Details

sample233.0ms

Algorithm

intervals

Results

190.0ms	244×	body	80	valid
14.0ms	368×	body	80	nan
7.0ms	197×	body	80	overflowed
2.0ms	19×	body	160	valid

simplify72.0ms

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

prune5.0ms

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: 2.9b

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))
3.4b	(- (exp (* 2.0 x)) 1.0)
3.4b	(- (exp x) 1.0)

rewrite34.0ms

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:

9.0ms	(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)
7.0ms	(- (exp x) 1.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms	(- (exp (* 2.0 x)) 1.0)
10.0ms	(- (exp x) 1.0)

simplify121.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune239.0ms

Filtered

135 candidates to 92 candidates (31.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.2b

Counts

136 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(sqrt (exp (* 2.0 x)))
0.3b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
3.4b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.4b	(- (exp x) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
9×	`add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
8×	`associate-/l/`
7×	`add-cube-cbrt` `difference-of-squares`
6×	`flip3--` `flip--`
5×	`pow1` `times-frac` `associate-/r*` `distribute-lft-out--`
4×	`frac-times`
3×	`sqrt-pow1` `flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `associate-/r/`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `frac-2neg` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 82

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
19.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series27.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (exp (* 2.0 x)))
18.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
2.0ms	(- (exp x) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	418	958
1	1889	760
2	5001	736

prune218.0ms

Filtered

94 candidates to 67 candidates (28.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Merged error: 0.2b

Counts

98 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
3.4b	(- (exp (* 2.0 x)) 1.0)
3.4b	(log (exp (- (exp x) 1.0)))
3.4b	(- (exp x) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
42×	`log-pow`
35×	`exp-prod`
28×	`add-cube-cbrt`
19×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log-prod` `associate-/l*`
3×	`sub-neg` `flip3--` `flip--`
2×	`diff-log` `exp-sum` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-sub` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
4.0ms	(- (exp (* 2.0 x)) 1.0)
5.0ms	(log (exp (- (exp x) 1.0)))
4.0ms	(- (exp x) 1.0)

series14.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- (exp (* 2.0 x)) 1.0) (log (exp (- (exp x) 1.0))))
2.0ms	(- (exp (* 2.0 x)) 1.0)
2.0ms	(log (exp (- (exp x) 1.0)))
2.0ms	(- (exp x) 1.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	380	1252
1	1042	1148
2	4117	1107
3	5003	1105

prune205.0ms

Filtered

134 candidates to 87 candidates (35.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	134	4	138

Merged error: 0.2b

Counts

138 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
24.8b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	279	280
1	1132	268
2	5002	257

prune55.0ms

Filtered

43 candidates to 31 candidates (27.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	43	4	47

Merged error: 0.2b

Counts

47 → 4

regimes45.0ms

Accuracy

90.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 3.7b

bsearch30.0ms

Steps

Iters	Range		Point
9	1.8861453929162526e-07	2.0501072009103303	0.00014337737389655462
8	-0.05940270564741191	-8.789307139906393e-06	-2.8536062808639043e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

475.0ms	12616×	body	80	nan
290.0ms	7334×	body	80	valid
236.0ms	6557×	body	80	overflowed
72.0ms	784×	body	160	valid

Details

sample233.0ms

simplify72.0ms

prune5.0ms

localize12.0ms

rewrite34.0ms

series41.0ms

simplify121.0ms

prune239.0ms

localize13.0ms

rewrite33.0ms

series27.0ms

simplify47.0ms

prune218.0ms

localize12.0ms

rewrite30.0ms

series14.0ms

simplify131.0ms

prune205.0ms

localize8.0ms

rewrite11.0ms

series11.0ms

simplify36.0ms

prune55.0ms

regimes45.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling