Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
3.0ms	296×	pre	80	false
3.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	100	11
4	190	11
5	330	11
6	557	11
7	1628	11
done	5000	11

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
27.7b	(/ (* b b) (* a a))

rewrite7.0ms

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:

1.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
5.0ms	(/ (* b b) (* a a))

series43.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
29.0ms	(/ (* b b) (* a a))

simplify2.8s

Counts

44 → 44

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	69	538
1	166	502
2	594	410
3	4461	395
done	5000	395

prune99.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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)))

rewrite5.0ms

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:

1.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
3.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series21.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
8.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

simplify1.0s

Counts

48 → 48

Iterations

Useful iterations: 4 (378.0ms)

Iter	Nodes	Cost
0	55	633
1	88	453
2	214	405
3	673	389
4	1355	383
done	5001	383

prune115.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
0.0b	(cbrt (pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3))
0.0b	(pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3)
0.4b	(pow (fabs (/ b a)) 2)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod` `add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`unpow-prod-down` `sqrt-prod`
12×	`cube-prod`
8×	`pow1`
6×	`add-exp-log` `pow-unpow`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp`
1×	`rem-sqrt-square` `pow1/3` `sqrt-pow2` `rem-cbrt-cube` `unpow2` `rem-cube-cbrt`

Counts

4 → 98

Calls

4 calls:

4.0ms	(sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
2.0ms	(cbrt (pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3))
2.0ms	(pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3)
1.0ms	(pow (fabs (/ b a)) 2)

series65.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
13.0ms	(cbrt (pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3))
32.0ms	(pow (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) 3)
8.0ms	(pow (fabs (/ b a)) 2)

simplify2.4s

Counts

110 → 110

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	105	1811
1	201	1351
2	486	1323
3	2912	1323
done	5000	1323

prune240.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
0.0b	(pow (* (cbrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) (cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))) 3)
0.4b	(pow (fabs (/ b a)) 2)
0.4b	(pow (fabs (/ b a)) 2)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `pow-unpow`
7×	`cbrt-prod` `unpow-prod-down`
6×	`pow-pow`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow1/3` `sqrt-prod` `sqr-pow`
2×	`pow-prod-down` `unpow2` `rem-cube-cbrt`
1×	`cube-mult` `unpow3` `cube-prod` `pow3` `prod-exp` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
4.0ms	(pow (* (cbrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) (cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))) 3)
1.0ms	(pow (fabs (/ b a)) 2)
1.0ms	(pow (fabs (/ b a)) 2)

series102.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))
32.0ms	(pow (* (cbrt (fabs (- 1 (pow (fabs (/ b a)) 2)))) (cbrt (sqrt (fabs (- 1 (pow (fabs (/ b a)) 2)))))) 3)
8.0ms	(pow (fabs (/ b a)) 2)
8.0ms	(pow (fabs (/ b a)) 2)

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	95	1418
1	179	1215
2	460	1099
3	2127	1099
done	5001	1099

prune303.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample604.0ms

Algorithm

intervals

Results

190.0ms	8000×	body	80	valid
96.0ms	8000×	pre	80	true
96.0ms	8113×	pre	80	false