Details

sample133.0ms

Algorithm

intervals

Results

108.0ms

604×

body

valid

simplify214.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

214.0ms

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2)
0.2b	(* (* b b) (- 1 (* 3 a)))
0.0b	(* (* a a) (+ 1 a))
0.0b	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))

rewrite163.0ms

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

86.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
42.0ms	(* (* b b) (- 1 (* 3 a)))
24.0ms	(* (* a a) (+ 1 a))
8.0ms	(pow (+ (* a a) (* b b)) 2)

series318.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))
75.0ms	(* (* b b) (- 1 (* 3 a)))
72.0ms	(* (* a a) (+ 1 a))
58.0ms	(pow (+ (* a a) (* b b)) 2)

simplify11.7s

Counts

76 → 123

Calls

76 calls:

Slowest

667.0ms	(* (- 1 a) (+ (* 1 1) (+ (* (* 3 a) (* 3 a)) (* 1 (* 3 a)))))
467.0ms	(* (* (* 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))))))
391.0ms	(+ (* 4 (pow a 2)) (+ (* 4 (pow b 2)) (* 4 (pow a 3))))
383.0ms	(* (- 1 a) (+ 1 (* 3 a)))
373.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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)))

rewrite92.0ms

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

38.0ms	(* (* a a) (* a a))
37.0ms	(* (* b b) (- 1 (* 3 a)))
12.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (* (* a a) (* a a)))
85.0ms	(* b (fma b b (* 2 (* a a))))
76.0ms	(* (* b b) (- 1 (* 3 a)))
39.0ms	(* (* a a) (* a a))

simplify9.0s

Counts

114 → 146

Calls

114 calls:

Slowest

969.0ms	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
430.0ms	(* (* (* (* a a) (* a a)) (* a a)) (* (* (* a a) (* a a)) (* a a)))
382.0ms	(* (* (* (* a a) a) (* (* a a) a)) (* (* (* a a) (* a a)) (* a a)))
348.0ms	(* (* b b) (- 1 (* 3 a)))
344.0ms	(* (* b b) (- 1 (* 3 a)))

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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))

rewrite101.0ms

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

54.0ms	(* (* b b) (- 1 (* 3 a)))
34.0ms	(* (* a a) (+ 1 a))
11.0ms	(* b (fma b b (* 2 (* a a))))
0.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))

series437.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(fma b (* b (fma b b (* 2 (* a a)))) (pow a 4))
109.0ms	(* b (fma b b (* 2 (* a a))))
102.0ms	(* (* a a) (+ 1 a))
81.0ms	(* (* b b) (- 1 (* 3 a)))

simplify7.7s

Counts

63 → 107

Calls

63 calls:

Slowest

1.0s	(* (* (* b b) b) (* (* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a)))) (fma b b (* 2 (* a a)))))
411.0ms	(* (* b b) (- 1 (* 3 a)))
392.0ms	(* (* b b) (- 1 (* 3 a)))
310.0ms	(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
294.0ms	(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

11.1b	(cbrt (fma b b (* 2 (* a a))))
11.1b	(cbrt (fma b b (* 2 (* a a))))
11.1b	(cbrt (fma b b (* 2 (* a a))))
0.4b	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `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` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

15.0ms	(* (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))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(cbrt (fma b b (* 2 (* a a))))
186.0ms	(cbrt (fma b b (* 2 (* a a))))
175.0ms	(cbrt (fma b b (* 2 (* a a))))
159.0ms	(* (cbrt (fma b b (* 2 (* a a)))) (cbrt (fma b b (* 2 (* a a)))))

simplify3.1s

Counts

65 → 97

Calls

65 calls:

Slowest

248.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
247.0ms	(+ (exp (* 1/3 (+ (log 2) (* 2 (log a))))) (* 1/6 (* (pow b 2) (exp (* 1/3 (- (log 2) (* 4 (log a))))))))
229.0ms	(* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a))))
228.0ms	(+ (exp (* 1/3 (+ (log 4) (* 4 (log a))))) (* 1/3 (* (exp (* 1/3 (- (log 4) (* 2 (log a))))) (pow b 2))))
209.0ms	(* (fma b b (* 2 (* a a))) (fma b b (* 2 (* a a))))

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

0% (0.0b remaining)

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

bsearch9.0ms

end0.0ms

sample5.8s

Algorithm

intervals

Results

5.4s

20149×

body

valid