Details

sample302.0ms

Algorithm

intervals

Results

68.0ms	192×	body	10240	exit
63.0ms	405×	body	80	nan
16.0ms	235×	body	80	valid
3.0ms	24×	body	160	valid

simplify1.3s

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	185	12
6	764	12
done	5000	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize25.0ms

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))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp x) 1.0)

rewrite182.0ms

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)))
72.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
18.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
89.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
29.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

167 → 167

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	232	2954
1	503	2694
2	1532	2473
done	5000	2423

prune786.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
0.1b	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))
4.6b	(fma 1.0 (- 1.0) (exp (+ x x)))
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite156.0ms

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:

74.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
30.0ms	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
30.0ms	(- (exp (* 2.0 x)) 1.0)

series386.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0)))
115.0ms	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))
35.0ms	(- (exp (* 2.0 x)) 1.0)

simplify2.2s

Counts

218 → 218

Iterations

Useful iterations: 2 (724.0ms)

Iter	Nodes	Cost
0	304	6392
1	889	6132
2	4341	5824
done	5000	5824

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))
0.1b	(* (sqrt (+ (exp x) 1.0)) (/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(fma 1.0 (- 1.0) (exp (+ x x)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
223×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
140×	`associate-r`
127×	`add-cube-cbrt`
86×	`sqrt-prod`
28×	`distribute-lft-out--` `difference-of-squares`
20×	`distribute-lft-out`
16×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r/`
9×	`prod-diff`
8×	`flip3-+` `flip-+` `unswap-sqr`
7×	`associate-l` `associate-/r*` `div-inv`
6×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`frac-times` `associate-*l/`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `fma-udef`

Counts

4 → 262

Calls

4 calls:

17.0ms	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))
188.0ms	(* (sqrt (+ (exp x) 1.0)) (/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))))
23.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))
157.0ms	(* (sqrt (+ (exp x) 1.0)) (/ (- (exp (* 2.0 x)) 1.0) (/ (fma 1.0 (- 1.0) (exp (+ x x))) (sqrt (+ (exp x) 1.0)))))
34.0ms	(- (exp (* 2.0 x)) 1.0)
75.0ms	(fma 1.0 (- 1.0) (exp (+ x x)))

simplify880.0ms

Counts

274 → 274

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	406	7538
1	1157	7060
done	5000	6617

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
0.1b	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.6b	(- (exp (* 2 x)) 1.0)

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
11×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-/l/` `add-log-exp`
6×	`pow1` `flip3-+` `fma-neg` `flip-+`
5×	`times-frac` `associate-r` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `sub-neg` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u`
2×	`cbrt-undiv` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

84.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
81.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
20.0ms	(- (exp (* 2.0 x)) 1.0)
31.0ms	(- (exp (* 2 x)) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
54.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
36.0ms	(- (exp (* 2.0 x)) 1.0)
29.0ms	(- (exp (* 2 x)) 1.0)

simplify2.5s

Counts

158 → 158

Iterations

Useful iterations: 2 (668.0ms)

Iter	Nodes	Cost
0	236	3252
1	713	2869
2	4161	2429
done	5000	2429

prune699.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes63.0ms

Accuracy

76.2% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.7b

bsearch80.0ms

Steps

Iters	Range		Point
8	-3.092080667674878e-11	-1.991891315317258e-14	-3.031481252135206e-11

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	33
1	27	33
done	27	33

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.2s	6601×	body	10240	exit
1.0s	12770×	body	80	nan
517.0ms	7395×	body	80	valid
158.0ms	718×	body	160	valid