Details

sample465.0ms

Algorithm

intervals

Results

392.0ms

645×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	2726
4	907
3	333
2	110
1	47
0	23

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* i t) (* z c))
3.4b	(fma (- (* a c) (* i y)) j (fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x)))
3.8b	(* (- (* z y) (* t a)) x)
5.9b	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

rewrite45.0ms

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:

11.0ms	(- (* i t) (* z c))
0.0ms	(fma (- (* a c) (* i y)) j (fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x)))
31.0ms	(* (- (* z y) (* t a)) x)
0.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* i t) (* z c))
785.0ms	(fma (- (* a c) (* i y)) j (fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x)))
96.0ms	(* (- (* z y) (* t a)) x)
276.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

simplify2.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	3422
2	899
1	298
0	122

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* i t) (* z c))
3.6b	(* (- (* a c) (* i y)) j)
3.8b	(* (- (* z y) (* t a)) x)
5.9b	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

6.0ms	(- (* i t) (* z c))
23.0ms	(* (- (* a c) (* i y)) j)
51.0ms	(* (- (* z y) (* t a)) x)
0.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

series576.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* i t) (* z c))
109.0ms	(* (- (* a c) (* i y)) j)
94.0ms	(* (- (* z y) (* t a)) x)
321.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

simplify3.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
3	4908
2	1243
1	382
0	149

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize99.0ms

Local error

Found 4 expressions with local error:

5.7b	(cbrt (- (* a c) (* i y)))
5.7b	(cbrt (- (* a c) (* i y)))
5.7b	(cbrt (- (* a c) (* i y)))
5.9b	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

8.0ms	(cbrt (- (* a c) (* i y)))
9.0ms	(cbrt (- (* a c) (* i y)))
21.0ms	(cbrt (- (* a c) (* i y)))
1.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

series877.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (- (* a c) (* i y)))
200.0ms	(cbrt (- (* a c) (* i y)))
170.0ms	(cbrt (- (* a c) (* i y)))
320.0ms	(fma (- (* i t) (* z c)) b (* (- (* z y) (* t a)) x))

simplify1.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5002
3	1856
2	654
1	253
0	102

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.7b

localize87.0ms

Local error

Found 4 expressions with local error:

4.8b	(cbrt (- (* z y) (* t a)))
4.8b	(cbrt (- (* z y) (* t a)))
4.8b	(cbrt (- (* z y) (* t a)))
5.9b	(fma (- (* i t) (* z c)) b (* (* (cbrt (- (* z y) (* t a))) (cbrt (- (* z y) (* t a)))) (* (cbrt (- (* z y) (* t a))) x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

8.0ms	(cbrt (- (* z y) (* t a)))
6.0ms	(cbrt (- (* z y) (* t a)))
4.0ms	(cbrt (- (* z y) (* t a)))
0.0ms	(fma (- (* i t) (* z c)) b (* (* (cbrt (- (* z y) (* t a))) (cbrt (- (* z y) (* t a)))) (* (cbrt (- (* z y) (* t a))) x)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (- (* z y) (* t a)))
186.0ms	(cbrt (- (* z y) (* t a)))
182.0ms	(cbrt (- (* z y) (* t a)))
323.0ms	(fma (- (* i t) (* z c)) b (* (* (cbrt (- (* z y) (* t a))) (cbrt (- (* z y) (* t a)))) (* (cbrt (- (* z y) (* t a))) x)))

simplify2.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	1869
2	645
1	248
0	100

prune766.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.7b

regimes2.6s

Accuracy

3.4% (7.9b remaining)

Error of 12.3b against oracle of 4.3b and baseline of 12.6b

bsearch236.0ms

Steps

Iters	Range		Point
9	-1.584138811304868e-303	1.2483219091912466e-306	1.2317454213813665e-306
4	-7.704391687148978e-17	-4.494774876304711e-17	-7.304458212992854e-17

simplify19.0ms

Iterations

Iter	Nodes
done	67
1	67
0	48

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.8s

19133×

body

valid