Details

sample206.0ms

Algorithm

intervals

Results

118.0ms

649×

body

valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2724
4	907
3	333
2	110
1	47
0	23

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
3.5b	(* j (- (* c t) (* i y)))
3.5b	(* x (- (* y z) (* t a)))
4.2b	(* b (- (* c z) (* i a)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-*r/`
11×	`sub-neg` `prod-diff`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
8×	`flip3--` `flip--`
6×	`associate--l+` `associate--r+` `add-log-exp`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log`

Counts

4 → 116

Calls

4 calls:

27.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
20.0ms	(* j (- (* c t) (* i y)))
24.0ms	(* x (- (* y z) (* t a)))
26.0ms	(* b (- (* c z) (* i a)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
114.0ms	(* j (- (* c t) (* i y)))
84.0ms	(* x (- (* y z) (* t a)))
102.0ms	(* b (- (* c z) (* i a)))

simplify2.0s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2831
1	741
0	247

prune1.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.8b

localize53.0ms

Local error

Found 4 expressions with local error:

3.5b	(* j (- (* c t) (* i y)))
3.5b	(* x (fma y z (- (* a t))))
4.2b	(* b (- (* c z) (* i a)))
51.4b	(fma (- a) t (* a t))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `sub-neg` `prod-diff` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
2×	`flip3--` `flip--`

Counts

4 → 88

Calls

4 calls:

20.0ms	(* j (- (* c t) (* i y)))
9.0ms	(* x (fma y z (- (* a t))))
54.0ms	(* b (- (* c z) (* i a)))
1.0ms	(fma (- a) t (* a t))

series392.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* j (- (* c t) (* i y)))
111.0ms	(* x (fma y z (- (* a t))))
115.0ms	(* b (- (* c z) (* i a)))
44.0ms	(fma (- a) t (* a t))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	4671
2	1272
1	437
0	183

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* i a) (* z c))
2.7b	(fma (- (* t c) (* i y)) j (fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x)))
3.5b	(* (- (* z y) (* t a)) x)
3.9b	(fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x))

rewrite34.0ms

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×	`flip3--` `associate-*l/` `fma-udef` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(- (* i a) (* z c))
0.0ms	(fma (- (* t c) (* i y)) j (fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x)))
26.0ms	(* (- (* z y) (* t a)) x)
0.0ms	(fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x))

series1.1s

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* i a) (* z c))
734.0ms	(fma (- (* t c) (* i y)) j (fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x)))
88.0ms	(* (- (* z y) (* t a)) x)
271.0ms	(fma (- (* i a) (* z c)) b (* (- (* z y) (* t a)) x))

simplify2.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5002
3	3407
2	898
1	298
0	122

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.5b

localize124.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (* j (- (* c t) (* i y))))
6.7b	(cbrt (* j (- (* c t) (* i y))))
6.7b	(cbrt (* j (- (* c t) (* i y))))
51.4b	(fma (- a) t (* a t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

9.0ms	(cbrt (* j (- (* c t) (* i y))))
8.0ms	(cbrt (* j (- (* c t) (* i y))))
9.0ms	(cbrt (* j (- (* c t) (* i y))))
0.0ms	(fma (- a) t (* a t))

series720.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (* j (- (* c t) (* i y))))
198.0ms	(cbrt (* j (- (* c t) (* i y))))
224.0ms	(cbrt (* j (- (* c t) (* i y))))
41.0ms	(fma (- a) t (* a t))

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	1945
2	602
1	208
0	88

prune987.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.5b

regimes2.9s

Accuracy

11.1% (5.4b remaining)

Error of 11.6b against oracle of 6.2b and baseline of 12.2b

bsearch301.0ms

Steps

Iters	Range		Point
8	1.5776781430240956e-145	7.177528025261375e-141	2.083531344283219e-145
6	-3.2425151790462807e-283	-2.932479106747331e-284	-1.692024971176755e-283

simplify18.0ms

Iterations

Iter	Nodes
done	82
2	82
1	80
0	54

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.4s

19204×

body

valid