Details

sample135.0ms

Algorithm

intervals

Results

63.0ms	107×	body	2560	valid
22.0ms	68×	body	1280	valid
12.0ms	272×	body	80	nan
11.0ms	39×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	7×	body	80	valid

simplify3.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5114
8	4456
7	1199
6	436
5	201
4	131
3	70
2	41
1	19
0	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b	(* 5.0 (* v v))
0.8b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`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×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `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 → 63

Calls

3 calls:

22.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
16.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series178.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
41.0ms	(* 5.0 (* v v))
5.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1180
1	359
0	139

prune362.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* 5.0 (* v v))))
0.1b	(* 5.0 (* v v))
0.1b	(* 5.0 (* v v))
0.8b	(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) 1) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

13.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
26.0ms	(* 5.0 (* v v))
26.0ms	(* 5.0 (* v v))
2.0ms	(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) 1) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(sqrt (- 1.0 (* 5.0 (* v v))))
48.0ms	(* 5.0 (* v v))
28.0ms	(* 5.0 (* v v))
9.0ms	(acos (* (/ (sqrt (- 1.0 (* 5.0 (* v v)))) 1) (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0))))

simplify3.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5009
3	4489
2	911
1	272
0	111

prune438.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.8b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow2` `acos-asin` `pow3` `pow-sqr`
1×	`cbrt-prod` `pow1/3` `associate-l` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
30.0ms	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
16.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
72.0ms	(* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
12.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify5.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
5	4947
4	2006
3	748
2	343
1	152
0	59

prune335.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize105.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod`
22×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `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 → 71

Calls

4 calls:

1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
10.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
90.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (* (* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

series681.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
198.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
249.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
11.0ms	(cbrt (* (* (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))) (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (* (* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

simplify2.4s

Counts

83 → 83

Iterations

Iter	Nodes
done	5002
3	1221
2	375
1	153
0	72

prune477.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes221.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.7s	2989×	body	2560	valid
1.2s	2536×	body	1280	valid
486.0ms	8173×	body	80	nan
338.0ms	1199×	body	640	valid
135.0ms	650×	body	320	valid
60.0ms	435×	body	160	valid
15.0ms	191×	body	80	valid