Details

sample354.0ms

Algorithm

intervals

Results

42.0ms	216×	body	10240	exit
23.0ms	413×	body	80	nan
9.0ms	234×	body	80	valid
2.0ms	26×	body	160	valid

simplify76.0ms

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	2657	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.2b

Counts

2 → 1

localize12.0ms

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))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
51×	`times-frac`
43×	`add-cube-cbrt`
31×	`sqrt-prod`
26×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
15×	`sqrt-div`
10×	`associate-/r` `associate-/l`
8×	`add-log-exp`
6×	`add-exp-log` `flip3--` `fma-neg` `add-cbrt-cube` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
2×	`sub-neg` `rem-sqrt-square` `frac-2neg` `diff-log` `clear-num` `div-inv`
1×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `div-sub` `div-exp`

Counts

4 → 169

Calls

4 calls:

15.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
7.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series222.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
28.0ms	(- (exp (* 2.0 x)) 1.0)
34.0ms	(- (exp x) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	495	1844
1	1504	1646
2	5002	1629

prune344.0ms

Filtered

181 candidates to 120 candidates (33.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	2	182

Merged error: 0.2b

Counts

182 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.2b	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
5.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.6b	(- (exp (* 2.0 x)) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

7.0ms	(+ (exp x) 1.0)
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
8.0ms	(- (exp (* 2.0 x)) 1.0)

series291.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 1.0)
206.0ms	(/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x))))
49.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	358	957
1	1252	826
2	5001	822

prune284.0ms

Filtered

107 candidates to 79 candidates (26.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Merged error: 0b

Counts

109 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 1.0 (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`sqrt-prod`
11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`associate-r` `add-log-exp`
3×	`fma-def` `associate-l`
2×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `pow1/2` `pow-prod-down` `sum-log` `*-commutative`

Counts

2 → 46

Calls

2 calls:

8.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(sqrt (* 1.0 (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	209	271
1	713	261
2	2680	253
3	5001	252

prune95.0ms

Filtered

52 candidates to 39 candidates (25.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Merged error: 0b

Counts

55 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (- 1.0 (exp x)) (exp (+ x x)))
0.1b	(pow (exp x) 3)
0.3b	(/ (+ (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (- 1.0 (exp x)) (exp (+ x x))))
5.7b	(- 1.0 (exp x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`times-frac`
19×	`pow-unpow`
16×	`sum-cubes`
11×	`unpow-prod-down`
9×	`prod-diff` `associate-/l*`
8×	`distribute-lft-out`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-/r*`
2×	`pow-exp` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `unpow3` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

1.0ms	(fma 1.0 (- 1.0 (exp x)) (exp (+ x x)))
3.0ms	(pow (exp x) 3)
15.0ms	(/ (+ (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (- 1.0 (exp x)) (exp (+ x x))))
5.0ms	(- 1.0 (exp x))

series175.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma 1.0 (- 1.0 (exp x)) (exp (+ x x)))
28.0ms	(pow (exp x) 3)
94.0ms	(/ (+ (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (- 1.0 (exp x)) (exp (+ x x))))
14.0ms	(- 1.0 (exp x))

simplify68.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	481	1299
1	1878	1184
2	5001	1180

prune302.0ms

Filtered

130 candidates to 84 candidates (35.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	131	2	133

Merged error: 0b

Counts

133 → 2

regimes15.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6626×	body	10240	exit
369.0ms	12421×	body	80	nan
254.0ms	7402×	body	80	valid
54.0ms	724×	body	160	valid