Details

sample123.0ms

Algorithm

intervals

Results

54.0ms	73×	body	1280	valid
24.0ms	45×	body	640	valid
14.0ms	24×	body	2560	valid
12.0ms	34×	body	320	valid
5.0ms	69×	body	80	valid
2.0ms	11×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	7

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
0.5b	(+ x (hypot 1 x))
2.9b	(log (+ x (hypot 1 x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log` `rem-log-exp` `log-pow`

Counts

3 → 47

Calls

3 calls:

1.0ms	(hypot 1 x)
9.0ms	(+ x (hypot 1 x))
7.0ms	(log (+ x (hypot 1 x)))

series409.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(hypot 1 x)
116.0ms	(+ x (hypot 1 x))
226.0ms	(log (+ x (hypot 1 x)))

simplify1.9s

Counts

56 → 56

Iterations

Iter	Nodes
4	4269
3	1489
2	592
1	243
0	108

prune334.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma -1/6 (* (* x x) x) x)
0.1b	(* (* x x) x)
19.4b	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

0.0ms	(fma -1/6 (* (* x x) x) x)
15.0ms	(* (* x x) x)
0.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

series192.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(fma -1/6 (* (* x x) x) x)
38.0ms	(* (* x x) x)
61.0ms	(fma 3/40 (pow x 5) (fma -1/6 (* (* x x) x) x))

simplify3.2s

Counts

62 → 62

Iterations

Iter	Nodes
4	5740
3	1305
2	365
1	134
0	70

prune407.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ x (hypot 1 x))
0.5b	(+ x (hypot 1 x))
2.9b	(log (sqrt (+ x (hypot 1 x))))
2.9b	(log (sqrt (+ x (hypot 1 x))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`fma-def` `add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 82

Calls

4 calls:

4.0ms	(+ x (hypot 1 x))
4.0ms	(+ x (hypot 1 x))
4.0ms	(log (sqrt (+ x (hypot 1 x))))
4.0ms	(log (sqrt (+ x (hypot 1 x))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ x (hypot 1 x))
80.0ms	(+ x (hypot 1 x))
185.0ms	(log (sqrt (+ x (hypot 1 x))))
141.0ms	(log (sqrt (+ x (hypot 1 x))))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
4	2930
3	1132
2	493
1	216
0	101

prune803.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -1/16 (pow x 5))
0.5b	(/ -1/8 (* (* x x) x))
10.2b	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
18.8b	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

178×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
135×	`times-frac`
118×	`add-cube-cbrt`
100×	`prod-diff`
59×	`unpow-prod-down`
27×	`distribute-lft-out`
25×	`fma-neg`
21×	`sqr-pow`
19×	`add-exp-log`
15×	`add-cbrt-cube`
9×	`log-prod` `add-log-exp`
8×	`associate-/r*` `difference-of-squares`
7×	`div-inv`
6×	`div-exp` `frac-sub` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3-+` `flip3--` `diff-log` `frac-add` `flip-+` `flip--`
1×	`pow-to-exp` `sum-log` `sub-neg` `rem-log-exp` `pow-exp` `log-pow` `associate--r+`

Counts

4 → 251

Calls

4 calls:

5.0ms	(/ -1/16 (pow x 5))
14.0ms	(/ -1/8 (* (* x x) x))
144.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
194.0ms	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ -1/16 (pow x 5))
49.0ms	(/ -1/8 (* (* x x) x))
135.0ms	(log (- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
67.0ms	(- (/ -1/16 (pow x 5)) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))

simplify1.0s

Counts

263 → 263

Iterations

Iter	Nodes
2	2561
1	839
0	361

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.9b

bsearch110.0ms

Steps

Iters	Range		Point
9	5.277777168093308e-05	15.597049771107491	0.007700169734768205
10	-1231591086050.0088	-0.0006858147917088189	-1.0776022250282242

simplify7.0ms

Iterations

Iter	Nodes
2	33
1	33
0	30

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	2298×	body	1280	valid
897.0ms	1629×	body	640	valid
637.0ms	801×	body	2560	valid
286.0ms	800×	body	320	valid
203.0ms	2076×	body	80	valid
74.0ms	396×	body	160	valid