Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	198×	body	80	valid
8.0ms	24×	body	2560	valid
4.0ms	9×	body	5120	valid
4.0ms	13×	body	1280	valid
2.0ms	8×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
29.9b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (82.0ms)

Iter	Nodes	Cost
0	155	205
1	421	183
2	1067	180
3	3190	179
4	5001	178

prune129.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.5b	(+ (hypot re im) re)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
3.0ms	(+ (hypot re im) re)

series105.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(hypot re im)
57.0ms	(+ (hypot re im) re)

simplify72.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	87	85
1	176	79
2	380	79
3	1030	78
4	3143	78
5	5001	78

prune99.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.4b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
7.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
5.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series194.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(hypot re im)
47.0ms	(hypot re im)
48.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
55.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify158.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 3 (152.0ms)

Iter	Nodes	Cost
0	172	342
1	600	287
2	3388	275
3	5001	274

prune219.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(hypot re im)
0.0b	(hypot re im)
13.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`hypot-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 45

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series315.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (hypot re im))
45.0ms	(hypot re im)
47.0ms	(hypot re im)
139.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify45.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	128	219
1	344	188
2	1419	179
3	5002	174

prune174.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.8b

regimes91.0ms

Accuracy

24.5% (4.5b remaining)

Error of 11.9b against oracle of 7.4b and baseline of 13.4b

bsearch37.0ms

Steps

Iters	Range		Point
6	-2.0199682458946676e+123	-4.2189696159604594e+122	-5.904936880911102e+122

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	24	12

end0.0ms

sample650.0ms

Algorithm

intervals

Results

188.0ms	6005×	body	80	valid
140.0ms	735×	body	2560	valid
73.0ms	460×	body	1280	valid
67.0ms	296×	body	5120	valid
33.0ms	283×	body	640	valid
13.0ms	144×	body	320	valid
5.0ms	77×	body	160	valid