Details

sample312.0ms

Algorithm

intervals

Results

26.0ms	457×	body	80	nan
13.0ms	226×	body	80	valid
12.0ms	226×	body	80	overflowed
4.0ms	32×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.3b	(- (exp (* 2.0 x)) 1.0)
6.4b	(- (exp x) 1.0)

rewrite58.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series194.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune380.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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)))
6.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.3b	(- (exp (* 2.0 x)) 1.0)

rewrite41.0ms

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:

7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
20.0ms	(/ (- (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)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
110.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (80.0ms)

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

prune623.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
0.3b	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
6.3b	(- (exp (* 2.0 x)) 1.0)
6.3b	(- (exp (* 2 x)) 1.0)

rewrite63.0ms

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:

26.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
21.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
7.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(- (exp (* 2 x)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0))
83.0ms	(/ (* (+ (exp x) 1.0) (- (exp (* 2.0 x)) 1.0)) (- (exp (* 2 x)) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
17.0ms	(- (exp (* 2 x)) 1.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	660	1778
1	3049	1385
2	5001	1381

prune335.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0)))
6.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.3b	(- (exp (* 2.0 x)) 1.0)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

750×	`times-frac`
654×	`*-un-lft-identity`
442×	`add-sqr-sqrt`
348×	`cbrt-prod`
306×	`add-cube-cbrt`
106×	`distribute-lft-out`
87×	`unpow-prod-down` `cube-prod`
70×	`associate-/r*`
68×	`distribute-lft-out--` `difference-of-squares`
29×	`cube-mult` `unpow3` `sqr-pow`
20×	`associate-/l*`
15×	`associate-/r/`
11×	`add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
8×	`div-inv`
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 → 554

Calls

4 calls:

11.0ms	(/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0))
34.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0))
106.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)) (+ (exp x) 1.0)))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
23.0ms	(- (exp (* 2.0 x)) 1.0)

simplify124.0ms

Algorithm

egg-herbie

Counts

566 → 566

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1587	11825
1	5002	11415

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes23.0ms

Accuracy

75.2% (0.6b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.7b

bsearch39.0ms

Steps

Iters	Range		Point
6	-3.45304144449549e-15	-4.53965370491993e-16	-1.95283781379911e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	39	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

678.0ms	12746×	body	80	nan
430.0ms	7482×	body	80	valid
345.0ms	6660×	body	80	overflowed
84.0ms	669×	body	160	valid