Details

sample244.0ms

Algorithm

intervals

Results

121.0ms	100×	body	2560	valid
52.0ms	78×	body	1280	valid
23.0ms	229×	body	80	nan
22.0ms	40×	body	640	valid
7.0ms	20×	body	320	valid
3.0ms	11×	body	160	valid
1.0ms	7×	body	80	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	467
3	171
2	65
1	25
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.1b	(* 5 (* v v))
0.6b	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`times-frac`
15×	`add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `difference-of-squares`
6×	`associate-/r*`
4×	`difference-of-sqr-1`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 74

Calls

3 calls:

23.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
15.0ms	(* 5 (* v v))
3.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
34.0ms	(* 5 (* v v))
6.0ms	(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify1.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	2001
3	2001
2	1125
1	378
0	148

prune420.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0b	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.1b	(* 5 (* v v))
0.7b	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`times-frac`
16×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
9×	`pow1`
6×	`associate-/r*` `add-log-exp`
4×	`difference-of-sqr-1` `insert-posit16`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

29.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
17.0ms	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
30.0ms	(* 5 (* v v))
2.0ms	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
51.0ms	(- (/ PI 2) (asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
38.0ms	(* 5 (* v v))
3.0ms	(asin (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	2041
3	2041
2	1354
1	466
0	181

prune494.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* v v) 1) (- 1 (* 5 (* v v))))
0.0b	(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))))
0.1b	(* 5 (* v v))
0.7b	(asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
19×	`times-frac`
16×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
9×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`difference-of-sqr-1` `insert-posit16`
3×	`associate-/r` `flip3--` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

41.0ms	(/ (- (* v v) 1) (- 1 (* 5 (* v v))))
24.0ms	(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))))
27.0ms	(* 5 (* v v))
2.0ms	(asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- (* v v) 1) (- 1 (* 5 (* v v))))
67.0ms	(- (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))))
50.0ms	(* 5 (* v v))
6.0ms	(asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))

simplify1.4s

Counts

103 → 103

Iterations

Iter	Nodes
done	2004
3	2004
2	1237
1	458
0	186

prune536.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (- (pow (/ PI 2) 3) (pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)) (+ (* (/ PI 2) (/ PI 2)) (+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))))
1.0b	(pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)
1.0b	(pow (/ PI 2) 3)
2.0b	(+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

244×	`add-sqr-sqrt`
149×	`times-frac`
100×	`*-un-lft-identity`
96×	`difference-of-squares`
88×	`unpow-prod-down` `cube-prod`
60×	`add-cube-cbrt`
42×	`sqr-pow`
33×	`associate-/l*`
20×	`distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/`
6×	`pow1` `pow-unpow` `frac-add` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`difference-cubes` `insert-posit16`
3×	`associate-/r*` `pow-exp` `div-inv` `rem-cube-cbrt`
2×	`cube-mult` `frac-times` `pow-to-exp` `cbrt-undiv` `pow-pow` `unpow3` `div-exp` `associate-l/` `associate-r/` `associate-/l/`
1×	`cube-div` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-rgt-out` `flip3--` `div-sub` `flip--`

Counts

4 → 243

Calls

4 calls:

147.0ms	(/ (- (pow (/ PI 2) 3) (pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)) (+ (* (/ PI 2) (/ PI 2)) (+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))))
4.0ms	(pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)
8.0ms	(pow (/ PI 2) 3)
18.0ms	(+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))

series774.0ms

Counts

4 → 10

Calls

4 calls:

623.0ms	(/ (- (pow (/ PI 2) 3) (pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)) (+ (* (/ PI 2) (/ PI 2)) (+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))))
48.0ms	(pow (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) 3)
0.0ms	(pow (/ PI 2) 3)
103.0ms	(+ (* (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v)))))) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))) (* (/ PI 2) (asin (/ 1 (/ (- (* v v) 1) (- 1 (* 5 (* v v))))))))

simplify1.9s

Counts

253 → 253

Iterations

Iter	Nodes
done	2004
2	2004
1	1138
0	365

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes122.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.7s	3023×	body	2560	valid
1.9s	2402×	body	1280	valid
1.3s	8155×	body	80	nan
714.0ms	1264×	body	640	valid
366.0ms	658×	body	320	valid
117.0ms	443×	body	160	valid
31.0ms	210×	body	80	valid