
21×difference-of-squares
11×*-commutative
10×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out--
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Calls
4 calls:
Slowest
56.0ms
(- (- b) (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b))))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series441.0ms

Calls
4 calls:
Slowest
129.0ms
(sqrt (fma (* a c) -4 (* b b)))
128.0ms
(sqrt (fma (* a c) -4 (* b b)))
124.0ms
(- (- b) (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b))))))
59.0ms
(fma (* a c) -4 (* b b))

simplify2.8m

Calls
1017 calls:
Slowest
617.0ms
(fma (- (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))))
610.0ms
(fma -1 b (- (* (* (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))))))
601.0ms
(fma (- (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))))
584.0ms
(fma (- (sqrt b)) (sqrt b) (- (* (* (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (* (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (cbrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))))))
541.0ms
(fma (- (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b)))))) (* (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt (sqrt (sqrt (fma (* a c) -4 (* b b))))))))

prune7.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize71.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (fma a (* c -4) (* b b)))
25.6b
(sqrt (fma a (* c -4) (* b b)))
25.6b
(sqrt (fma a (* c -4) (* b b)))
1.7b
(+ b (sqrt (fma a (* c -4) (* b b))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square fma-def sqrt-pow1 pow1/2
1×+-commutative sum-log flip3-+ flip-+ distribute-lft-out
Calls
4 calls:
Slowest
9.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
2.0ms
(sqrt (fma a (* c -4) (* b b)))
2.0ms
(sqrt (fma a (* c -4) (* b b)))
2.0ms
(sqrt (fma a (* c -4) (* b b)))

series432.0ms

Calls
4 calls:
Slowest
123.0ms
(+ b (sqrt (fma a (* c -4) (* b b))))
110.0ms
(sqrt (fma a (* c -4) (* b b)))
109.0ms
(sqrt (fma a (* c -4) (* b b)))
89.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify756.0ms

Calls
31 calls:
Slowest
226.0ms
(- (* 2 b) (* 2 (/ (* a c) b)))
99.0ms
(* 2 (/ (* a c) b))
46.0ms
(* (exp b) (exp (sqrt (fma a (* c -4) (* b b)))))
46.0ms
(sqrt (* (cbrt (fma a (* c -4) (* b b))) (cbrt (fma a (* c -4) (* b b)))))
43.0ms
(sqrt (sqrt (fma a (* c -4) (* b b))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes497.0ms

Accuracy

84.6% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 35.1b

bsearch807.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.2s1077×body2560valid
907.0ms5797×body80valid
859.0ms919×body1280valid
824.0ms3023×body80nan
377.0ms476×body640valid
168.0ms99×body5120valid
104.0ms251×body320valid
29.0ms106×body160valid