Details

sample40.0ms

Algorithm

intervals

Results

21.0ms	95×	body	1280	valid
5.0ms	121×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

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: 16.0b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot 1.0 x)
102.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
102.0ms	(/ 1.0 (hypot 1.0 x))
363.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	539	998
1	2059	745
2	5001	742

prune222.0ms

Filtered

99 candidates to 81 candidates (81.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	6	100

Merged error: 15.2b

Counts

100 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series462.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
101.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(/ 1.0 (hypot 1.0 x))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	319	561
1	1141	522
2	5001	520

prune285.0ms

Filtered

97 candidates to 85 candidates (87.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Merged error: 0.3b

Counts

103 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.8b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 86

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series703.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ 1.0 (hypot 1.0 x))
100.0ms	(/ 1.0 (hypot 1.0 x))
150.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
150.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify174.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	279	665
1	931	600
2	4763	594
3	5001	592

prune308.0ms

Filtered

98 candidates to 84 candidates (85.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	98	5	103

Merged error: 0.3b

Counts

103 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3)
0.5b	(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
1.7b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-prod`
9×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `fma-udef` `div-inv` `rem-cube-cbrt`

Counts

4 → 87

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3)
2.0ms	(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series676.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1.0 (hypot 1.0 x))
286.0ms	(pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3)
146.0ms	(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
144.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	444	863
1	1861	806
2	5001	799

prune284.0ms

Filtered

99 candidates to 71 candidates (71.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	98	6	104

Merged error: 0.3b

Counts

104 → 6

regimes366.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	40
1	46	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

636.0ms	2812×	body	1280	valid
167.0ms	4052×	body	80	valid
117.0ms	658×	body	640	valid
43.0ms	315×	body	320	valid
16.0ms	163×	body	160	valid