Details

sample127.0ms

Algorithm

intervals

Results

61.0ms	78×	body	1280	valid
24.0ms	46×	body	640	valid
13.0ms	22×	body	2560	valid
12.0ms	34×	body	320	valid
6.0ms	67×	body	80	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1 x)
1.1b	(+ x (hypot 1 x))
2.3b	(log (+ x (hypot 1 x)))

rewrite23.0ms

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:

0.0ms	(hypot 1 x)
11.0ms	(+ x (hypot 1 x))
10.0ms	(log (+ x (hypot 1 x)))

series437.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(hypot 1 x)
117.0ms	(+ x (hypot 1 x))
247.0ms	(log (+ x (hypot 1 x)))

simplify2.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5010
3	2035
2	666
1	244
0	108

prune242.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (* (* x x) x) -1/6 x)
0.1b	(* (* x x) x)
19.5b	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

0.0ms	(fma (* (* x x) x) -1/6 x)
29.0ms	(* (* x x) x)
0.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

series212.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(fma (* (* x x) x) -1/6 x)
45.0ms	(* (* x x) x)
73.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5004
3	1783
2	503
1	195
0	84

prune302.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ x (hypot 1 x))
1.1b	(+ x (hypot 1 x))
1.1b	(+ x (hypot 1 x))
2.3b	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
62×	`log-prod`
54×	`cbrt-div`
49×	`cbrt-prod`
41×	`*-un-lft-identity`
39×	`associate-l`
30×	`flip3-+` `flip-+` `unswap-sqr`
28×	`frac-times`
26×	`log-div`
24×	`pow1`
19×	`add-cube-cbrt`
16×	`log-pow`
14×	`associate-r` `associate-*l/`
13×	`swap-sqr`
10×	`add-exp-log` `distribute-lft-out` `add-log-exp`
9×	`fma-def` `pow1/3` `pow-prod-up`
8×	`associate-*r/`
6×	`pow-plus`
5×	`pow-prod-down` `*-commutative`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative` `sum-log` `rem-log-exp` `prod-exp` `pow-sqr`
2×	`pow2` `pow3`

Counts

4 → 171

Calls

4 calls:

11.0ms	(+ x (hypot 1 x))
11.0ms	(+ x (hypot 1 x))
10.0ms	(+ x (hypot 1 x))
228.0ms	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ x (hypot 1 x))
99.0ms	(+ x (hypot 1 x))
101.0ms	(+ x (hypot 1 x))
189.0ms	(log (* (* (cbrt (+ x (hypot 1 x))) (cbrt (+ x (hypot 1 x)))) (cbrt (+ x (hypot 1 x)))))

simplify2.2s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
3	4283
2	1408
1	647
0	287

prune568.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 (* x x)) x)
0.3b	(/ 1/8 (* x x))
10.7b	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
18.7b	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

16909×	`add-sqr-sqrt`
16795×	`times-frac`
15270×	`*-un-lft-identity`
15253×	`add-cube-cbrt`
12065×	`associate-/l*`
10663×	`associate-/r*`
9880×	`frac-sub`
8912×	`log-div`
8910×	`frac-add`
3775×	`prod-diff`
3646×	`unpow-prod-down`
2751×	`associate-/l/`
2317×	`swap-sqr`
2313×	`associate-r` `associate-l`
2013×	`clear-num` `frac-2neg`
1220×	`sqr-pow`
775×	`*-commutative` `unswap-sqr`
391×	`div-inv`
151×	`fma-neg`
28×	`difference-of-squares`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`flip3--` `flip--`
7×	`cbrt-undiv` `div-exp`
6×	`log-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`distribute-lft-out`
2×	`prod-exp` `cbrt-unprod`
1×	`sub-neg` `flip3-+` `diff-log` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 14208

Calls

4 calls:

50.0ms	(/ (/ 1/8 (* x x)) x)
13.0ms	(/ 1/8 (* x x))
2.1s	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
594.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (/ 1/8 (* x x)) x)
40.0ms	(/ 1/8 (* x x))
145.0ms	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
180.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

simplify32.2s

Counts

14220 → 14220

Iterations

Iter	Nodes
done	34683
0	34683

prune55.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.5b

bsearch92.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.009171061219366458
9	-101227.54480913779	-5.532094628653386e-05	-1.0682549790295666

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	2293×	body	1280	valid
908.0ms	1570×	body	640	valid
398.0ms	775×	body	2560	valid
176.0ms	824×	body	320	valid
134.0ms	2096×	body	80	valid
59.0ms	442×	body	160	valid