Details

sample117.0ms

Algorithm

intervals

Results

56.0ms

622×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1195
3	333
2	110
1	47
0	23

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* a i) (* z c))
4.5b	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
5.3b	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
6.1b	(* (fma (- a) t (* z y)) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

6.0ms	(- (* a i) (* z c))
0.0ms	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
0.0ms	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
5.0ms	(* (fma (- a) t (* z y)) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* a i) (* z c))
300.0ms	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
775.0ms	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
93.0ms	(* (fma (- a) t (* z y)) x)

simplify1.9s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3857
2	743
1	248
0	112

prune839.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.3b

localize78.0ms

Local error

Found 4 expressions with local error:

6.1b	(* (fma (- a) t (* z y)) x)
6.5b	(cbrt (fma (- c) z (* a i)))
6.5b	(cbrt (fma (- c) z (* a i)))
6.5b	(cbrt (fma (- c) z (* a i)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

6.0ms	(* (fma (- a) t (* z y)) x)
1.0ms	(cbrt (fma (- c) z (* a i)))
1.0ms	(cbrt (fma (- c) z (* a i)))
9.0ms	(cbrt (fma (- c) z (* a i)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (fma (- a) t (* z y)) x)
271.0ms	(cbrt (fma (- c) z (* a i)))
255.0ms	(cbrt (fma (- c) z (* a i)))
228.0ms	(cbrt (fma (- c) z (* a i)))

simplify1.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	3104
2	538
1	198
0	97

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.3b

localize79.0ms

Local error

Found 4 expressions with local error:

5.3b	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (* (cbrt (fma (- a) t (* z y))) (cbrt (fma (- a) t (* z y)))) (* (cbrt (fma t (- a) (* z y))) x))))
7.9b	(cbrt (fma (- a) t (* z y)))
7.9b	(cbrt (fma (- a) t (* z y)))
7.9b	(cbrt (fma t (- a) (* z y)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (* (cbrt (fma (- a) t (* z y))) (cbrt (fma (- a) t (* z y)))) (* (cbrt (fma t (- a) (* z y))) x))))
1.0ms	(cbrt (fma (- a) t (* z y)))
1.0ms	(cbrt (fma (- a) t (* z y)))
1.0ms	(cbrt (fma t (- a) (* z y)))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.5s	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (* (cbrt (fma (- a) t (* z y))) (cbrt (fma (- a) t (* z y)))) (* (cbrt (fma t (- a) (* z y))) x))))
298.0ms	(cbrt (fma (- a) t (* z y)))
285.0ms	(cbrt (fma (- a) t (* z y)))
253.0ms	(cbrt (fma t (- a) (* z y)))

simplify865.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
3	1656
2	511
1	221
0	109

prune909.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize85.0ms

Local error

Found 4 expressions with local error:

7.9b	(cbrt (fma (- a) t (* z y)))
7.9b	(cbrt (fma (- a) t (* z y)))
7.9b	(cbrt (fma (- a) t (* z y)))
7.9b	(cbrt (fma (- a) t (* z y)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma (- a) t (* z y)))
1.0ms	(cbrt (fma (- a) t (* z y)))
1.0ms	(cbrt (fma (- a) t (* z y)))
1.0ms	(cbrt (fma (- a) t (* z y)))

series1.0s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt (fma (- a) t (* z y)))
254.0ms	(cbrt (fma (- a) t (* z y)))
255.0ms	(cbrt (fma (- a) t (* z y)))
263.0ms	(cbrt (fma (- a) t (* z y)))

simplify509.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	1042
2	279
1	119
0	57

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.2b

regimes2.0s

Accuracy

-8.8% (9.0b remaining)

Error of 13.3b against oracle of 4.3b and baseline of 12.6b

bsearch406.0ms

Steps

Iters	Range		Point
8	4.516688367575099e+209	2.7850176051691004e+212	5.6489348679381404e+209
8	2.9688942850529494e+171	1.2330517699086064e+174	1.2162219411019788e+174

simplify21.0ms

Iterations

Iter	Nodes
done	79
3	79
2	72
1	62
0	43

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.3s

19197×

body

valid