Details

sample3.5s

Algorithm

intervals

Results

1.3s	326×	body	80	nan
807.0ms	211×	body	10240	exit
72.0ms	244×	body	80	valid
15.0ms	15×	body	160	valid

simplify22.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5038
8	4409
7	1194
6	341
5	135
4	66
3	38
2	27
1	19
0	10

prune174.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize495.0ms

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))
3.4b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite726.0ms

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:

64.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
387.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
32.0ms	(- (exp x) 1.0)

series2.0s

Counts

4 → 12

Calls

4 calls:

871.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
287.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
232.0ms	(- (exp (* 2.0 x)) 1.0)
538.0ms	(- (exp x) 1.0)

simplify11.4s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
3	4016
2	1192
1	502
0	232

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize559.0ms

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))
3.4b	(- (exp x) 1.0)
3.4b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite81.0ms

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-exp-log` `add-cbrt-cube`
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` `sub-neg` `rem-sqrt-square` `exp-prod` `exp-to-pow` `frac-2neg` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(sqrt (exp (* 2.0 x)))
33.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
34.0ms	(- (exp x) 1.0)
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series930.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (exp (* 2.0 x)))
501.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
28.0ms	(- (exp x) 1.0)
311.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify12.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
3	2680
2	783
1	316
0	157

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
25.5b	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

1.0ms	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
14.0ms	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

series606.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(fma x (fma 0.4999999999999998 x 1.0) 2.0)
477.0ms	(sqrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

simplify4.7s

Counts

31 → 31

Iterations

Iter	Nodes
done	5002
3	1470
2	417
1	147
0	65

prune294.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

14.9b	(sqrt (* (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0)) (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))))
26.4b	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
26.4b	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
26.4b	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 60

Calls

4 calls:

10.0ms	(sqrt (* (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0)) (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))))
2.0ms	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
2.0ms	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
8.0ms	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

series2.8s

Counts

4 → 12

Calls

4 calls:

701.0ms	(sqrt (* (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0)) (cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))))
646.0ms	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
494.0ms	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))
1.0s	(cbrt (fma x (fma 0.4999999999999998 x 1.0) 2.0))

simplify5.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	1569
2	541
1	216
0	98

prune991.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes429.0ms

Accuracy

80.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.6b

bsearch78.0ms

Steps

Iters	Range		Point
6	-0.00015200343398984049	-1.963203309137196e-05	-1.9984726555003664e-05

simplify22.0ms

Iterations

Iter	Nodes
done	20
1	20
0	19

end0.0ms

sample31.9s

Algorithm

intervals

Results

20.6s	6584×	body	10240	exit
5.3s	12492×	body	80	nan
4.7s	7320×	body	80	valid
409.0ms	798×	body	160	valid