Details

sample111.0ms

Algorithm

intervals

Results

44.0ms	99×	body	2560	valid
25.0ms	82×	body	1280	valid
11.0ms	251×	body	80	nan
10.0ms	40×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	4×	body	80	valid

simplify884.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	293
1	20	293
2	43	293
3	84	293
4	155	293
5	254	293
6	944	293
done	5000	293

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

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)))

rewrite68.0ms

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×	`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×	`acos-asin` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 69

Calls

3 calls:

37.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
26.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
50.0ms	(* 5.0 (* v v))
8.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.9s

Counts

78 → 78

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	145	24673
1	373	21792
2	1832	21390
done	5000	21342

prune382.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* v v) (* v v) (* v v))
0.0b	(* (fma (* v v) (* v v) (* v v)) 4.0)
0.5b	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
1×	`acos-asin` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

1.0ms	(fma (* v v) (* v v) (* v v))
11.0ms	(* (fma (* v v) (* v v) (* v v)) 4.0)
2.0ms	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))

series309.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(fma (* v v) (* v v) (* v v))
170.0ms	(* (fma (* v v) (* v v) (* v v)) 4.0)
8.0ms	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))

simplify1.2s

Counts

49 → 49

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	66	13480
1	128	10534
2	776	10334
done	5002	10334

prune216.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))
1.0b	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
1.0b	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
1.0b	(* (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))) (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))))

rewrite26.0ms

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:

2.0ms	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))
2.0ms	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
2.0ms	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
16.0ms	(* (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))) (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))
36.0ms	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
43.0ms	(sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0)))
10.0ms	(* (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))) (sqrt (acos (- (* (fma (* v v) (* v v) (* v v)) 4.0) 1.0))))

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	75	39698
1	147	33834
2	655	33794
done	5000	33754

prune377.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

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))))
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))))

rewrite17.0ms

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:

13.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
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))))
1.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series786.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
207.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
209.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
157.0ms	(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify7.5s

Counts

93 → 93

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	65	48319
1	143	43021
2	521	43021
3	3624	42341
done	5000	42341

prune371.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes179.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	268
1	9	268
done	9	268

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.0s	3049×	body	2560	valid
1.5s	2440×	body	1280	valid
580.0ms	8164×	body	80	nan
347.0ms	1214×	body	640	valid
248.0ms	629×	body	320	valid
103.0ms	451×	body	160	valid
18.0ms	217×	body	80	valid