Details

sample80.0ms

Algorithm

intervals

Results

37.0ms	42×	body	640	valid
11.0ms	198×	body	80	nan
10.0ms	62×	body	1280	valid
4.0ms	121×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

8.0ms	(sqrt (+ x 1.0))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.2s

Counts

95 → 95

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	137	1993
1	301	1432
2	677	1124
3	1959	950
done	5000	846

prune132.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
27×	`sqrt-prod`
21×	`distribute-lft-out`
20×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
6×	`fma-def` `associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 84

Calls

3 calls:

14.0ms	(sqrt (+ x 1.0))
27.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
68.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
158.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.0s

Counts

93 → 93

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	158	1171
1	364	1060
2	967	972
3	2933	955
done	5000	954

prune317.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt x) (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

28.0ms	(/ 1.0 (+ (sqrt x) (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
40.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
9.0ms	(cbrt (+ x 1.0))

series671.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ 1.0 (+ (sqrt x) (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
135.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
124.0ms	(cbrt (+ x 1.0))
128.0ms	(cbrt (+ x 1.0))

simplify2.4s

Counts

106 → 106

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	334	2583
1	890	2401
2	3255	2231
done	5000	2206

prune659.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

66×	`cbrt-prod`
43×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
36×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`cbrt-div`
16×	`sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 125

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
5.0ms	(cbrt (sqrt (+ x 1.0)))
10.0ms	(cbrt (sqrt (+ x 1.0)))
57.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (+ x 1.0))
148.0ms	(cbrt (sqrt (+ x 1.0)))
118.0ms	(cbrt (sqrt (+ x 1.0)))
113.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))

simplify2.9s

Counts

137 → 137

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	188	2149
1	384	1945
2	985	1861
3	2617	1665
done	5000	1522

prune700.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

end0.0ms

sample1.8s

Algorithm

intervals

Results

553.0ms	1772×	body	1280	valid
446.0ms	8006×	body	80	nan
172.0ms	1252×	body	640	valid
157.0ms	4002×	body	80	valid
71.0ms	657×	body	320	valid
23.0ms	317×	body	160	valid