Details

sample137.0ms

Algorithm

intervals

Results

112.0ms

639×

body

valid

simplify243.0ms

Calls

1 calls:

Slowest

243.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ a 3) (* b b))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0b	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
0.0b	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`associate-r`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `swap-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`
2×	`associate-*l/`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Calls

4 calls:

Slowest

42.0ms	(* (+ a 3) (* b b))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
0.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series406.0ms

Calls

4 calls:

Slowest

154.0ms	(fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1))
109.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
86.0ms	(fma a (* (- 1 a) a) (* (+ a 3) (* b b)))
57.0ms	(* (+ a 3) (* b b))

simplify3.7s

Calls

44 calls:

Slowest

442.0ms	(* (- (* a a) (* 3 3)) (* b b))
384.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
326.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
316.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
296.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cbrt (+ a 3)) (cbrt (+ a 3))) (* (cbrt (+ a 3)) (* b b)))
0.2b	(* (cbrt (+ a 3)) (* b b))
0.2b	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.1b	(cbrt (+ a 3))

rewrite436.0ms

Algorithm

rewrite-expression-head

Rules

413×	`add-sqr-sqrt`
281×	`unswap-sqr`
157×	`cbrt-prod`
82×	`add-cbrt-cube`
81×	`cbrt-unprod`
80×	`associate-r`
59×	`swap-sqr` `associate-l`
58×	`cbrt-div`
49×	`*-un-lft-identity`
39×	`*-commutative`
34×	`associate-*l/`
30×	`pow1` `add-exp-log`
29×	`flip3-+` `add-cube-cbrt` `flip-+`
28×	`frac-times`
18×	`pow-prod-down` `prod-exp`
9×	`distribute-lft-out`
8×	`associate-*r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow1/3` `fma-udef`

Calls

4 calls:

Slowest

377.0ms	(* (* (cbrt (+ a 3)) (cbrt (+ a 3))) (* (cbrt (+ a 3)) (* b b)))
36.0ms	(* (cbrt (+ a 3)) (* b b))
6.0ms	(cbrt (+ a 3))
0.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)

series364.0ms

Calls

4 calls:

Slowest

132.0ms	(* (cbrt (+ a 3)) (* b b))
95.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
74.0ms	(* (* (cbrt (+ a 3)) (cbrt (+ a 3))) (* (cbrt (+ a 3)) (* b b)))
63.0ms	(cbrt (+ a 3))

simplify32.0s

Calls

407 calls:

Slowest

1.2s	(* (* (cbrt (+ (pow a 3) (pow 3 3))) (cbrt (- (* a a) (* 3 3)))) (* (cbrt (+ a 3)) (* b b)))
564.0ms	(* (* (cbrt (+ (pow a 3) (pow 3 3))) (cbrt (+ (pow a 3) (pow 3 3)))) (* (cbrt (+ (pow a 3) (pow 3 3))) (* b b)))
444.0ms	(* (* (cbrt (+ a 3)) (cbrt (+ (pow a 3) (pow 3 3)))) (* (cbrt (- (* a a) (* 3 3))) (* b b)))
425.0ms	(* (+ a 3) (* (* (* b b) b) (* (* b b) b)))
400.0ms	(* (* (cbrt (+ (pow a 3) (pow 3 3))) (cbrt (+ a 3))) (* (cbrt (- (* a a) (* 3 3))) (* b b)))

prune4.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ a 3) (* b b))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.3b	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log`
7×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `swap-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`associate-*l/`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Calls

4 calls:

Slowest

34.0ms	(* (+ a 3) (* b b))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series515.0ms

Calls

4 calls:

Slowest

159.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
159.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
155.0ms	(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
43.0ms	(* (+ a 3) (* b b))

simplify2.3s

Calls

53 calls:

Slowest

281.0ms	(* (- (* a a) (* 3 3)) (* b b))
210.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))
190.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
189.0ms	(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
188.0ms	(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (+ a 3) (* b b))
0.4b	(* (+ a 3) (* b b))
0.4b	(* (+ a 3) (* b b))
0.3b	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
54×	`associate-r`
29×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`associate-l` `unswap-sqr`
19×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`swap-sqr`
9×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
6×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `flip-+` `distribute-lft-out`
1×	`pow1/3`

Calls

4 calls:

Slowest

34.0ms	(* (+ a 3) (* b b))
31.0ms	(* (+ a 3) (* b b))
29.0ms	(* (+ a 3) (* b b))
1.0ms	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series299.0ms

Calls

4 calls:

Slowest

165.0ms	(cbrt (fma 4 (fma a (* (- 1 a) a) (* (+ a 3) (* b b))) (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
48.0ms	(* (+ a 3) (* b b))
43.0ms	(* (+ a 3) (* b b))
43.0ms	(* (+ a 3) (* b b))

simplify4.2s

Calls

111 calls:

Slowest

298.0ms	(- (pow -1 1/3) (+ (* 4/3 (* (pow a 2) (pow -1 1/3))) (* 4 (* (pow b 2) (pow -1 1/3)))))
280.0ms	(* (- (* a a) (* 3 3)) (* b b))
278.0ms	(* (- (* a a) (* 3 3)) (* b b))
278.0ms	(* (- (* a a) (* 3 3)) (* b b))
211.0ms	(* (+ (pow a 3) (pow 3 3)) (* b b))

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes127.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

3.0s

20611×

body

valid