Details

sample77.0ms

Algorithm

intervals

Results

29.0ms	63×	body	1280	valid
17.0ms	51×	body	640	valid
13.0ms	203×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	18
3	18
2	16
1	13
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
3.5b	(- (exp x) 1)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

27.0ms	(/ (- (exp x) 1) x)
8.0ms	(- (exp x) 1)

series58.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- (exp x) 1) x)
18.0ms	(- (exp x) 1)

simplify1.4s

Counts

70 → 70

Iterations

Iter	Nodes
4	3127
3	1236
2	514
1	234
0	108

prune673.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* x (+ (* 1/6 x) 1/2)))
0.1b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`insert-posit16`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

3 → 56

Calls

3 calls:

11.0ms	(+ 1 (* x (+ (* 1/6 x) 1/2)))
36.0ms	(* x (+ (* 1/6 x) 1/2))
11.0ms	(* 1/6 x)

series134.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ 1 (* x (+ (* 1/6 x) 1/2)))
83.0ms	(* x (+ (* 1/6 x) 1/2))
25.0ms	(* 1/6 x)

simplify1.6s

Counts

65 → 65

Iterations

Iter	Nodes
3	3337
2	833
1	255
0	96

prune447.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (log (exp (* x (+ (* 1/6 x) 1/2)))))
0.1b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
3.6b	(log (exp (* x (+ (* 1/6 x) 1/2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`pow1` `log-prod` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`associate-+r+`
4×	`exp-sum` `log-pow` `insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`flip3-+` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `exp-prod` `sum-log` `exp-to-pow` `rem-log-exp`

Counts

4 → 78

Calls

4 calls:

10.0ms	(+ 1 (log (exp (* x (+ (* 1/6 x) 1/2)))))
31.0ms	(* x (+ (* 1/6 x) 1/2))
5.0ms	(* 1/6 x)
4.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ 1 (log (exp (* x (+ (* 1/6 x) 1/2)))))
92.0ms	(* x (+ (* 1/6 x) 1/2))
26.0ms	(* 1/6 x)
107.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
3	3765
2	863
1	291
0	125

prune722.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 x)
0.3b	(* 1/6 x)
3.6b	(log (exp (* x (+ (* 1/6 x) 1/2))))
3.6b	(log (exp (* x (+ (* 1/6 x) 1/2))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`pow1` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `log-pow` `add-log-exp`
4×	`exp-sum` `insert-posit16`
2×	`distribute-rgt-in` `exp-prod` `distribute-lft-in` `exp-to-pow` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

10.0ms	(* 1/6 x)
10.0ms	(* 1/6 x)
8.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))
8.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* 1/6 x)
26.0ms	(* 1/6 x)
89.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))
84.0ms	(log (exp (* x (+ (* 1/6 x) 1/2))))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
4	4336
3	826
2	243
1	118
0	69

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.3b

bsearch24.0ms

Steps

Iters	Range		Point
6	-0.0002706832727749338	-6.606666156357114e-05	-0.00017431816494063913

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	2297×	body	1280	valid
581.0ms	1650×	body	640	valid
410.0ms	5466×	body	80	valid
202.0ms	812×	body	320	valid
54.0ms	406×	body	160	valid