Details

sample152.0ms

Algorithm

intervals

Results

126.0ms

677×

body

valid

simplify192.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

192.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

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

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

Slowest

69.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
41.0ms	(* (* b b) (- 1 (* 3 a)))
24.0ms	(* (* a a) (+ 1 a))
17.0ms	(pow (+ (* a a) (* b b)) 2)

series384.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
101.0ms	(* (* b b) (- 1 (* 3 a)))
71.0ms	(* (* a a) (+ 1 a))
52.0ms	(pow (+ (* a a) (* b b)) 2)

simplify8.5s

Counts

68 → 118

Calls

68 calls:

Slowest

363.0ms	(+ (* 4 (pow a 2)) (+ (* 4 (pow b 2)) (* 4 (pow a 3))))
336.0ms	(* (* b b) (- 1 (* 3 a)))
322.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
305.0ms	(- (pow b 2) (* 3 (* a (pow b 2))))
305.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* 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)))

rewrite103.0ms

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

46.0ms	(* (* a a) (* a a))
41.0ms	(* (* b b) (- 1 (* 3 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)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
120.0ms	(* b (fma b b (* 2 (* a a))))
89.0ms	(* (* b b) (- 1 (* 3 a)))
41.0ms	(* (* a a) (* a a))

simplify9.3s

Counts

114 → 146

Calls

114 calls:

Slowest

955.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
787.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
409.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) a) (* (* a a) a)))
381.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
368.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

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	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
0.1b	(* (* a a) (+ 1 a))

rewrite84.0ms

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

44.0ms	(* (* a a) (+ 1 a))
32.0ms	(* (* 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))

series403.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

123.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
120.0ms	(* b (fma b b (* 2 (* a a))))
87.0ms	(* (* a a) (+ 1 a))
72.0ms	(* (* b b) (- 1 (* 3 a)))

simplify7.6s

Counts

63 → 107

Calls

63 calls:

Slowest

1.1s	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
371.0ms	(* (* b b) (- 1 (* 3 a)))
321.0ms	(* (* b b) (- 1 (* 3 a)))
293.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
279.0ms	(+ (pow b 3) (* 2 (* (pow a 2) b)))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

125×	`pow1`
36×	`pow-prod-up`
29×	`pow-prod-down`
26×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
14×	`prod-exp` `cbrt-unprod`
13×	`pow2`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-r` `add-cube-cbrt`
6×	`distribute-rgt-in` `distribute-lft-in` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `unswap-sqr`
2×	`sub-neg`
1×	`flip3-+` `flip3--` `swap-sqr` `flip-+` `fma-udef` `flip--` `distribute-lft-out`

Counts

4 → 138

Calls

4 calls:

Slowest

44.0ms	(* (* a a) (* a a))
44.0ms	(* (* a a) (+ 1 a))
26.0ms	(* (* b b) (- 1 (* 3 a)))
0.0ms	(fma (fma 2 (* a a) (* b b)) (* b b) (* (* a a) (* a a)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

90.0ms	(* (* b b) (- 1 (* 3 a)))
86.0ms	(fma (fma 2 (* a a) (* b b)) (* b b) (* (* a a) (* a a)))
81.0ms	(* (* a a) (+ 1 a))
46.0ms	(* (* a a) (* a a))

simplify7.5s

Counts

118 → 150

Calls

118 calls:

Slowest

459.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
361.0ms	(* (* (* (* 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)))
352.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) a) (* (* a a) a)))
335.0ms	(* (* b b) (- 1 (* 3 a)))

prune2.3s

Pruning

5 alts after pruning (3 fresh and 2 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

bsearch9.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

5.7s

20571×

body

valid