Details

sample59.0ms

Algorithm

intervals

Results

18.0ms	82×	body	1280	valid
14.0ms	165×	body	80	valid
7.0ms	45×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.6b	(- (exp (* a x)) 1.0)

rewrite25.0ms

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:

3.0ms	(exp (* a x))
21.0ms	(- (exp (* a x)) 1.0)

series69.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(exp (* a x))
54.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

46 → 46

Iterations

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

prune208.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.6b	(* (* 1/6 a) (* (* x a) (* x a)))
1.4b	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
12.6b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite129.0ms

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:

11.0ms	(* 1/6 a)
98.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
14.0ms	(* x (+ a (* (* 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))))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* 1/6 a)
61.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
158.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
151.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2797
1	447
0	147

prune516.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
0.6b	(* (* 1/6 a) (* (* x a) (* x a)))
4.1b	(* x (* (* 1/6 a) (* (* x a) (* x a))))
12.6b	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

6.0ms	(* 1/6 a)
70.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
235.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
1.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/6 a)
76.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
98.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
148.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.4s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	3098
1	459
0	151

prune856.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.2b	(* 3 (* a x))
0.2b	(/ (- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0)) (fma (exp (* a x)) (+ (exp (* a x)) 1.0) (* 1.0 1.0)))
2.6b	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `times-frac`
8×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `exp-prod` `clear-num` `sub-neg` `frac-2neg` `exp-to-pow` `diff-log` `div-sub` `div-exp` `associate-r` `*-commutative` `div-inv` `rem-exp-log`

Counts

4 → 84

Calls

4 calls:

5.0ms	(exp (* a x))
19.0ms	(* 3 (* a x))
46.0ms	(/ (- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0)) (fma (exp (* a x)) (+ (exp (* a x)) 1.0) (* 1.0 1.0)))
23.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

series245.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (* a x))
29.0ms	(* 3 (* a x))
137.0ms	(/ (- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0)) (fma (exp (* a x)) (+ (exp (* a x)) 1.0) (* 1.0 1.0)))
61.0ms	(- (exp (* 3 (* a x))) (* (* 1.0 1.0) 1.0))

simplify1.5s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1848
1	408
0	163

prune601.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes409.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch1.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	41
3	41
2	39
1	36
0	28

end0.0ms

sample1.6s

Algorithm

intervals

Results

653.0ms	2696×	body	1280	valid
336.0ms	1292×	body	640	valid
254.0ms	5427×	body	80	valid
78.0ms	757×	body	320	valid
29.0ms	410×	body	160	valid