Details

sample317.0ms

Algorithm

intervals

Results

36.0ms	195×	body	10240	exit
10.0ms	351×	body	80	nan
8.0ms	233×	body	80	valid
2.0ms	24×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	41	12
4	76	12
5	175	12
6	495	12
7	1569	12
done	5001	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.8b	(- (exp (* 2.0 x)) 1.0)
5.0b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
18.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series210.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp x) 1.0)

simplify1.9s

Counts

167 → 167

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	232	2954
1	482	2688
2	1088	2471
3	3791	2398
done	5001	2396

prune390.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.8b	(- (exp (* 2.0 x)) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

10.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
21.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series255.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
119.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify1.0s

Counts

218 → 218

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	304	6392
1	804	6107
2	2566	5820
done	5000	5811

prune663.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
0.1b	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.8b	(- (exp (* 2.0 x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
48×	`times-frac`
47×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
12×	`distribute-lft-out`
9×	`prod-diff`
8×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `fma-neg`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `diff-log` `div-exp` `flip--` `rem-cbrt-cube` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 150

Calls

4 calls:

11.0ms	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
12.0ms	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
98.0ms	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify834.0ms

Counts

162 → 162

Iterations

Useful iterations: done (828.0ms)

Iter	Nodes	Cost
0	237	3906
1	579	3368
2	1693	3020
done	5000	3011

prune414.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
0.1b	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
4.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.8b	(- (exp (* 2.0 x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
48×	`times-frac`
47×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
12×	`distribute-lft-out`
9×	`prod-diff`
8×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `fma-neg`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `diff-log` `div-exp` `flip--` `rem-cbrt-cube` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 150

Calls

4 calls:

11.0ms	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
10.0ms	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(cbrt (pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3))
97.0ms	(pow (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) 3)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify836.0ms

Counts

162 → 162

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	237	3906
1	579	3368
2	1693	3020
done	5000	3011

prune475.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

76% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.9b

bsearch33.0ms

Steps

Iters	Range		Point
5	-2.108208213391104e-15	-1.0156163510189785e-15	-1.290720371833936e-15

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	46
1	35	46
done	35	46

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6724×	body	10240	exit
383.0ms	12569×	body	80	nan
237.0ms	7366×	body	80	valid
59.0ms	738×	body	160	valid