Details

sample183.0ms

Algorithm

intervals

Results

158.0ms

673×

body

valid

simplify220.0ms

Calls

1 calls:

Slowest

219.0ms

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

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)))

rewrite2.0ms

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

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

series499.0ms

Calls

4 calls:

Slowest

168.0ms	(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))
134.0ms	(fma (* a a) a (* a a))
123.0ms	(fma (fma b b (* a a)) (fma b b (* a a)) -1)
74.0ms	(fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a)))

simplify2.5s

Calls

12 calls:

Slowest

448.0ms	(- (+ (pow a 2) (pow b 2)) (* 3 (* a (pow b 2))))
405.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
339.0ms	(- (+ (pow a 2) (pow a 3)) (* 3 (* a (pow b 2))))
288.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
273.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune796.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

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

875.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
109.0ms	(* (* b b) (- 1 (* 3 a)))
52.0ms	(* (* a a) (+ 1 a))
28.0ms	(pow (+ (* a a) (* b b)) 2)

series302.0ms

Calls

4 calls:

Slowest

96.0ms	(* (* b b) (- 1 (* 3 a)))
89.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
68.0ms	(* (* a a) (+ 1 a))
49.0ms	(pow (+ (* a a) (* b b)) 2)

simplify1.2m

Calls

365 calls:

Slowest

914.0ms	(* 4 (* (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a)))) (* b b)))
782.0ms	(* (* b b) (fma (- (cbrt a)) (* 3 (* (cbrt a) (cbrt a))) (* (cbrt a) (* 3 (* (cbrt a) (cbrt a))))))
635.0ms	(* 4 (* (* b b) (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a))))))
586.0ms	(* (- 1 a) (+ (* 1 1) (+ (* (* 3 a) (* 3 a)) (* 1 (* 3 a)))))
579.0ms	(* 4 (* (* b b) (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a))))))

prune5.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

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))

rewrite205.0ms

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

84.0ms	(* (* b b) (- 1 (* 3 a)))
65.0ms	(* (* a a) (* a a))
41.0ms	(* (* a a) (+ 1 a))
6.0ms	(* b (fma b b (* 2 (* a a))))

series260.0ms

Calls

4 calls:

Slowest

97.0ms	(* b (fma b b (* 2 (* a a))))
63.0ms	(* (* b b) (- 1 (* 3 a)))
60.0ms	(* (* a a) (+ 1 a))
40.0ms	(* (* a a) (* a a))

simplify18.8s

Calls

353 calls:

Slowest

609.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
302.0ms	(* (* b b) (fma (- (* 3 a)) 1 (* (* 3 a) 1)))
270.0ms	(* (* b b) (- 1 (* 3 a)))
266.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
263.0ms	(* (* b b) (- 1 (* 3 a)))

prune3.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

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))

rewrite93.0ms

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

54.0ms	(* (* b b) (- 1 (* 3 a)))
28.0ms	(* (* a a) (+ 1 a))
8.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series265.0ms

Calls

4 calls:

Slowest

84.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
64.0ms	(* b (fma b b (* 2 (* a a))))
59.0ms	(* (* b b) (- 1 (* 3 a)))
58.0ms	(* (* a a) (+ 1 a))

simplify16.8s

Calls

175 calls:

Slowest

604.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
548.0ms	(* (* b b) (fma (- (* (sqrt 3) (sqrt a))) (* (sqrt 3) (sqrt a)) (* (* (sqrt 3) (sqrt a)) (* (sqrt 3) (sqrt a)))))
249.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))
248.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))
245.0ms	(* (fma (- (cbrt (* 3 a))) (* (cbrt (* 3 a)) (cbrt (* 3 a))) (* (cbrt (* 3 a)) (* (cbrt (* 3 a)) (cbrt (* 3 a))))) (* b b))

prune2.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

3.6s

20682×

body

valid