Details

sample46.0ms

Algorithm

intervals

Results

22.0ms

510×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	19	13
2	50	13
3	159	13
4	298	13
5	384	13
6	392	13
7	463	13
8	620	13
9	632	13
done	632	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.7b	(* (* y 4.0) (- (* z z) t))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg`
4×	`distribute-rgt-in` `add-sqr-sqrt` `distribute-lft-in` `associate-r` `associate--r+` `add-log-exp`
3×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-*r/` `flip--`
1×	`diff-log` `associate-l` `*-commutative` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

22.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
57.0ms	(* (* y 4.0) (- (* z z) t))

series227.0ms

Counts

2 → 6

Calls

2 calls:

133.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
95.0ms	(* (* y 4.0) (- (* z z) t))

simplify3.7s

Counts

47 → 47

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	93	707
1	264	669
2	982	583
3	4561	577
done	5001	577

prune130.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* y (* (- (pow z 2) t) 4.0)))
5.7b	(* y (* (- (pow z 2) t) 4.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`sub-neg` `diff-log` `associate-r` `*-commutative`

Counts

2 → 32

Calls

2 calls:

14.0ms	(- (* x x) (* y (* (- (pow z 2) t) 4.0)))
84.0ms	(* y (* (- (pow z 2) t) 4.0))

series172.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (* x x) (* y (* (- (pow z 2) t) 4.0)))
76.0ms	(* y (* (- (pow z 2) t) 4.0))

simplify2.3s

Counts

38 → 38

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	81	600
1	223	560
2	758	480
3	3770	474
done	5001	472

prune125.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
0.3b	(* (* y 4.0) (sqrt (- (* z z) t)))
5.4b	(sqrt (- (* z z) t))
5.4b	(sqrt (- (* z z) t))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 89

Calls

4 calls:

143.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
48.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
10.0ms	(sqrt (- (* z z) t))
11.0ms	(sqrt (- (* z z) t))

series309.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
102.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
74.0ms	(sqrt (- (* z z) t))
62.0ms	(sqrt (- (* z z) t))

simplify2.3s

Counts

101 → 101

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	136	1685
1	368	1362
2	1297	1120
done	5000	1116

prune393.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.7b

localize30.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (- (* z z) t))
5.4b	(sqrt (- (* z z) t))
5.4b	(sqrt (- (* z z) t))
5.4b	(sqrt (- (* z z) t))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

14.0ms	(sqrt (- (* z z) t))
17.0ms	(sqrt (- (* z z) t))
17.0ms	(sqrt (- (* z z) t))
19.0ms	(sqrt (- (* z z) t))

series231.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (- (* z z) t))
51.0ms	(sqrt (- (* z z) t))
51.0ms	(sqrt (- (* z z) t))
75.0ms	(sqrt (- (* z z) t))

simplify1.8s

Counts

76 → 76

Iterations

Useful iterations: 4 (345.0ms)

Iter	Nodes	Cost
0	56	816
1	124	728
2	265	664
3	494	656
4	1013	652
5	2555	652
done	5000	652

prune303.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 2.7b

regimes438.0ms

Accuracy

85.5% (0.5b remaining)

Error of 3.0b against oracle of 2.5b and baseline of 6.0b

bsearch183.0ms

Steps

Iters	Range		Point
8	2.545703430091905e+149	1.2262819834048186e+154	6.75315246229018e+153
8	-1.769171722317776e+149	-1.7344183351890289e+146	-1.74920595474598e+149

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	55
1	34	39
done	34	39

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s

15607×

body

valid