Details

sample57.0ms

Algorithm

intervals

Results

29.0ms	92×	body	1280	valid
8.0ms	134×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	42
6	42
5	40
4	34
3	32
2	26
1	19
0	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize53.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
0.0b	(sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0))
1.9b	(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
12×	`prod-diff` `add-cube-cbrt`
7×	`add-log-exp`
6×	`pow1`
5×	`sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `pow-prod-down` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 64

Calls

3 calls:

12.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
21.0ms	(sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0))
12.0ms	(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0)))

series1.0s

Counts

3 → 9

Calls

3 calls:

157.0ms	(+ 0.5 (/ 0.5 (hypot 1.0 x)))
374.0ms	(sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0))
492.0ms	(- 1.0 (sqrt (* (+ 0.5 (/ 0.5 (hypot 1.0 x))) 1.0)))

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	2001
1	453
0	176

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 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 (/ 0.5 (hypot 1.0 x)))))))
0.0b	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
1.4b	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`prod-diff`
11×	`add-log-exp`
10×	`distribute-lft-out`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`associate-/r*` `times-frac`
4×	`expm1-log1p-u` `associate-*r/` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`cbrt-undiv` `sum-log` `sqrt-pow1` `flip3--` `sqrt-div` `diff-log` `div-exp` `associate-/r/` `flip--` `distribute-lft-out--` `associate-/l/`
1×	`+-commutative` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*` `associate--r+` `difference-of-squares`

Counts

4 → 98

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
122.0ms	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
10.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
35.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

series3.0s

Counts

4 → 12

Calls

4 calls:

454.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
2.0s	(/ (* 1.0 (- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))))
348.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
150.0ms	(- 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))

simplify762.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
1	950
0	323

prune784.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt` `*-un-lft-identity`
74×	`prod-diff`
62×	`add-cube-cbrt`
48×	`times-frac`
23×	`distribute-lft-out--`
20×	`difference-of-squares`
14×	`log-prod`
11×	`associate--l+`
9×	`pow1` `add-log-exp`
8×	`log-div`
7×	`exp-sum`
6×	`flip3--` `frac-sub` `flip--`
5×	`fma-neg` `add-exp-log` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `exp-diff` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `log-pow`
1×	`associate--l-` `flip3-+` `pow1/2` `rem-log-exp` `pow-prod-down` `sqrt-prod` `flip-+` `rem-exp-log`

Counts

4 → 165

Calls

4 calls:

45.0ms	(log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
10.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
23.0ms	(exp (log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))
59.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

381.0ms	(log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
408.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
208.0ms	(exp (log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))
171.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify2.0s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
2	3957
1	923
0	375

prune920.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `distribute-lft-out`
20×	`times-frac`
19×	`add-cube-cbrt`
14×	`pow1`
8×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
7×	`difference-of-squares`
6×	`swap-sqr` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-times` `associate-r` `associate-l` `associate-r/` `log1p-expm1-u` `associate-/l`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1` `flip3--` `sqrt-div` `pow-prod-down` `associate-*l/` `associate-/r/` `flip--` `associate--r+` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

87.0ms	(/ (- (* 1.0 1.0) (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ (+ 1.0 (/ 0.5 (hypot 1.0 x))) 0.5))
10.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
79.0ms	(* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
7.0ms	(- (* 1.0 1.0) (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))

series1.9s

Counts

4 → 12

Calls

4 calls:

993.0ms	(/ (- (* 1.0 1.0) (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ (+ 1.0 (/ 0.5 (hypot 1.0 x))) 0.5))
382.0ms	(sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x)))))
198.0ms	(* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5))
349.0ms	(- (* 1.0 1.0) (* (+ (/ 0.5 (hypot 1.0 x)) 0.5) (+ (/ 0.5 (hypot 1.0 x)) 0.5)))

simplify633.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
1	1096
0	347

prune870.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes178.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.1b

bsearch287.0ms

Steps

Iters	Range		Point
7	0.00012587414935880383	0.030359728269424062	0.0005078281910445067
11	-14746478108.679678	-8.433739504313006e-14	-0.000361777145262516

simplify22.0ms

Iterations

Iter	Nodes
done	84
2	84
1	82
0	66

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.6s	2829×	body	1280	valid
381.0ms	4058×	body	80	valid
164.0ms	627×	body	640	valid
58.0ms	334×	body	320	valid
17.0ms	152×	body	160	valid