Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	91×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

28.0ms	(+ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series290.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ 1.0 (sqrt (+ x 1.0)))
231.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 3 (945.0ms)

Iter	Nodes	Cost
0	121	771
1	289	722
2	872	665
3	3751	657
done	5000	657

prune150.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

21.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

365.0ms	(* (cbrt x) (cbrt x))
262.0ms	(cbrt x)
351.0ms	(cbrt x)
275.0ms	(cbrt x)

simplify5.4s

Counts

93 → 93

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune324.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
8.3b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 160

Calls

4 calls:

19.0ms	(+ 1.0 (sqrt (+ x 1.0)))
40.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
132.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
47.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series525.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ 1.0 (sqrt (+ x 1.0)))
180.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
225.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
54.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify1.2s

Counts

172 → 172

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	236	3088
1	502	2412
2	1676	2178
done	5002	2166

prune443.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`associate-r`
28×	`times-frac`
24×	`sqrt-prod`
21×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`add-exp-log` `fma-def` `add-cbrt-cube`
6×	`associate-l` `unswap-sqr`
4×	`pow1` `add-log-exp`
2×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `div-inv`

Counts

2 → 79

Calls

2 calls:

42.0ms	(+ (sqrt (+ x 1.0)) 1.0)
108.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series205.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(+ (sqrt (+ x 1.0)) 1.0)
161.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify1.3s

Counts

85 → 85

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	154	1234
1	402	1042
2	1364	916
done	5000	902

prune260.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

98.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.4b

bsearch15.0ms

Steps

Iters	Range		Point
3	2.5852715992345188e-23	3.219064609783079e-23	2.653971370452548e-23

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	18	27
done	18	27

end0.0ms

sample701.0ms

Algorithm

intervals

Results

361.0ms	7994×	body	80	valid
106.0ms	2707×	body	80	nan
1.0ms	6×	body	1280	valid