Details

sample217.0ms

Algorithm

intervals

Results

184.0ms

650×

body

valid

simplify181.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

180.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* b b) (- 1 (* 3 a)))
0.3b	(pow (+ (* a a) (* b b)) 2)
0.0b	(* (* a a) (+ 1 a))
0.0b	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
17×	`pow1` `add-exp-log`
16×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`associate-r`
7×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `flip3--` `*-commutative` `flip--` `unswap-sqr`
2×	`sub-neg`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `unpow2` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

Slowest

103.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
43.0ms	(* (* a a) (+ 1 a))
30.0ms	(* (* b b) (- 1 (* 3 a)))
16.0ms	(pow (+ (* a a) (* b b)) 2)

series322.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

94.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
81.0ms	(* (* a a) (+ 1 a))
76.0ms	(* (* b b) (- 1 (* 3 a)))
71.0ms	(pow (+ (* a a) (* b b)) 2)

simplify11.2s

Counts

76 → 123

Calls

76 calls:

Slowest

608.0ms	(* (- 1 a) (+ (* 1 1) (+ (* (* 3 a) (* 3 a)) (* 1 (* 3 a)))))
552.0ms	(* (* (* 4 4) 4) (* (* (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))) (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
399.0ms	(* (+ (* 1 1) (- (* a a) (* 1 a))) (+ 1 (* 3 a)))
398.0ms	(+ (* (* (* a a) (+ 1 a)) (* (* a a) (+ 1 a))) (- (* (* (* b b) (- 1 (* 3 a))) (* (* b b) (- 1 (* 3 a)))) (* (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
364.0ms	(* (* b b) (- 1 (* 3 a)))

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize106.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* b b) (- 1 (* 3 a)))
0.2b	(* (* a a) (* a a))
0.2b	(* b (fma b b (* 2 (* a a))))
0.1b	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

122×	`pow1`
36×	`pow-prod-up`
27×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
13×	`pow2`
12×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef` `unswap-sqr`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `swap-sqr` `flip--`

Counts

4 → 134

Calls

4 calls:

Slowest

50.0ms	(* (* a a) (* a a))
50.0ms	(* (* b b) (- 1 (* 3 a)))
16.0ms	(* b (fma b b (* 2 (* a a))))
1.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
93.0ms	(* b (fma b b (* 2 (* a a))))
77.0ms	(* (* b b) (- 1 (* 3 a)))
72.0ms	(* (* a a) (* a a))

simplify9.6s

Counts

114 → 146

Calls

114 calls:

Slowest

977.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
801.0ms	(* (* b b) (- 1 (* 3 a)))
424.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
379.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
357.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize106.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (* b b) (- 1 (* 3 a)))
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	(* (* a a) (+ 1 a))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`associate-r` `add-cube-cbrt`
7×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef` `unswap-sqr`
2×	`sub-neg`
1×	`flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

Slowest

31.0ms	(* (* a a) (+ 1 a))
28.0ms	(* (* b b) (- 1 (* 3 a)))
6.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series426.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

127.0ms	(* b (fma b b (* 2 (* a a))))
102.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
101.0ms	(* (* b b) (- 1 (* 3 a)))
96.0ms	(* (* a a) (+ 1 a))

simplify7.4s

Counts

63 → 107

Calls

63 calls:

Slowest

888.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
385.0ms	(* (* b b) (- 1 (* 3 a)))
321.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
298.0ms	(- (pow b 2) (* 3 (* a (pow b 2))))
289.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize106.0ms

Local error

Found 4 expressions with local error:

9.9b	(cbrt (fma b b (* 2 (* a a))))
9.9b	(cbrt (fma b b (* 2 (* a a))))
9.9b	(cbrt (fma b b (* 2 (* a a))))
1.1b	(* (* b b) (- 1 (* 3 a)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `pow1` `add-cbrt-cube` `add-exp-log`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

Slowest

45.0ms	(* (* b b) (- 1 (* 3 a)))
2.0ms	(cbrt (fma b b (* 2 (* a a))))
2.0ms	(cbrt (fma b b (* 2 (* a a))))
1.0ms	(cbrt (fma b b (* 2 (* a a))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

194.0ms	(cbrt (fma b b (* 2 (* a a))))
186.0ms	(cbrt (fma b b (* 2 (* a a))))
179.0ms	(cbrt (fma b b (* 2 (* a a))))
84.0ms	(* (* b b) (- 1 (* 3 a)))

simplify4.6s

Counts

44 → 88

Calls

44 calls:

Slowest

308.0ms	(* (* b b) (- 1 (* 3 a)))
296.0ms	(* (* b b) (- 1 (* 3 a)))
282.0ms	(- (pow b 2) (* 3 (* a (pow b 2))))
264.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
258.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes245.0ms

Accuracy

0% (0.0b remaining)

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

bsearch8.0ms

end0.0ms

sample6.2s

Algorithm

intervals

Results

5.7s

20764×

body

valid