Details

sample169.0ms

Algorithm

intervals

Results

145.0ms

673×

body

valid

simplify188.0ms

Calls

1 calls:

Slowest

187.0ms

(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1)

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(fma (* a a) a (* a a))
0.0b	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0b	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

4 calls:

Slowest

1.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma (* a a) a (* a a))
0.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))
0.0ms	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series466.0ms

Calls

4 calls:

Slowest

135.0ms	(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
130.0ms	(fma (* a a) a (* a a))
113.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
88.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.5s

Calls

12 calls:

Slowest

403.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
388.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
388.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
320.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
274.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune853.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* b b) (- 1 (* 3 a)))
0.3b	(pow (+ (* a a) (* b b)) 2)
0.1b	(* (* a a) (+ 1 a))
0.0b	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt` `prod-diff`
202×	`distribute-rgt-in` `distribute-lft-in`
188×	`*-un-lft-identity`
152×	`associate-+r+`
146×	`add-cube-cbrt`
118×	`associate-l`
86×	`associate-r`
35×	`unswap-sqr`
25×	`*-commutative`
18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-cbrt-cube` `distribute-lft-out`
12×	`swap-sqr`
8×	`+-commutative` `associate-+l+` `unpow-prod-down`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`sub-neg`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `flip3--` `flip--`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`

Calls

4 calls:

Slowest

935.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
107.0ms	(* (* b b) (- 1 (* 3 a)))
44.0ms	(pow (+ (* a a) (* b b)) 2)
29.0ms	(* (* a a) (+ 1 a))

series227.0ms

Calls

4 calls:

Slowest

66.0ms	(* (* a a) (+ 1 a))
63.0ms	(* (* b b) (- 1 (* 3 a)))
60.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
37.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.3m

Calls

365 calls:

Slowest

875.0ms	(* 4 (* (fma (- (* (cbrt 3) a)) (* (cbrt 3) (cbrt 3)) (* (* (cbrt 3) a) (* (cbrt 3) (cbrt 3)))) (* b b)))
678.0ms	(* (fma (- (sqrt a)) (* 3 (sqrt a)) (* (sqrt a) (* 3 (sqrt a)))) (* b b))
638.0ms	(* 4 (* (* b b) (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a))))))
579.0ms	(* 4 (* (* b b) (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a))))))
558.0ms	(* (- 1 a) (+ (* 1 1) (+ (* (* 3 a) (* 3 a)) (* 1 (* 3 a)))))

prune5.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* b b) (- 1 (* 3 a)))
0.2b	(* b (fma b b (* 2 (* a a))))
0.2b	(* (* a a) (* a a))
0.1b	(* (* a a) (+ 1 a))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
127×	`pow1`
92×	`*-un-lft-identity`
87×	`associate-l`
80×	`add-cube-cbrt`
72×	`prod-diff`
67×	`associate-r`
64×	`unswap-sqr`
53×	`swap-sqr`
41×	`distribute-rgt-in` `distribute-lft-in`
36×	`pow-prod-up`
30×	`pow-prod-down` `*-commutative`
28×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
15×	`prod-exp` `cbrt-unprod`
13×	`pow2`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`+-commutative` `sub-neg` `fma-udef` `distribute-lft-out--`
1×	`flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out`

Calls

4 calls:

Slowest

66.0ms	(* (* b b) (- 1 (* 3 a)))
43.0ms	(* (* a a) (* a a))
28.0ms	(* (* a a) (+ 1 a))
11.0ms	(* b (fma b b (* 2 (* a a))))

series280.0ms

Calls

4 calls:

Slowest

91.0ms	(* (* b b) (- 1 (* 3 a)))
84.0ms	(* b (fma b b (* 2 (* a a))))
63.0ms	(* (* a a) (+ 1 a))
43.0ms	(* (* a a) (* a a))

simplify22.8s

Calls

353 calls:

Slowest

674.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
607.0ms	(* (* b b) (fma (- (* 3 a)) 1 (* (* 3 a) 1)))
359.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))
338.0ms	(* (* b b) (fma (- (* (sqrt 3) a)) (sqrt 3) (* (* (sqrt 3) a) (sqrt 3))))
337.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))

prune4.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* b b) (- 1 (* 3 a)))
0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(* (* a a) (+ 1 a))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
72×	`prod-diff`
68×	`*-un-lft-identity`
60×	`add-cube-cbrt`
58×	`associate-l`
41×	`distribute-rgt-in` `distribute-lft-in`
40×	`associate-r`
23×	`unswap-sqr`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`*-commutative`
8×	`swap-sqr`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`fma-udef`
2×	`+-commutative` `sub-neg` `distribute-lft-out--`
1×	`flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out`

Calls

4 calls:

Slowest

73.0ms	(* (* b b) (- 1 (* 3 a)))
34.0ms	(* (* a a) (+ 1 a))
5.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series281.0ms

Calls

4 calls:

Slowest

96.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
65.0ms	(* b (fma b b (* 2 (* a a))))
65.0ms	(* (* b b) (- 1 (* 3 a)))
55.0ms	(* (* a a) (+ 1 a))

simplify20.9s

Calls

175 calls:

Slowest

735.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
614.0ms	(* (* b b) (- 1 (* 3 a)))
334.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))
314.0ms	(* (* b b) (fma (- (* 3 a)) 1 (* (* 3 a) 1)))
311.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))

prune3.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch9.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

4.6s

20682×

body

valid