Details

sample100.0ms

Algorithm

intervals

Results

41.0ms	203×	body	80	valid
14.0ms	16×	body	2560	valid
11.0ms	256×	pre	80	true
11.0ms	18×	body	1280	valid
6.0ms	12×	body	640	valid
2.0ms	2×	body	5120	valid
1.0ms	3×	body	160	valid
1.0ms	2×	body	320	valid

simplify23.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* p p) 4))
0.0b	(* (* p p) 4)
0.3b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
16.4b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`insert-posit16`
3×	`flip3-+` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`+-commutative` `sum-log` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

9.0ms	(+ (* x x) (* (* p p) 4))
19.0ms	(* (* p p) 4)
14.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (* x x) (* (* p p) 4))
31.0ms	(* (* p p) 4)
90.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
71.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	2963
2	877
1	282
0	109

prune637.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x)
0.4b	(log (exp (+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))))
2.0b	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
16.4b	(sqrt (+ (* (* p p) 4) (* x x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`associate-l`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
13×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`add-log-exp`
4×	`log-prod` `sqrt-div` `log-pow` `insert-posit16`
3×	`exp-prod` `flip3-+` `associate-r` `flip-+` `unswap-sqr`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 90

Calls

4 calls:

66.0ms	(* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x)
13.0ms	(log (exp (+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))))
10.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
22.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x)
78.0ms	(log (exp (+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))))
76.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
48.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	3023
2	979
1	352
0	153

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

localize47.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
2.0b	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
16.4b	(sqrt (+ (* (* p p) 4) (* x x)))
16.4b	(sqrt (+ (* (* p p) 4) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

7.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
6.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
22.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
22.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
72.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
47.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
46.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
4	4095
3	1566
2	512
1	175
0	68

prune925.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

localize58.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
2.0b	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
16.4b	(sqrt (+ (* (* p p) 4) (* x x)))
16.4b	(sqrt (+ (* (* p p) 4) (* x x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

6.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
6.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
22.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
22.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
73.0ms	(+ 0.5 (* (/ 0.5 (sqrt (+ (* (* p p) 4) (* x x)))) x))
48.0ms	(sqrt (+ (* (* p p) 4) (* x x)))
47.0ms	(sqrt (+ (* (* p p) 4) (* x x)))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
4	4095
3	1566
2	512
1	175
0	68

prune970.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.4b

regimes161.0ms

Accuracy

0% (0.7b remaining)

Error of 13.6b against oracle of 12.9b and baseline of 13.6b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	36
1	36
0	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

823.0ms	735×	body	2560	valid
597.0ms	6049×	body	80	valid
387.0ms	616×	body	1280	valid
288.0ms	8000×	pre	80	true
129.0ms	302×	body	640	valid
59.0ms	165×	body	320	valid
41.0ms	58×	body	5120	valid
13.0ms	75×	body	160	valid