Details

sample398.0ms

Algorithm

intervals

Results

58.0ms	195×	body	10240	exit
14.0ms	399×	body	80	nan
8.0ms	233×	body	80	valid
2.0ms	30×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7
done	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.5b	(- (exp (* 2.0 x)) 1.0)
6.6b	(- (exp x) 1.0)

rewrite110.0ms

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:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
45.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
15.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series207.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify53.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470
done	5001	1470

prune403.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
6.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.5b	(- (exp (* 2.0 x)) 1.0)

rewrite86.0ms

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:

16.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
43.0ms	(/ (- (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)))
16.0ms	(- (exp (* 2.0 x)) 1.0)

series256.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
116.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
48.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify109.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382
done	5003	3382

prune657.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.5b	(log1p (- (exp (* 2.0 x)) 1.0))
6.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.5b	(- (exp (* 2.0 x)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
88×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
18×	`associate-/r*`
12×	`distribute-lft-out`
9×	`add-exp-log` `prod-diff` `associate-/r/` `add-cbrt-cube`
6×	`add-log-exp`
5×	`expm1-log1p-u` `div-inv`
4×	`pow1` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `div-exp` `associate-/l*`
1×	`sub-neg` `log1p-udef` `flip3--` `frac-2neg` `diff-log` `div-sub` `log1p-expm1` `clear-num` `flip--` `fma-udef` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 142

Calls

4 calls:

20.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
17.0ms	(- (exp (* 2.0 x)) 1.0)

series716.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
411.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify85.0ms

Counts

154 → 154

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	606	2553
1	2612	2205
2	5001	2183
done	5001	2183

prune548.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.5b	(log1p (- (exp (* 2.0 x)) 1.0))
6.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.5b	(- (exp (* 2.0 x)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

17.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series562.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
422.0ms	(log1p (- (exp (* 2.0 x)) 1.0))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify37.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	318	817
1	1029	688
2	5001	676
done	5001	676

prune341.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes33.0ms

Accuracy

99.1% (0.0b remaining)

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

bsearch81.0ms

Steps

Iters	Range		Point
6	1.6364485262755118e-17	1.0549554552646143e-16	5.5130004635374716e-17
6	-9.626479235102698e-17	-2.3270530211208605e-17	-4.064503060548636e-17

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	43
1	54	43
done	54	43

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	6515×	body	10240	exit
366.0ms	12164×	body	80	nan
243.0ms	7421×	body	80	valid
53.0ms	699×	body	160	valid