Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	256×	pre	80	true
9.0ms	256×	body	80	valid
4.0ms	246×	pre	80	false

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	103	11
4	330	11
5	1613	11
done	5000	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
29.4b	(/ (* b b) (* a a))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `add-sqr-sqrt` `div-exp` `prod-exp` `cbrt-unprod`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

2 → 38

Calls

2 calls:

2.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
23.0ms	(/ (* b b) (* a a))

series55.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
32.0ms	(/ (* b b) (* a a))

simplify1.1s

Counts

44 → 44

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	69	538
1	193	502
2	1676	410
done	5001	410

prune127.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
0.4b	(* (fabs (/ b a)) (fabs (/ b a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

2.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
13.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series43.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
16.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

simplify1.6s

Counts

48 → 48

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	55	633
1	116	456
2	899	405
done	5001	399

prune132.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
0.0b	(* (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))) (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))))
0.4b	(pow (fabs (/ b a)) 2)
0.4b	(pow (fabs (/ b a)) 2)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-prod`
54×	`add-sqr-sqrt`
36×	`sqrt-pow1`
31×	`pow1`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`add-exp-log`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 138

Calls

4 calls:

3.0ms	(sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
29.0ms	(* (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))) (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))))
5.0ms	(pow (fabs (/ b a)) 2)
6.0ms	(pow (fabs (/ b a)) 2)

series114.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
19.0ms	(* (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))) (sqrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))))
13.0ms	(pow (fabs (/ b a)) 2)
10.0ms	(pow (fabs (/ b a)) 2)

simplify1.6s

Counts

150 → 150

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	112	3000
1	243	1848
2	1128	1692
done	5001	1655

prune472.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13
done	11	13

end0.0ms

sample1.8s

Algorithm

intervals

Results

840.0ms	8000×	body	80	valid
155.0ms	8000×	pre	80	true
155.0ms	8175×	pre	80	false