Details

sample82.0ms

Algorithm

intervals

Results

58.0ms

642×

body

valid

simplify3.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2195
3	588
2	179
1	55
0	19

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

75.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
49.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(pow (+ (* a a) (* b b)) 2.0)
24.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
92.0ms	(* (* a a) (+ 1.0 a))
166.0ms	(pow (+ (* a a) (* b b)) 2.0)
78.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	4499
1	620
0	201

prune775.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (pow (+ (* a a) (* b b)) 2.0))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

52.0ms	(+ (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (pow (+ (* a a) (* b b)) 2.0))
25.0ms	(* (* a a) (+ 1.0 a))
8.0ms	(pow (+ (* a a) (* b b)) 2.0)
42.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(+ (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))) (pow (+ (* a a) (* b b)) 2.0))
118.0ms	(* (* a a) (+ 1.0 a))
143.0ms	(pow (+ (* a a) (* b b)) 2.0)
83.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	4471
1	624
0	201

prune784.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
7.3b	(cbrt (fma b b (pow a 2)))
7.3b	(cbrt (fma b b (pow a 2)))
7.3b	(cbrt (fma b b (pow a 2)))

rewrite33.0ms

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` `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 → 72

Calls

4 calls:

27.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(cbrt (fma b b (pow a 2)))
1.0ms	(cbrt (fma b b (pow a 2)))
1.0ms	(cbrt (fma b b (pow a 2)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
168.0ms	(cbrt (fma b b (pow a 2)))
149.0ms	(cbrt (fma b b (pow a 2)))
154.0ms	(cbrt (fma b b (pow a 2)))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1844
1	293
0	110

prune840.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize120.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot b a))
0.8b	(* (* b b) (- 1.0 (* 3.0 a)))
7.3b	(cbrt (fma b b (pow a 2)))
7.3b	(cbrt (fma b b (pow a 2)))

rewrite27.0ms

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` `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 → 72

Calls

4 calls:

1.0ms	(cbrt (hypot b a))
23.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(cbrt (fma b b (pow a 2)))
1.0ms	(cbrt (fma b b (pow a 2)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (hypot b a))
69.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
147.0ms	(cbrt (fma b b (pow a 2)))
149.0ms	(cbrt (fma b b (pow a 2)))

simplify1.6s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2000
1	340
0	136

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes243.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample4.4s

Algorithm

intervals

Results

3.8s

20748×

body

valid