Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	93×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `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 → 71

Calls

3 calls:

15.0ms	(sqrt (+ x 1.0))
30.0ms	(+ 1.0 (sqrt (+ x 1.0)))
74.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series866.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(sqrt (+ x 1.0))
70.0ms	(+ 1.0 (sqrt (+ x 1.0)))
635.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.4s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1194
1	343
0	146

prune564.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
0.1b	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
0.2b	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
6.7b	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
14×	`flip3-+` `flip-+`
12×	`times-frac` `sqrt-div`
9×	`pow1`
8×	`add-exp-log` `frac-times` `cbrt-div` `add-cbrt-cube`
7×	`associate-r` `distribute-lft-out`
6×	`add-log-exp`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`pow3` `associate-/r/` `pow-prod-up` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `cbrt-prod` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv`

Counts

4 → 109

Calls

4 calls:

13.0ms	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
88.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
23.0ms	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
26.0ms	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x)))))
111.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
272.0ms	(/ x (+ 1.0 (cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))))
86.0ms	(cbrt (* (+ 1.0 x) (sqrt (+ 1.0 x))))

simplify2.9s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	1697
1	488
0	211

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
6.7b	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite988.0ms

Algorithm

rewrite-expression-head

Rules

88×	`frac-times`
87×	`flip3-+` `flip-+`
52×	`cbrt-div`
44×	`associate-*l/`
34×	`*-un-lft-identity`
30×	`pow1`
26×	`associate-*r/` `associate-/r/`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
13×	`add-exp-log`
12×	`times-frac` `add-cbrt-cube`
8×	`associate-r`
7×	`pow-plus` `pow-prod-up` `distribute-lft-out`
6×	`swap-sqr`
5×	`cbrt-prod` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-sqr` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `pow1/3` `div-exp` `clear-num` `rem-cbrt-cube` `div-inv`

Counts

4 → 198

Calls

4 calls:

367.0ms	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
34.0ms	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
243.0ms	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
322.0ms	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))
266.0ms	(/ x (cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0))))))
138.0ms	(* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
88.0ms	(cbrt (* (* (+ 1.0 (sqrt (+ x 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ 1.0 (sqrt (+ x 1.0)))))

simplify6.8s

Counts

210 → 210

Iterations

Iter	Nodes
done	5002
2	3456
1	910
0	318

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `associate-/r*` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `hypot-def`

Counts

4 → 144

Calls

4 calls:

83.0ms	(sqrt (+ x 1.0))
54.0ms	(+ 1.0 (sqrt (+ x 1.0)))
70.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
226.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ x 1.0))
77.0ms	(+ 1.0 (sqrt (+ x 1.0)))
816.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
242.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify6.8s

Counts

156 → 156

Iterations

Iter	Nodes
done	5002
2	2007
1	582
0	224

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes147.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 6.9b

bsearch355.0ms

Steps

Iters	Range		Point
8	87.84726908649233	263824.51516633737	1614.0612239232446

simplify29.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end6.0ms

sample2.2s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
116.0ms	2661×	body	80	nan