Details

sample116.0ms

Algorithm

intervals

Results

62.0ms	78×	body	1280	valid
18.0ms	46×	body	640	valid
12.0ms	22×	body	2560	valid
8.0ms	34×	body	320	valid
5.0ms	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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize15.0ms

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)))

rewrite9.0ms

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)
4.0ms	(+ x (hypot 1 x))
3.0ms	(log (+ x (hypot 1 x)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(hypot 1 x)
71.0ms	(+ x (hypot 1 x))
161.0ms	(log (+ x (hypot 1 x)))

simplify1.4s

Counts

56 → 56

Iterations

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

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))

rewrite22.0ms

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 (* (* x x) x) -1/6 x)
21.0ms	(* (* x x) x)
0.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

series235.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(fma (* (* x x) x) -1/6 x)
50.0ms	(* (* x x) x)
76.0ms	(fma (pow x 5) 3/40 (fma (* (* x x) x) -1/6 x))

simplify1.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
3	1430
2	359
1	134
0	71

prune178.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (hypot 1 x))
0.3b	(cbrt (hypot 1 x))
2.3b	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
12.9b	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (hypot 1 x))
1.0ms	(cbrt (hypot 1 x))
4.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
9.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (hypot 1 x))
158.0ms	(cbrt (hypot 1 x))
150.0ms	(log (+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
90.0ms	(+ x (* (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5008
3	2629
2	903
1	315
0	134

prune319.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize31.0ms

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)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

1367×	`times-frac`
775×	`add-sqr-sqrt`
754×	`*-un-lft-identity`
737×	`add-cube-cbrt`
625×	`prod-diff`
228×	`unpow-prod-down`
135×	`div-inv`
78×	`sqr-pow`
25×	`fma-neg`
19×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`difference-of-squares`
10×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`log-prod` `add-log-exp`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`frac-add` `distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `rem-log-exp` `log-pow` `flip-+` `associate-/l/`

Counts

4 → 778

Calls

4 calls:

19.0ms	(/ (/ 1/8 (* x x)) x)
6.0ms	(/ 1/8 (* x x))
78.0ms	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
42.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ 1/8 (* x x)) x)
42.0ms	(/ 1/8 (* x x))
135.0ms	(log (+ (/ -1/2 x) (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))))
189.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

simplify1.9s

Counts

790 → 790

Iterations

Iter	Nodes
done	5000
1	2307
0	1032

prune4.1s

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

bsearch102.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.01035404049421089
9	-101227.54480913779	-5.532094628653386e-05	-1.0682549790295666

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	2293×	body	1280	valid
929.0ms	1570×	body	640	valid
414.0ms	775×	body	2560	valid
244.0ms	824×	body	320	valid
128.0ms	2096×	body	80	valid
94.0ms	442×	body	160	valid