Details

sample66.0ms

Algorithm

intervals

Results

32.0ms	83×	body	1280	valid
10.0ms	53×	body	640	valid
6.0ms	169×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3485
6	450
5	118
4	51
3	27
2	18
1	11
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (exp (* a x)) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
6×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 40

Calls

2 calls:

7.0ms	(exp (* a x))
23.0ms	(- (exp (* a x)) 1.0)

series81.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
57.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
3	3404
2	600
1	183
0	79

prune202.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
1.4b	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
1.8b	(* (* 1/6 a) (* (* x a) (* x a)))
12.1b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1` `add-cbrt-cube` `add-exp-log`
33×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* 1/6 a)
13.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
88.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
0.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/6 a)
169.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
65.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
157.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5004
2	2780
1	447
0	147

prune556.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

12.1b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))
17.5b	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
17.5b	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
17.5b	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

rewrite3.0ms

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:

0.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))
1.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
1.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
1.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

199.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))
469.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
379.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
356.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

simplify1.6s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
2	841
1	222
0	93

prune474.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize131.0ms

Local error

Found 4 expressions with local error:

13.5b	(fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2))
17.5b	(cbrt (fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2)))
17.5b	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
17.5b	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

rewrite3.0ms

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:

0.0ms	(fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2))
1.0ms	(cbrt (fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2)))
1.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
1.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2))
398.0ms	(cbrt (fma (fma (* (* a x) (* a x)) (* a 1/6) a) x (* (* (* a x) (* a x)) 1/2)))
375.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))
346.0ms	(cbrt (fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))))

simplify1.7s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
2	951
1	249
0	111

prune592.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes663.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	35
2	35
1	34
0	26

end0.0ms

sample1.9s

Algorithm

intervals

Results

822.0ms	2738×	body	1280	valid
348.0ms	5502×	body	80	valid
282.0ms	1280×	body	640	valid
85.0ms	757×	body	320	valid
30.0ms	393×	body	160	valid