Details

sample77.0ms

Algorithm

intervals

Results

39.0ms	98×	body	1280	valid
9.0ms	115×	body	80	valid
8.0ms	24×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `fma-neg` `sqrt-prod` `log1p-expm1-u` `associate-/l`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 70

Calls

3 calls:

0.0ms	(hypot 1.0 x)
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series770.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(hypot 1.0 x)
143.0ms	(/ 1.0 (hypot 1.0 x))
539.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	2095
1	483
0	200

prune368.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.5b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
30×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
2×	`flip3--` `associate-/r/` `flip--` `associate--r+` `associate-/l/`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `fma-neg` `diff-log` `div-sub` `prod-diff` `flip-+`

Counts

4 → 114

Calls

4 calls:

8.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
57.0ms	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
14.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ 1.0 (hypot 1.0 x))
140.0ms	(/ 1.0 (hypot 1.0 x))
1.6s	(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
149.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify546.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
1	989
0	321

prune834.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.5b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-pow`
18×	`exp-prod`
10×	`pow1` `associate-/l*`
8×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
7×	`associate-/r*`
6×	`log-prod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-sum`
2×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `exp-diff` `div-exp` `prod-diff` `associate-/r/` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip3--` `fma-neg` `diff-log` `div-sub` `rem-log-exp` `flip-+` `flip--`

Counts

4 → 124

Calls

4 calls:

7.0ms	(/ 1.0 (hypot 1.0 x))
90.0ms	(/ (log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
13.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
24.0ms	(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series2.2s

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ 1.0 (hypot 1.0 x))
1.7s	(/ (log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (+ (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0))
157.0ms	(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
174.0ms	(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify581.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
1	1032
0	371

prune964.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
0.0b	(expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))
1.8b	(fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
1.8b	(log (exp (expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`expm1-log1p-u` `pow1`
4×	`add-cbrt-cube` `add-exp-log` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`expm1-udef`
1×	`log-div` `log1p-udef` `expm1-log1p` `exp-diff` `rem-log-exp` `log1p-expm1` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
0.0ms	(expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))
0.0ms	(fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
2.0ms	(log (exp (expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

358.0ms	(log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
559.0ms	(expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))
192.0ms	(fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
571.0ms	(log (exp (expm1 (log1p (fma 1.0 1.0 (* 0.5 (- (+ (/ 1.0 (hypot 1.0 x)) 1.0))))))))

simplify594.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	1141
1	299
0	133

prune513.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.5b

regimes332.0ms

Accuracy

0% (0.2b remaining)

Error of 14.9b against oracle of 14.7b and baseline of 14.9b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	34
2	34
1	26
0	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	2820×	body	1280	valid
755.0ms	4078×	body	80	valid
206.0ms	635×	body	640	valid
57.0ms	317×	body	320	valid
17.0ms	150×	body	160	valid