Details

sample118.0ms

Algorithm

intervals

Results

98.0ms

673×

body

valid

simplify200.0ms

Calls

1 calls:

Slowest

199.0ms

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.0b	(* 4 (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b	(+ (* a a) (* b b))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
28×	`fma-def`
22×	`associate-l`
21×	`associate-r`
19×	`add-cube-cbrt`
17×	`distribute-lft-out`
16×	`unpow-prod-down`
13×	`swap-sqr`
10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow-exp`

Calls

4 calls:

Slowest

357.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
54.0ms	(pow (+ (* a a) (* b b)) 2)
42.0ms	(+ (* a a) (* b b))
20.0ms	(* 4 (* b b))

series210.0ms

Calls

4 calls:

Slowest

76.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
50.0ms	(pow (+ (* a a) (* b b)) 2)
47.0ms	(* 4 (* b b))
37.0ms	(+ (* a a) (* b b))

simplify5.1s

Calls

87 calls:

Slowest

389.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
353.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
347.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
311.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
301.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (fma b b (* 2 (* a a))))
0.2b	(* (* a a) (* a a))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
0.0b	(* 2 (* a a))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
112×	`add-sqr-sqrt`
49×	`swap-sqr` `unswap-sqr`
48×	`associate-r`
38×	`associate-l`
36×	`*-un-lft-identity` `pow-prod-up`
32×	`add-cube-cbrt`
27×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
21×	`*-commutative`
18×	`pow-plus`
13×	`pow2`
12×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Calls

4 calls:

Slowest

72.0ms	(* (* a a) (* a a))
39.0ms	(* 2 (* a a))
11.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series314.0ms

Calls

4 calls:

Slowest

112.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
109.0ms	(* b (fma b b (* 2 (* a a))))
48.0ms	(* 2 (* a a))
45.0ms	(* (* a a) (* a a))

simplify6.5s

Calls

232 calls:

Slowest

895.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
350.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
349.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
335.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
324.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) a) (* (* a a) a)))

prune2.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
0.0b	(* 2 (* a a))
0.0b	(* 4 (* b b))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`associate-r`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
15×	`associate-l` `unswap-sqr`
8×	`swap-sqr`
7×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Calls

4 calls:

Slowest

23.0ms	(* 4 (* b b))
22.0ms	(* 2 (* a a))
6.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series277.0ms

Calls

4 calls:

Slowest

116.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
90.0ms	(* b (fma b b (* 2 (* a a))))
40.0ms	(* 2 (* a a))
30.0ms	(* 4 (* b b))

simplify4.3s

Calls

84 calls:

Slowest

827.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
325.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
306.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
297.0ms	(* (* (* 4 4) 4) (* (* (* b b) b) (* (* b b) b)))
269.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

8.5b	(cbrt (fma b b (* 2 (* a a))))
8.5b	(cbrt (fma b b (* 2 (* a a))))
8.5b	(cbrt (fma b b (* 2 (* a a))))
0.5b	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Calls

4 calls:

Slowest

13.0ms	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))

series747.0ms

Calls

4 calls:

Slowest

209.0ms	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))
190.0ms	(cbrt (fma b b (* 2 (* a a))))
176.0ms	(cbrt (fma b b (* 2 (* a a))))
173.0ms	(cbrt (fma b b (* 2 (* a a))))

simplify3.9s

Calls

68 calls:

Slowest

394.0ms	(* (fma b b (* 2 (* a a))) (* (* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a))))) (cbrt (fma b b (* 2 (* a a))))))
384.0ms	(* (* (* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a))))) (cbrt (fma b b (* 2 (* a a))))) (* (* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a))))) (cbrt (fma b b (* 2 (* a a))))))
257.0ms	(* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a))))
235.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
230.0ms	(+ (exp (* 1/3 (+ (log 4) (* 4 (log a))))) (* 1/3 (* (exp (* 1/3 (- (log 4) (* 2 (log a))))) (pow b 2))))

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.2s

20682×

body

valid