Details

sample100.0ms

Algorithm

intervals

Results

30.0ms	22×	body	2560	valid
22.0ms	198×	body	80	valid
10.0ms	256×	pre	80	true
8.0ms	16×	body	1280	valid
4.0ms	9×	body	640	valid
3.0ms	8×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	2×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	40
4	40
3	38
2	34
1	27
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) (* (* p p) 4))))
0.0b	(* (* p p) 4)
0.4b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3-+` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `associate-l` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

17.0ms	(/ x (sqrt (+ (* x x) (* (* p p) 4))))
14.0ms	(* (* p p) 4)
12.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
13.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ x (sqrt (+ (* x x) (* (* p p) 4))))
53.0ms	(* (* p p) 4)
117.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
72.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	2564
2	881
1	331
0	152

prune953.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* p p) 4)
0.2b	(* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))
1.8b	(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))) 0.5)
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
18×	`add-exp-log`
14×	`add-cbrt-cube` `sqrt-prod`
12×	`pow1`
7×	`prod-exp`
6×	`add-log-exp` `unswap-sqr`
5×	`cbrt-unprod`
4×	`sqrt-div` `associate-l` `pow-prod-down` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`div-exp` `associate-/r/` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `sum-log` `sqrt-pow1` `pow1/2` `1-exp` `associate-*r/` `un-div-inv` `div-inv`

Counts

4 → 98

Calls

4 calls:

15.0ms	(* (* p p) 4)
28.0ms	(* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))
33.0ms	(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))) 0.5)
20.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* p p) 4)
77.0ms	(* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))
106.0ms	(+ (* 0.5 (* x (/ 1 (sqrt (+ (* x x) (* (* p p) 4)))))) 0.5)
69.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify3.1s

Counts

110 → 110

Iterations

Iter	Nodes
3	4026
2	1231
1	449
0	176

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.9b

localize108.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (* x x) (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*` `sqrt-pow1` `times-frac` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 72

Calls

4 calls:

14.0ms	(/ (* x x) (+ (* x x) (* (* p p) 4)))
10.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
12.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
9.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (* x x) (+ (* x x) (* (* p p) 4)))
50.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
49.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
80.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify965.0ms

Counts

84 → 84

Iterations

Iter	Nodes
3	2895
2	774
1	206
0	80

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.9b

localize74.0ms

Local error

Found 4 expressions with local error:

18.9b	(sqrt (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))
18.9b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

17.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
6.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
7.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
7.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
55.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
63.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
77.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
5	2940
4	1679
3	741
2	257
1	98
0	42

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.9b

regimes231.0ms

Accuracy

0% (0.7b remaining)

Error of 13.9b against oracle of 13.1b and baseline of 13.9b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	33
1	33
0	23

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	757×	body	2560	valid
769.0ms	6007×	body	80	valid
442.0ms	618×	body	1280	valid
428.0ms	8000×	pre	80	true
177.0ms	333×	body	640	valid
56.0ms	68×	body	5120	valid
51.0ms	151×	body	320	valid
14.0ms	66×	body	160	valid