Details

sample329.0ms

Algorithm

intervals

Results

93.0ms	195×	body	10240	exit
79.0ms	237×	body	80	valid
34.0ms	427×	body	80	nan
4.0ms	21×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4825
7	1216
6	342
5	135
4	66
3	38
2	27
1	19
0	10

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.1b	(- (exp (* 2.0 x)) 1.0)
4.2b	(- (exp x) 1.0)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
22.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

series157.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)
39.0ms	(- (exp x) 1.0)

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5004
3	3308
2	981
1	412
0	171

prune557.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

5.0ms	(sqrt (exp (* 2.0 x)))
24.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
17.0ms	(- (exp x) 1.0)
0.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series314.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (exp (* 2.0 x)))
149.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
19.0ms	(- (exp x) 1.0)
114.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify2.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	2465
2	778
1	315
0	157

prune565.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
4.2b	(- (exp x) 1.0)
4.2b	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
5.4b	(log (sqrt (exp (* 2.0 x))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

18.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
10.0ms	(- (exp x) 1.0)
0.0ms	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
8.0ms	(log (sqrt (exp (* 2.0 x))))

series844.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0)) (- (exp x) 1.0))
24.0ms	(- (exp x) 1.0)
119.0ms	(fma (sqrt (exp (* 2.0 x))) (exp (log (sqrt (exp (* 2.0 x))))) (- 1.0))
543.0ms	(log (sqrt (exp (* 2.0 x))))

simplify2.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5007
3	2341
2	794
1	336
0	174

prune728.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 1 expressions with local error:

26.2b

(sqrt (fma x (fma x 0.5 1.0) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
1×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

7.0ms

(sqrt (fma x (fma x 0.5 1.0) 2.0))

series139.0ms

Counts

1 → 3

Calls

1 calls:

139.0ms

(sqrt (fma x (fma x 0.5 1.0) 2.0))

simplify2.8s

Counts

18 → 18

Iterations

Iter	Nodes
done	5000
4	4664
3	1112
2	354
1	126
0	53

prune80.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

78.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.4b

bsearch40.0ms

Steps

Iters	Range		Point
7	-0.00027856517442265854	-4.347642122658769e-06	-9.471958066473225e-06

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	21

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.9s	6556×	body	10240	exit
1.2s	12569×	body	80	nan
567.0ms	7407×	body	80	valid
94.0ms	716×	body	160	valid