Details

sample78.0ms

Algorithm

intervals

Results

40.0ms	75×	body	1280	valid
12.0ms	45×	body	640	valid
9.0ms	26×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	71×	body	80	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune3.0ms

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: 52.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
3.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5099	600

prune125.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	6	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Merged error: 0.1b

Counts

52 → 6

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
0.1b	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-l`
49×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
10×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`pow1` `cube-div` `associate-*l/` `pow-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `flip3-+` `unpow3` `div-exp` `frac-add` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 87

Calls

2 calls:

9.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
16.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series45.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
16.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify28.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5129	1007

prune192.0ms

Filtered

51 candidates to 93 candidates (-82.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 0.1b

Counts

99 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)
0.0b	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
0.0b	(exp (pow (/ x (sqrt 1.0)) 3))
1.9b	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

100×	`exp-prod`
72×	`times-frac`
66×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `add-cube-cbrt`
53×	`unpow-prod-down`
51×	`pow-pow`
44×	`cube-prod`
36×	`sqrt-prod`
14×	`log-prod`
7×	`associate-+r+`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `sqr-pow`
4×	`add-cbrt-cube` `div-inv`
3×	`pow-unpow` `rem-log-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
1×	`+-commutative` `flip3-+` `sum-log` `log-pow` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 162

Calls

4 calls:

14.0ms	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)
18.0ms	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
11.0ms	(exp (pow (/ x (sqrt 1.0)) 3))
11.0ms	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

series179.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)
47.0ms	(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
7.0ms	(exp (pow (/ x (sqrt 1.0)) 3))
92.0ms	(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

simplify54.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5449	1630

prune406.0ms

Filtered

95 candidates to 174 candidates (-83.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	174	7	181

Merged error: 0.1b

Counts

181 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (pow (/ x (sqrt 1.0)) 3))
0.0b	(+ (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/12)) (log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)))
0.1b	(* (pow (/ x (sqrt 1.0)) 3) -1/12)
1.9b	(log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
76×	`times-frac`
67×	`*-un-lft-identity`
65×	`add-cube-cbrt`
59×	`unpow-prod-down`
50×	`exp-prod` `associate-l`
47×	`cube-prod`
44×	`sqrt-prod`
20×	`log-prod`
14×	`add-exp-log`
10×	`associate-+r+`
8×	`add-log-exp` `unswap-sqr`
6×	`add-cbrt-cube`
5×	`sqr-pow`
4×	`pow1` `prod-exp` `div-inv`
3×	`rem-log-exp` `associate-r` `pow-exp` `sum-log`
2×	`cube-mult` `pow-to-exp` `unpow3`
1×	`+-commutative` `cube-div` `associate-+l+` `flip3-+` `div-exp` `associate-l/` `log-pow` `-commutative` `cbrt-unprod` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 178

Calls

4 calls:

11.0ms	(exp (pow (/ x (sqrt 1.0)) 3))
20.0ms	(+ (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/12)) (log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)))
16.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/12)
9.0ms	(log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))

series143.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (pow (/ x (sqrt 1.0)) 3))
22.0ms	(+ (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/12)) (log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6)))
16.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/12)
98.0ms	(log (pow (sqrt (exp (pow (/ x (sqrt 1.0)) 3))) -1/6))

simplify59.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5146	2292

prune570.0ms

Filtered

102 candidates to 190 candidates (-86.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	190	7	197

Merged error: 0.1b

Counts

197 → 7

regimes116.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.4b

bsearch24.0ms

Steps

Iters	Range		Point
8	0.06592465963988953	1253.8160530937032	0.8954644157812223
5	-2.244380864214425	-0.6973264211480649	-1.015486663634488

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	55
1	39	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2272×	body	1280	valid
442.0ms	1578×	body	640	valid
274.0ms	820×	body	2560	valid
135.0ms	805×	body	320	valid
89.0ms	2093×	body	80	valid
43.0ms	432×	body	160	valid

Details

sample78.0ms

simplify3.0ms

prune3.0ms

localize7.0ms

rewrite17.0ms

series19.0ms

simplify38.0ms

prune125.0ms

localize9.0ms

rewrite29.0ms

series45.0ms

simplify28.0ms

prune192.0ms

localize12.0ms

rewrite63.0ms

series179.0ms

simplify54.0ms

prune406.0ms

localize16.0ms

rewrite65.0ms

series143.0ms

simplify59.0ms

prune570.0ms

regimes116.0ms

bsearch24.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling