Details

sample235.0ms

Algorithm

intervals

Results

79.0ms	54×	body	10240	exit
47.0ms	53×	body	1280	valid
37.0ms	305×	body	80	valid
26.0ms	44×	body	640	valid
12.0ms	20×	body	320	valid
3.0ms	12×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
4	1357
3	352
2	122
1	46
0	19

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
2.0b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
31×	`flip3-+` `flip3--` `flip-+` `flip--`
21×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
14×	`associate-l`
10×	`pow1` `add-cbrt-cube` `add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out--`

Counts

4 → 172

Calls

4 calls:

58.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
66.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
16.0ms	(* (+ 1.0 eps) x)
54.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
75.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
42.0ms	(* (+ 1.0 eps) x)
308.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.2s

Counts

184 → 184

Iterations

Iter	Nodes
done	5002
2	4474
1	1224
0	396

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* (* x x) 0.6666666666666667))
0.1b	(* (* x x) 0.6666666666666667)
6.2b	(- (* x (* (* x x) 0.6666666666666667)) (* (* x x) 1.0))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
2×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

62.0ms	(* x (* (* x x) 0.6666666666666667))
28.0ms	(* (* x x) 0.6666666666666667)
49.0ms	(- (* x (* (* x x) 0.6666666666666667)) (* (* x x) 1.0))

series239.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* x (* (* x x) 0.6666666666666667))
36.0ms	(* (* x x) 0.6666666666666667)
152.0ms	(- (* x (* (* x x) 0.6666666666666667)) (* (* x x) 1.0))

simplify3.9s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
3	3996
2	769
1	222
0	83

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (- (* x (+ 1.0 eps)))) eps)
0.0b	(* x (+ 1.0 eps))
0.0b	(* x (+ 1.0 eps))
1.9b	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-cbrt-cube`
9×	`add-exp-log` `add-log-exp`
8×	`pow1` `distribute-neg-in` `associate-r` `exp-sum`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
5×	`associate-/l*`
4×	`associate-*r/`
3×	`associate-/r*` `flip3-+` `flip-+` `distribute-lft-out`
2×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `associate-/l/`
1×	`neg-sub0` `exp-neg` `cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `exp-diff` `div-exp` `associate--l+` `div-inv` `flip--`

Counts

4 → 103

Calls

4 calls:

12.0ms	(/ (exp (- (* x (+ 1.0 eps)))) eps)
16.0ms	(* x (+ 1.0 eps))
16.0ms	(* x (+ 1.0 eps))
326.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))

series263.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (exp (- (* x (+ 1.0 eps)))) eps)
57.0ms	(* x (+ 1.0 eps))
57.0ms	(* x (+ 1.0 eps))
112.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))

simplify1.7s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1512
1	475
0	197

prune878.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ 1.0 eps))
0.0b	(* x (+ 1.0 eps))
1.9b	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))
5.9b	(log (exp (* x (+ 1.0 eps))))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`pow1` `add-cube-cbrt`
8×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
5×	`log-prod`
4×	`associate-*r/`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `log-pow` `flip-+` `distribute-lft-out`
2×	`diff-log` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`exp-prod` `sum-log` `sub-neg` `times-frac` `flip3--` `exp-to-pow` `rem-log-exp` `associate--l+` `flip--`

Counts

4 → 82

Calls

4 calls:

18.0ms	(* x (+ 1.0 eps))
15.0ms	(* x (+ 1.0 eps))
415.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))
6.0ms	(log (exp (* x (+ 1.0 eps))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* x (+ 1.0 eps))
59.0ms	(* x (+ 1.0 eps))
119.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ 1.0 eps)))) eps))
40.0ms	(log (exp (* x (+ 1.0 eps))))

simplify1.6s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1271
1	389
0	155

prune788.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes104.0ms

Accuracy

0% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 0.9b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	47
3	47
2	42
1	35
0	24

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.9s	1944×	body	10240	exit
1.8s	10175×	body	80	valid
1.7s	1743×	body	1280	valid
861.0ms	1238×	body	640	valid
283.0ms	629×	body	320	valid
140.0ms	301×	body	160	valid