Details

sample112.0ms

Algorithm

intervals

Results

63.0ms

574×

body

valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* t c) (* i y))
4.8b	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
5.5b	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
6.8b	(* (fma (- a) t (* z y)) x)

rewrite26.0ms

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:

13.0ms	(- (* t c) (* i y))
0.0ms	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
1.0ms	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
11.0ms	(* (fma (- a) t (* z y)) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* t c) (* i y))
834.0ms	(fma (- (* t c) (* i y)) j (fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x)))
330.0ms	(fma b (- (* a i) (* z c)) (* (fma (- a) t (* z y)) x))
133.0ms	(* (fma (- a) t (* z y)) x)

simplify2.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3882
2	744
1	248
0	112

prune890.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize80.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (fma i (- y) (* c t)))
6.5b	(cbrt (fma i (- y) (* c t)))
6.5b	(cbrt (fma i (- y) (* c t)))
6.8b	(* (fma (- a) t (* z y)) x)

rewrite16.0ms

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:

1.0ms	(cbrt (fma i (- y) (* c t)))
1.0ms	(cbrt (fma i (- y) (* c t)))
1.0ms	(cbrt (fma i (- y) (* c t)))
10.0ms	(* (fma (- a) t (* z y)) x)

series794.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (fma i (- y) (* c t)))
203.0ms	(cbrt (fma i (- y) (* c t)))
273.0ms	(cbrt (fma i (- y) (* c t)))
114.0ms	(* (fma (- a) t (* z y)) x)

simplify1.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	3123
2	543
1	198
0	97

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.2b

localize130.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (fma (- i) y (* t c)))
6.5b	(cbrt (fma (- i) y (* t c)))
6.5b	(cbrt (fma (- i) y (* t c)))
6.8b	(* (fma (- a) t (* z y)) x)

rewrite16.0ms

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:

1.0ms	(cbrt (fma (- i) y (* t c)))
1.0ms	(cbrt (fma (- i) y (* t c)))
1.0ms	(cbrt (fma (- i) y (* t c)))
11.0ms	(* (fma (- a) t (* z y)) x)

series792.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt (fma (- i) y (* t c)))
228.0ms	(cbrt (fma (- i) y (* t c)))
246.0ms	(cbrt (fma (- i) y (* t c)))
104.0ms	(* (fma (- a) t (* z y)) x)

simplify1.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
3	3123
2	543
1	198
0	97

prune1.3s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 6.2b

localize107.0ms

Local error

Found 4 expressions with local error:

5.9b	(* b (fma (- c) z (* a i)))
6.3b	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
6.3b	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
6.3b	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`fma-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

11.0ms	(* b (fma (- c) z (* a i)))
0.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
1.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
1.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))

series1.1s

Counts

4 → 12

Calls

4 calls:

125.0ms	(* b (fma (- c) z (* a i)))
343.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
321.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))
339.0ms	(fma (fma t (- a) (* z y)) x (* b (fma (- c) z (* a i))))

simplify1.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
3	1945
2	438
1	142
0	69

prune800.0ms

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 6.2b

regimes2.9s

Accuracy

28.4% (5.7b remaining)

Error of 10.4b against oracle of 4.7b and baseline of 12.6b

bsearch424.0ms

Steps

Iters	Range		Point
9	6.145664524408899e+34	4.697004975121908e+42	4.6256669465840515e+42
8	-9.805978792272694e+76	-1.1074460972934387e+73	-2.1482946555590227e+74

simplify14.0ms

Iterations

Iter	Nodes
done	60
2	60
1	58
0	41

end0.0ms

sample6.0s

Algorithm

intervals

Results

4.0s

18706×

body

valid