Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	76×	body	1280	valid
5.0ms	136×	body	80	valid
5.0ms	28×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
6	37
5	35
4	30
3	28
2	24
1	19
0	9

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
0.0b	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
0.0b	(/ 0.5 (hypot 1.0 x))
1.8b	(- 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `sqrt-prod` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `div-inv` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

8.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
13.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
7.0ms	(/ 0.5 (hypot 1.0 x))
32.0ms	(- 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
112.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
12.0ms	(/ 0.5 (hypot 1.0 x))
120.0ms	(- 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))

simplify578.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
2	833
1	245
0	116

prune289.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
0.0b	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
1.3b	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
14×	`times-frac` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
8×	`associate-/r*`
7×	`distribute-lft-out`
4×	`pow1` `associate-/l*`
3×	`cbrt-undiv` `div-exp` `sqrt-prod`
2×	`clear-num` `sum-log` `frac-2neg` `flip3-+` `flip3--` `diff-log` `associate-*r/` `associate-/r/` `flip-+` `div-inv` `flip--` `distribute-lft-out--` `associate-/l/`
1×	`+-commutative` `sub-neg` `prod-exp` `cbrt-unprod` `associate--r+` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

4.0ms	(/ 0.5 (hypot 1.0 x))
66.0ms	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
4.0ms	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
31.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 0.5 (hypot 1.0 x))
243.0ms	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
110.0ms	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
40.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1816
1	404
0	155

prune478.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 16.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sqrt (hypot 1.0 x)))
0.2b	(/ 0.5 (sqrt (hypot 1.0 x)))
0.2b	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 0.5 (sqrt (hypot 1.0 x))))
1.3b	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
94×	`times-frac`
71×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
9×	`add-log-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`cbrt-unprod` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `diff-log` `distribute-lft-out--`
1×	`frac-times` `sum-log` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out` `associate--r+` `inv-pow` `difference-of-squares`

Counts

4 → 184

Calls

4 calls:

9.0ms	(/ 1 (sqrt (hypot 1.0 x)))
10.0ms	(/ 0.5 (sqrt (hypot 1.0 x)))
58.0ms	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 0.5 (sqrt (hypot 1.0 x))))
43.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (sqrt (hypot 1.0 x)))
63.0ms	(/ 0.5 (sqrt (hypot 1.0 x)))
7.0ms	(* (/ 1 (sqrt (hypot 1.0 x))) (/ 0.5 (sqrt (hypot 1.0 x))))
41.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

simplify1.9s

Counts

196 → 196

Iterations

Iter	Nodes
done	5000
2	3427
1	579
0	212

prune844.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
0.0b	(/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
0.1b	(exp (log (/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))))
1.3b	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
11×	`log-prod` `exp-sum` `add-log-exp`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `distribute-lft-out`
5×	`pow1` `associate-/r*`
4×	`exp-prod` `associate-/r/` `sqrt-prod`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sum-log` `flip3--` `diff-log` `div-exp` `associate-*l/` `div-inv` `flip--` `distribute-lft-out--` `associate-/l/`
1×	`+-commutative` `log-div` `clear-num` `sub-neg` `frac-2neg` `exp-diff` `prod-exp` `log-pow` `cbrt-unprod` `associate-/l*` `associate--r+` `difference-of-squares` `rem-exp-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
52.0ms	(/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
158.0ms	(exp (log (/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))))
53.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))
307.0ms	(/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))
256.0ms	(exp (log (/ (* (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))) 1.0) (+ 1.0 (sqrt (* 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))))))
39.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

simplify1.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2231
1	396
0	162

prune446.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 16.0b

regimes137.0ms

Accuracy

0% (0.0b remaining)

Error of 15.6b against oracle of 15.6b and baseline of 15.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	26
1	26
0	18

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	2806×	body	1280	valid
695.0ms	4038×	body	80	valid
159.0ms	664×	body	640	valid
91.0ms	342×	body	320	valid
21.0ms	150×	body	160	valid