Details

sample94.0ms

Algorithm

intervals

Results

62.0ms

656×

body

valid

simplify5.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	178	28
3	545	28
4	1672	28
5	4797	28
done	5000	28

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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)
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite238.0ms

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×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

100.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
50.0ms	(* (* a a) (+ 1.0 a))
19.0ms	(pow (+ (* a a) (* b b)) 2.0)
65.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
93.0ms	(* (* a a) (+ 1.0 a))
168.0ms	(pow (+ (* a a) (* b b)) 2.0)
73.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.7s

Counts

112 → 112

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	201	1802
1	540	1621
2	2054	1446
done	5000	1435

prune573.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 2 (* a a) (* b b))
0.2b	(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 2 (* a a) (* b b))
0.0ms	(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

series169.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(fma 2 (* a a) (* b b))
117.0ms	(fma (* b b) (fma 2 (* a a) (* b b)) (pow a 4))

simplify3.2s

Counts

26 → 26

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	40	395
1	74	392
2	186	340
3	647	340
4	3436	340
done	5000	340

prune178.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 3.0 a))
0.1b	(* (* a a) (+ 1.0 a))
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
2.3b	(* (pow a 2) (pow b 2))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

14.0ms	(- 1.0 (* 3.0 a))
44.0ms	(* (* a a) (+ 1.0 a))
45.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
53.0ms	(* (pow a 2) (pow b 2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (* 3.0 a))
82.0ms	(* (* a a) (+ 1.0 a))
105.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
69.0ms	(* (pow a 2) (pow b 2))

simplify1.8s

Counts

144 → 144

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	203	1642
1	503	1513
2	1760	1249
done	5000	1225

prune701.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.3b	(pow (/ -1 a) -4.0)
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `unpow-prod-down` `*-un-lft-identity`
24×	`add-cube-cbrt`
18×	`times-frac`
17×	`add-exp-log` `fma-def`
15×	`pow1`
14×	`add-cbrt-cube`
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`
2×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+` `div-inv` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `div-exp` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 121

Calls

4 calls:

90.0ms	(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
53.0ms	(* (* a a) (+ 1.0 a))
7.0ms	(pow (/ -1 a) -4.0)
67.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(+ (pow (/ -1 a) -4.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
95.0ms	(* (* a a) (+ 1.0 a))
316.0ms	(pow (/ -1 a) -4.0)
91.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.1s

Counts

133 → 133

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	241	1768
1	623	1652
2	2163	1462
done	5000	1450

prune687.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

35.7% (1.5b remaining)

Error of 1.5b against oracle of 0.0b and baseline of 2.3b

bsearch382.0ms

Steps

Iters	Range		Point
7	3.744599964535267e-06	8.937283511995443e-05	8.82997045828262e-05
10	-50.53194642688064	-2.0220103258854106e-10	-0.0031084792160490805

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	39	144
1	50	94
done	50	94

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.4s

20728×

body

valid