Details

sample76.0ms

Algorithm

intervals

Results

20.0ms	182×	body	80	valid
16.0ms	27×	body	2560	valid
11.0ms	24×	body	1280	valid
8.0ms	256×	pre	80	true
4.0ms	11×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	1×	body	5120	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* p p) 4))
0.0b	(* (* p p) 4)
1.6b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.4b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite53.0ms

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:

8.0ms	(+ (* x x) (* (* p p) 4))
18.0ms	(* (* p p) 4)
15.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
11.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x x) (* (* p p) 4))
31.0ms	(* (* p p) 4)
98.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
54.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	2963
2	877
1	282
0	109

prune760.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
0.8b	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
1.6b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.4b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

12.0ms	(exp (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
11.0ms	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
17.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(exp (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
205.0ms	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
92.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
59.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
4	5120
3	1850
2	631
1	242
0	114

prune839.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow E (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
0.8b	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
1.6b	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
12.4b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`log-prod` `add-exp-log` `add-log-exp`
4×	`log-div` `pow-unpow` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16`
3×	`unpow-prod-up` `unpow-prod-down` `sqrt-prod`
2×	`sqrt-div` `pow-exp` `log-pow` `pow-sub`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `e-exp-1` `sum-log` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

13.0ms	(pow E (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
11.0ms	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
12.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
6.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(pow E (log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)))
219.0ms	(log (+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5))
95.0ms	(+ (* 0.5 (/ x (sqrt (+ (* x x) (* (* p p) 4))))) 0.5)
55.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify1.0s

Counts

80 → 80

Iterations

Iter	Nodes
3	2500
2	838
1	315
0	129

prune857.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.5b

localize46.0ms

Local error

Found 4 expressions with local error:

2.0b	(log (+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5))
7.9b	(+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5)
12.4b	(sqrt (+ (* x x) (* (* p p) 4)))
12.4b	(sqrt (+ (* x x) (* (* p p) 4)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

49.0ms	(log (+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5))
56.0ms	(+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5)
9.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
20.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(log (+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5))
96.0ms	(+ (* 0.5 (/ x (* (sqrt (sqrt (+ (* x x) (* (* p p) 4)))) (sqrt (sqrt (+ (* x x) (* (* p p) 4))))))) 0.5)
66.0ms	(sqrt (+ (* x x) (* (* p p) 4)))
56.0ms	(sqrt (+ (* x x) (* (* p p) 4)))

simplify811.0ms

Counts

71 → 71

Iterations

Iter	Nodes
3	2229
2	629
1	222
0	96

prune910.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.5b

regimes122.0ms

Accuracy

-33.2% (8.1b remaining)

Error of 15.0b against oracle of 6.9b and baseline of 13.0b

bsearch87.0ms

Steps

Iters	Range		Point
6	-1.0697684771676703e+19	-1.5506507125207496e+18	-1.0089186447096822e+19

simplify7.0ms

Iterations

Iter	Nodes
2	34
1	34
0	30

end0.0ms

sample3.0s

Algorithm

intervals

Results

794.0ms	6044×	body	80	valid
755.0ms	8000×	pre	80	true
576.0ms	730×	body	2560	valid
381.0ms	631×	body	1280	valid
155.0ms	309×	body	640	valid
104.0ms	138×	body	320	valid
49.0ms	59×	body	5120	valid
20.0ms	89×	body	160	valid