Details

sample84.0ms

Algorithm

intervals

Results

36.0ms	98×	body	2560	valid
18.0ms	78×	body	1280	valid
7.0ms	272×	body	80	nan
7.0ms	41×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	4×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	14
1	20	14
2	42	14
3	88	14
4	159	14
5	258	14
6	410	14
7	1395	14
done	5000	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

10.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
25.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify427.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	145	1268
1	347	1231
2	1203	1120
done	5001	1120

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* 5.0 (* v v))))
0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
0.5b	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `associate-r` `*-commutative` `unswap-sqr`
1×	`acos-asin` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 69

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
8.0ms	(* 5.0 (* v v))
8.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series150.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
31.0ms	(* 5.0 (* v v))
29.0ms	(* 5.0 (* v v))
4.0ms	(acos (* (sqrt (- 1.0 (* 5.0 (* v v)))) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify1.8s

Counts

81 → 81

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	116	1023
1	263	817
2	836	747
3	4100	747
done	5001	747

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.5b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `acos-asin` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify1.5s

Counts

13 → 13

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	22	191
1	30	191
2	56	169
3	147	169
4	380	169
5	1380	169
done	5000	169

prune38.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0b	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.5b	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

4×	`expm1-log1p-u`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

3 → 32

Calls

3 calls:

0.0ms	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
0.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
0.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

series266.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0))))
153.0ms	(expm1 (log1p (acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))))
6.0ms	(acos (fma 4.0 (fma v v (pow v 4)) (- 1.0)))

simplify1.6s

Counts

41 → 41

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	44	616
1	56	590
2	89	516
3	182	516
4	462	516
5	1512	516
done	5000	516

prune104.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes88.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	13	24
done	13	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2937×	body	2560	valid
587.0ms	2545×	body	1280	valid
230.0ms	8079×	body	80	nan
211.0ms	1240×	body	640	valid
78.0ms	648×	body	320	valid
36.0ms	414×	body	160	valid
12.0ms	216×	body	80	valid