Details

sample237.0ms

Algorithm

intervals

Results

74.0ms	54×	body	10240	exit
52.0ms	53×	body	1280	valid
41.0ms	305×	body	80	valid
29.0ms	44×	body	640	valid
11.0ms	20×	body	320	valid
3.0ms	12×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1391
3	370
2	124
1	47
0	19

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize65.0ms

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)))))

rewrite225.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `distribute-lft-out--`

Counts

4 → 182

Calls

4 calls:

59.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
81.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
34.0ms	(* (+ 1.0 eps) x)
42.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
85.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
32.0ms	(* (+ 1.0 eps) x)
336.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.5s

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
2	4820
1	1323
0	409

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (* x x))
6.2b	(fma 0.6666666666666667 (* x (* x x)) (- 2.0 (* x (* x 1.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 36

Calls

2 calls:

25.0ms	(* x (* x x))
0.0ms	(fma 0.6666666666666667 (* x (* x x)) (- 2.0 (* x (* x 1.0))))

series144.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* x (* x x))
82.0ms	(fma 0.6666666666666667 (* x (* x x)) (- 2.0 (* x (* x 1.0))))

simplify3.8s

Counts

42 → 42

Iterations

Iter	Nodes
done	5033
4	3810
3	757
2	251
1	112
0	59

prune161.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
94×	`prod-diff`
91×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
61×	`times-frac`
25×	`distribute-rgt-in` `distribute-lft-in`
24×	`distribute-neg-in` `exp-sum`
23×	`distribute-lft-out`
13×	`associate-r`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-l` `add-log-exp`
6×	`associate-*r/`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u` `div-inv`
3×	`sub-neg` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`flip3--` `diff-log` `frac-sub` `flip--`
1×	`sum-log` `associate--l+`

Counts

4 → 198

Calls

4 calls:

36.0ms	(* x (- eps 1.0))
29.0ms	(* x (+ eps 1.0))
31.0ms	(* x (+ eps 1.0))
1.8s	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))

series253.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (- eps 1.0))
40.0ms	(* x (+ eps 1.0))
40.0ms	(* x (+ eps 1.0))
112.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))

simplify2.8s

Counts

210 → 210

Iterations

Iter	Nodes
done	5000
2	3047
1	990
0	385

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
76×	`prod-diff`
74×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
61×	`times-frac`
26×	`exp-sum`
24×	`distribute-neg-in`
23×	`distribute-lft-out`
15×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`pow1`
8×	`add-cbrt-cube` `associate-r` `add-exp-log`
6×	`associate-l`
5×	`log-prod`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `log-pow` `flip-+`
2×	`diff-log` `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` `flip3--` `exp-to-pow` `rem-log-exp` `associate--l+` `flip--`

Counts

4 → 170

Calls

4 calls:

17.0ms	(* x (+ eps 1.0))
16.0ms	(* x (+ eps 1.0))
2.0s	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))
3.0ms	(log (exp (* x (+ eps 1.0))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* x (+ eps 1.0))
45.0ms	(* x (+ eps 1.0))
139.0ms	(- (+ (/ (exp (* x (- eps 1.0))) eps) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))
65.0ms	(log (exp (* x (+ eps 1.0))))

simplify2.5s

Counts

182 → 182

Iterations

Iter	Nodes
done	5005
2	2572
1	848
0	336

prune1.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes156.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.8b

bsearch233.0ms

Steps

Iters	Range		Point
9	1.0117869227030548e-08	3.2218684848907064	0.9639489834403894

simplify22.0ms

Iterations

Iter	Nodes
done	51
2	51
1	45
0	33

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.8s	1944×	body	10240	exit
1.8s	10175×	body	80	valid
1.6s	1743×	body	1280	valid
1.1s	1238×	body	640	valid
678.0ms	629×	body	320	valid
103.0ms	301×	body	160	valid