Details

sample397.0ms

Algorithm

intervals

Results

53.0ms	182×	body	10240	exit
11.0ms	377×	body	80	nan
8.0ms	244×	body	80	valid
2.0ms	22×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.0b

localize12.0ms

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))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp x) 1.0)

rewrite107.0ms

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)))
44.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
14.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
23.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune375.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))
4.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.3b	(- (exp (* 2.0 x)) 1.0)

rewrite85.0ms

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:

44.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
15.0ms	(/ (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)

series222.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
56.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
22.0ms	(- (exp (* 2.0 x)) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (81.0ms)

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

prune622.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
4.3b	(- (exp (* 2.0 x)) 1.0)
4.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.4b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `fma-neg` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `cube-prod`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`cube-mult` `pow-to-exp` `distribute-rgt-out--` `unpow3` `pow-exp` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

4.0ms	(pow (exp x) 3)
14.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
11.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series110.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (exp x) 3)
22.0ms	(- (exp (* 2.0 x)) 1.0)
39.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	374	523
1	1648	414
2	5002	407

prune368.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
28.1b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite2.0ms

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:

0.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
2.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series93.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
73.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	139	185
1	458	173
2	2447	165
3	5001	162

prune72.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.3% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.5b

bsearch90.0ms

Steps

Iters	Range		Point
8	6.716498150468338e-20	2.261523262570876e-16	5.644932717281176e-17
7	-4.0039902443278174e-11	-1.678317386849929e-12	-3.952485205910728e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	6675×	body	10240	exit
377.0ms	12885×	body	80	nan
233.0ms	7439×	body	80	valid
52.0ms	698×	body	160	valid