Details

sample67.0ms

Algorithm

intervals

Results

29.0ms	72×	body	1280	valid
15.0ms	51×	body	640	valid
8.0ms	30×	body	2560	valid
3.0ms	26×	body	320	valid
2.0ms	62×	body	80	valid
1.0ms	15×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

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: 52.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1.0)))
3.5b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

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))

series261.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ x (sqrt (+ (* x x) 1.0)))
163.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	331	422
1	1127	385
2	5002	366

prune163.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	6	62

Merged error: 0.1b

Counts

62 → 6

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
184×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
126×	`*-un-lft-identity`
120×	`add-cube-cbrt`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
5×	`fma-neg` `prod-diff`
4×	`distribute-lft-out`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `diff-log` `log-pow` `frac-sub` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 300

Calls

2 calls:

14.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
56.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series280.0ms

Counts

2 → 6

Calls

2 calls:

149.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
130.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify122.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	888	2291
1	4768	1819
2	5001	1795

prune379.0ms

Filtered

306 candidates to 121 candidates (39.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	306	6	312

Merged error: 0.1b

Counts

312 → 6

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.4b	(+ x (hypot x (sqrt 1.0)))
3.5b	(log (+ x (hypot x (sqrt 1.0))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 44

Calls

3 calls:

1.0ms	(hypot x (sqrt 1.0))
3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series485.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(hypot x (sqrt 1.0))
126.0ms	(+ x (hypot x (sqrt 1.0)))
265.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify88.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	268	349
1	886	321
2	3696	305
3	5001	303

prune119.0ms

Filtered

53 candidates to 46 candidates (86.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	54	5	59

Merged error: 0.1b

Counts

59 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
0.4b	(+ x (hypot x (sqrt 1.0)))
0.4b	(+ x (hypot x (sqrt 1.0)))
3.0b	(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`pow1`
32×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
24×	`sqrt-div`
16×	`sqrt-pow1` `pow1/2`
14×	`add-cube-cbrt` `flip3-+` `log-pow` `flip-+`
11×	`swap-sqr`
10×	`pow-prod-up`
9×	`add-exp-log`
8×	`frac-times` `log-div` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`fma-def` `pow-prod-down` `pow-sqr` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `pow2` `pow-plus` `rem-log-exp` `prod-exp` `sum-log`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

11.0ms	(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(+ x (hypot x (sqrt 1.0)))
9.0ms	(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
130.0ms	(+ x (hypot x (sqrt 1.0)))
122.0ms	(+ x (hypot x (sqrt 1.0)))
277.0ms	(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	355	1184
1	1344	1050
2	5002	1012

prune270.0ms

Filtered

144 candidates to 95 candidates (66.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	143	6	149

Merged error: 0.1b

Counts

149 → 6

regimes37.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch80.0ms

Steps

Iters	Range		Point
9	1.2000045585397406e-10	0.001857967628030483	0.0010611615811147047
9	-164485.30314980465	-0.009598081335721272	-1.0094339040681148

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	30
1	41	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

958.0ms	2339×	body	1280	valid
357.0ms	1534×	body	640	valid
218.0ms	800×	body	2560	valid
105.0ms	785×	body	320	valid
64.0ms	2143×	body	80	valid
30.0ms	399×	body	160	valid