Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	93×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 15.2b

Counts

2 → 1

localize8.0ms

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	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite27.0ms

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`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series846.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
110.0ms	(/ 1.0 (hypot 1.0 x))
271.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
359.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5002	876

prune249.0ms

Filtered

104 candidates to 84 candidates (80.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	4	105

Merged error: 14.5b

Counts

105 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series847.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
270.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
318.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
157.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	499	686
1	1863	644
2	5001	643

prune275.0ms

Filtered

83 candidates to 74 candidates (89.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.2b

Counts

87 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
2.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
24×	`prod-diff`
17×	`log-prod`
14×	`exp-sum`
9×	`times-frac`
8×	`pow1`
7×	`sqrt-prod`
6×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`sub-neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ 1.0 (hypot 1.0 x))
268.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
373.0ms	(log (exp (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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

121 → 121

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	559	1699
1	1974	1226
2	5003	1080

prune310.0ms

Filtered

121 candidates to 90 candidates (74.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0.2b

Counts

125 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.9b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

5.0ms	(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

790.0ms	(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
153.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
153.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
154.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	383	1202
1	1549	1077
2	5002	970

prune304.0ms

Filtered

84 candidates to 69 candidates (82.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	84	4	88

Merged error: 0.2b

Counts

88 → 4

regimes264.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	44
1	52	44

end0.0ms

sample850.0ms

Algorithm

intervals

Results

497.0ms	2894×	body	1280	valid
123.0ms	4033×	body	80	valid
81.0ms	607×	body	640	valid
27.0ms	298×	body	320	valid
10.0ms	168×	body	160	valid