Details

Time bar (total: 1.1m)

sample127.0ms

Algorithm
intervals
Results
100.0ms674×body80valid

simplify202.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
202.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (+ (* a a) (* b b)) 2)
0.0b
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
0.0b
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b
(* 4 (* b b))

rewrite463.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity
16×add-cube-cbrt
11×add-exp-log add-log-exp
10×pow1
9×add-cbrt-cube prod-diff
8×fma-def
6×unpow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-unpow fma-neg associate-*l* pow-prod-down prod-exp cbrt-unprod
2×sum-log diff-log unpow2 difference-of-squares sqr-pow
1×pow-to-exp +-commutative expm1-def sub-neg pow-pow flip3-+ flip3-- difference-of-sqr-1 associate-*r* pow-exp associate--l+ *-commutative flip-+ flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
361.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
56.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
27.0ms
(* 4 (* b b))
17.0ms
(pow (+ (* a a) (* b b)) 2)

series303.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
110.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
92.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
57.0ms
(pow (+ (* a a) (* b b)) 2)
44.0ms
(* 4 (* b b))

simplify24.7s

Counts
120 → 111
Calls
120 calls:
Slowest
945.0ms
(* (* (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1) (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)) (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))
646.0ms
(- (* (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))) (* 1 1))
645.0ms
(fma (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))) (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))) (- (* (sqrt 1) (sqrt 1))))
594.0ms
(cbrt (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))
569.0ms
(fma (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))) (sqrt (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)
0.0b
(fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1))
0.0b
(* (hypot a b) (hypot a b))
0.0b
(* (hypot a b) (hypot a b))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
16×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
8×hypot-udef add-cbrt-cube add-exp-log
6×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 rem-square-sqrt pow-plus sqrt-unprod pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef unswap-sqr
Counts
4 → 82
Calls
4 calls:
Slowest
13.0ms
(* (hypot a b) (hypot a b))
12.0ms
(* (hypot a b) (hypot a b))
1.0ms
(fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)
0.0ms
(fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1))

series547.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1))
196.0ms
(fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)
80.0ms
(* (hypot a b) (hypot a b))
66.0ms
(* (hypot a b) (hypot a b))

simplify7.2s

Counts
96 → 94
Calls
96 calls:
Slowest
418.0ms
(exp (fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)))
354.0ms
(* (* (fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)) (fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1))) (fma b (* 4 b) (fma (* (hypot a b) (hypot a b)) (* (hypot a b) (hypot a b)) -1)))
339.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
335.0ms
(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))
326.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b)))
0.2b
(fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1)
0.2b
(* (sqrt (hypot a b)) (hypot a b))
0.0b
(fma b (* 4 b) (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
28×pow1
15×add-sqr-sqrt pow-prod-up
12×associate-*l*
11×add-cbrt-cube add-exp-log
10×sqrt-pow1 pow1/2
9×*-un-lft-identity add-cube-cbrt
7×sqrt-prod
6×pow-plus
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-unprod
2×hypot-udef cube-unmult *-commutative fma-udef unswap-sqr
Counts
4 → 87
Calls
4 calls:
Slowest
39.0ms
(* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b)))
15.0ms
(* (sqrt (hypot a b)) (hypot a b))
0.0ms
(fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1)
0.0ms
(fma b (* 4 b) (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1))

series592.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(fma b (* 4 b) (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1))
172.0ms
(fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1)
109.0ms
(* (sqrt (hypot a b)) (hypot a b))
83.0ms
(* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b)))

simplify9.7s

Counts
98 → 99
Calls
98 calls:
Slowest
580.0ms
(* (* (* (sqrt (hypot a b)) (sqrt (hypot a b))) (sqrt (hypot a b))) (* (* (hypot a b) (hypot a b)) (hypot a b)))
513.0ms
(sqrt (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1))
463.0ms
(* (* (* (sqrt (hypot a b)) (sqrt (hypot a b))) (sqrt (hypot a b))) (* (* (* (sqrt (hypot a b)) (sqrt (hypot a b))) (sqrt (hypot a b))) (* (* (hypot a b) (hypot a b)) (hypot a b))))
426.0ms
(exp (fma b (* 4 b) (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1)))
400.0ms
(exp (fma (* (sqrt (hypot a b)) (* (sqrt (hypot a b)) (hypot a b))) (* (hypot a b) (hypot a b)) -1))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))
0.3b
(* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b))))
0.3b
(* (sqrt (sqrt (hypot a b))) (hypot a b))
0.2b
(fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1)

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-pow1
68×pow1
54×pow-prod-up
34×pow1/2
24×associate-*l* sqrt-prod
20×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
14×pow-plus
13×*-un-lft-identity add-cube-cbrt
10×pow-prod-down prod-exp cbrt-unprod
6×sqrt-unprod
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×hypot-udef *-commutative unswap-sqr
1×fma-udef
Counts
4 → 125
Calls
4 calls:
Slowest
114.0ms
(* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b))))
50.0ms
(* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))
9.0ms
(* (sqrt (sqrt (hypot a b))) (hypot a b))
0.0ms
(fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1)

series592.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(* (sqrt (sqrt (hypot a b))) (hypot a b))
164.0ms
(fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1)
133.0ms
(* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))
114.0ms
(* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b))))

simplify14.1s

Counts
137 → 137
Calls
137 calls:
Slowest
578.0ms
(exp (fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1))
563.0ms
(* (* (* (sqrt (hypot a b)) (sqrt (hypot a b))) (sqrt (hypot a b))) (* (* (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b))) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))))
546.0ms
(* (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)))
518.0ms
(* (* (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b))))) (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))))
479.0ms
(* (* (fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1) (fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1)) (fma (* (sqrt (hypot a b)) (* (sqrt (sqrt (hypot a b))) (* (sqrt (sqrt (hypot a b))) (hypot a b)))) (* (hypot a b) (hypot a b)) -1))

prune1.9s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes358.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.1s20186×body80valid