Details

sample162.0ms

Algorithm

intervals

Results

58.0ms	99×	body	2560	valid
52.0ms	82×	body	1280	valid
14.0ms	251×	body	80	nan
13.0ms	40×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	4×	body	80	valid

simplify631.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	944
5	254
4	155
3	84
2	43
1	20
0	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
0.1b	(* (* v 5.0) v)
0.5b	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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-l` `*-commutative` `div-inv`

Counts

3 → 68

Calls

3 calls:

27.0ms	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
23.0ms	(* (* v 5.0) v)
2.0ms	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))
41.0ms	(* (* v 5.0) v)
8.0ms	(acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))

simplify1.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1976
1	373
0	148

prune391.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity` `prod-diff`
89×	`add-cube-cbrt`
24×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
13×	`fma-neg`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r*` `pow-prod-down`
2×	`difference-of-squares`
1×	`acos-asin` `clear-num` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `associate-l` `-commutative` `frac-sub` `flip--` `associate-/l` `distribute-lft-out--` `sub-div` `unswap-sqr`

Counts

4 → 180

Calls

4 calls:

44.0ms	(- (/ 1.0 (fma v v (- 1.0))) (/ (* (* v v) 5.0) (fma v v (- 1.0))))
21.0ms	(/ (* (* v v) 5.0) (fma v v (- 1.0)))
15.0ms	(* (* v v) 5.0)
10.0ms	(acos (- (/ 1.0 (fma v v (- 1.0))) (/ (* (* v v) 5.0) (fma v v (- 1.0)))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(- (/ 1.0 (fma v v (- 1.0))) (/ (* (* v v) 5.0) (fma v v (- 1.0))))
113.0ms	(/ (* (* v v) 5.0) (fma v v (- 1.0)))
48.0ms	(* (* v v) 5.0)
14.0ms	(acos (- (/ 1.0 (fma v v (- 1.0))) (/ (* (* v v) 5.0) (fma v v (- 1.0)))))

simplify2.5s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
2	4128
1	723
0	293

prune834.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))
1.0b	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
1.0b	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
1.0b	(* (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))) (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

1.0ms	(acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))
1.0ms	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
1.0ms	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
11.0ms	(* (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))) (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))
46.0ms	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
45.0ms	(sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0))))))
16.0ms	(* (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))) (sqrt (acos (* (/ 1 (fma v v (- 1.0))) (+ 1.0 (* (- v) (* v 5.0)))))))

simplify8.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
3	4604
2	638
1	163
0	79

prune525.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))
1.0b	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0b	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0b	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

17.0ms	(* (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))
1.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
1.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))

series980.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(* (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))) (cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0))))))
232.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
226.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))
234.0ms	(cbrt (acos (/ (fma (- v) (* v 5.0) 1.0) (fma v v (- 1.0)))))

simplify1.9s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	848
1	152
0	72

prune647.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes55.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.0s	3049×	body	2560	valid
1.2s	2440×	body	1280	valid
897.0ms	8164×	body	80	nan
424.0ms	1214×	body	640	valid
198.0ms	629×	body	320	valid
63.0ms	451×	body	160	valid
17.0ms	217×	body	80	valid