Details

sample87.0ms

Algorithm

intervals

Results

32.0ms	62×	body	1280	valid
18.0ms	71×	body	10240	exit
10.0ms	48×	body	640	valid
4.0ms	30×	body	320	valid
4.0ms	100×	body	80	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.8b	(- (exp x) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 51

Calls

2 calls:

15.0ms	(/ (exp x) (- (exp x) 1.0))
8.0ms	(- (exp x) 1.0)

series66.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (exp x) (- (exp x) 1.0))
22.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	2908
2	645
1	191
0	91

prune230.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (* x 1/12))
0.0b	(+ (/ 1 x) (+ 1/2 (* x 1/12)))
0.3b	(* x 1/12)

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`flip3-+` `associate-r` `associate-l` `flip-+`
2×	`+-commutative` `frac-add` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 46

Calls

3 calls:

8.0ms	(+ 1/2 (* x 1/12))
42.0ms	(+ (/ 1 x) (+ 1/2 (* x 1/12)))
11.0ms	(* x 1/12)

series120.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(+ 1/2 (* x 1/12))
27.0ms	(+ (/ 1 x) (+ 1/2 (* x 1/12)))
29.0ms	(* x 1/12)

simplify522.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
2	1075
1	250
0	84

prune150.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.8b	(- 1 (/ 1.0 (exp x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `associate-/r/` `div-inv` `flip--`
1×	`rec-exp` `sub-neg` `diff-log` `1-exp` `pow-flip` `inv-pow`

Counts

3 → 97

Calls

3 calls:

56.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
10.0ms	(/ 1.0 (exp x))
24.0ms	(- 1 (/ 1.0 (exp x)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
20.0ms	(/ 1.0 (exp x))
43.0ms	(- 1 (/ 1.0 (exp x)))

simplify703.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1153
1	345
0	162

prune338.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 1/12)
0.3b	(* x 1/12)
0.3b	(* x 1/12)
40.3b	(/ (+ (pow (+ (* x 1/12) 1/2) 3) (/ 1 (pow x 3))) (+ (* (+ (* x 1/12) 1/2) (+ (* x 1/12) (- 1/2 (/ 1 x)))) (/ (/ 1 x) x)))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
15×	`times-frac`
12×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `frac-add` `associate-/r/`
9×	`flip3-+` `associate-r` `associate-l` `flip-+`
8×	`distribute-lft-out`
5×	`div-inv` `associate-/l*`
4×	`frac-times` `add-log-exp` `associate-/l/`
3×	`associate-/r` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `associate-l/` `associate-r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`

Counts

4 → 103

Calls

4 calls:

6.0ms	(* x 1/12)
6.0ms	(* x 1/12)
6.0ms	(* x 1/12)
438.0ms	(/ (+ (pow (+ (* x 1/12) 1/2) 3) (/ 1 (pow x 3))) (+ (* (+ (* x 1/12) 1/2) (+ (* x 1/12) (- 1/2 (/ 1 x)))) (/ (/ 1 x) x)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* x 1/12)
27.0ms	(* x 1/12)
25.0ms	(* x 1/12)
107.0ms	(/ (+ (pow (+ (* x 1/12) 1/2) 3) (/ 1 (pow x 3))) (+ (* (+ (* x 1/12) 1/2) (+ (* x 1/12) (- 1/2 (/ 1 x)))) (/ (/ 1 x) x)))

simplify1.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2651
1	543
0	175

prune644.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

96.5% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 21.2b

bsearch1.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	2638×	body	10240	exit
682.0ms	2167×	body	1280	valid
477.0ms	1677×	body	640	valid
144.0ms	2836×	body	80	valid
114.0ms	891×	body	320	valid
35.0ms	431×	body	160	valid