Details

sample309.0ms

Algorithm

intervals

Results

18.0ms	392×	body	80	nan
11.0ms	246×	body	80	valid
8.0ms	196×	body	80	overflowed
2.0ms	14×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 2.4b

Counts

2 → 1

localize11.0ms

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))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
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 → 123

Calls

4 calls:

25.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series211.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
65.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify126.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4287	1301
3	5003	1293

prune293.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.0b

Counts

136 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
3.1b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.1b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

19.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
16.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
7.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series371.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
119.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
52.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	481	1464
1	2403	1163
2	5002	1124

prune276.0ms

Filtered

117 candidates to 83 candidates (70.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.1b	(log (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
3.0b	(- (exp (* 2.0 x)) 1.0)
3.1b	(- (exp x) 1.0)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
31×	`log-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log`
8×	`add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `diff-log` `div-exp` `rem-log-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `div-sub` `clear-num` `log-pow`

Counts

4 → 122

Calls

4 calls:

9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
8.0ms	(log (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
4.0ms	(- (exp x) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
131.0ms	(log (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
26.0ms	(- (exp (* 2.0 x)) 1.0)
15.0ms	(- (exp x) 1.0)

simplify127.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	426	1391
1	1185	1325
2	4691	1294
3	5001	1294

prune313.0ms

Filtered

134 candidates to 90 candidates (67.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	133	4	137

Merged error: 0b

Counts

137 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac`
108×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
41×	`unpow-prod-down`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `prod-exp`
3×	`cbrt-undiv` `div-inv`
2×	`frac-times` `pow-to-exp` `flip3--` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `flip3-+` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `distribute-lft-out--`

Counts

4 → 221

Calls

4 calls:

5.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
25.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
6.0ms	(/ (pow x 2) (sqrt 2.0))
5.0ms	(/ x (sqrt 2.0))

series343.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0))))
75.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
61.0ms	(/ (pow x 2) (sqrt 2.0))
62.0ms	(/ x (sqrt 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	607	1757
1	2614	1546
2	5002	1528

prune447.0ms

Filtered

233 candidates to 143 candidates (61.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	233	4	237

Merged error: 0b

Counts

237 → 4

regimes58.0ms

Accuracy

98.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 3.3b

bsearch98.0ms

Steps

Iters	Range		Point
8	1.8652500212734269e-07	6.042829624826513e-05	5.840110983247455e-07
8	-0.1152406257888697	-0.00010711273713490883	-0.0012905509290539541

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	36
1	46	36

end0.0ms

sample1.5s

Algorithm

intervals

Results

527.0ms	12504×	body	80	nan
341.0ms	7426×	body	80	valid
263.0ms	6589×	body	80	overflowed
76.0ms	701×	body	160	valid

Details

sample309.0ms

simplify73.0ms

prune4.0ms

localize11.0ms

rewrite51.0ms

series211.0ms

simplify126.0ms

prune293.0ms

localize13.0ms

rewrite49.0ms

series371.0ms

simplify70.0ms

prune276.0ms

localize11.0ms

rewrite31.0ms

series235.0ms

simplify127.0ms

prune313.0ms

localize14.0ms

rewrite50.0ms

series343.0ms

simplify74.0ms

prune447.0ms

regimes58.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling