Details

sample55.0ms

Algorithm

intervals

Results

21.0ms	187×	body	80	valid
10.0ms	24×	body	2560	valid
7.0ms	20×	body	1280	valid
4.0ms	8×	body	5120	valid
2.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.8b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

3.0ms	(+ (* re re) (* im im))
14.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* re re) (* im im))
187.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	296	446
1	1086	401
2	3561	382
3	5001	381

prune234.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
0.8b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
4×	`add-log-exp`
2×	`add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod`

Counts

2 → 29

Calls

2 calls:

5.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series264.0ms

Counts

2 → 6

Calls

2 calls:

201.0ms	(sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))
63.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify70.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	202	247
1	638	221
2	2370	213
3	5002	209

prune113.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))
0.4b	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
0.8b	(+ (* (sqrt 1) (hypot re im)) re)
0.8b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
31×	`sqrt-prod`
28×	`sqrt-div`
26×	`add-sqr-sqrt`
23×	`pow-prod-down`
20×	`pow1/2`
16×	`associate-*r/`
14×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `fma-def` `associate-*l/` `sum-log`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

6.0ms	(sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))
47.0ms	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)
4.0ms	(+ (* (sqrt 1) (hypot re im)) re)

series750.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re))))
397.0ms	(* (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))) (sqrt (sqrt (* 2.0 (+ (* (sqrt 1) (hypot re im)) re)))))
58.0ms	(+ (* (sqrt 1) (hypot re im)) re)
64.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	413	1260
1	1675	1125
2	5001	1073

prune368.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re)))
1.0b	(- (hypot re im) re)
6.5b	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re))))
20.7b	(/ (+ 0 (pow im 2)) (- (hypot re im) re))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
41×	`times-frac`
33×	`add-cube-cbrt`
26×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1` `prod-diff`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l*`
3×	`flip3--` `fma-neg` `associate-l` `flip--`
2×	`cbrt-undiv` `sqrt-pow1` `associate-*r/` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `flip3-+` `pow1/2` `sqrt-div` `diff-log` `clear-num` `sqrt-prod` `*-commutative` `flip-+`

Counts

4 → 136

Calls

4 calls:

34.0ms	(* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re)))
3.0ms	(- (hypot re im) re)
9.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re))))
18.0ms	(/ (+ 0 (pow im 2)) (- (hypot re im) re))

series467.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re)))
65.0ms	(- (hypot re im) re)
218.0ms	(sqrt (* 2.0 (/ (+ 0 (pow im 2)) (- (hypot re im) re))))
89.0ms	(/ (+ 0 (pow im 2)) (- (hypot re im) re))

simplify75.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	525	1142
1	2442	942
2	5001	924

prune380.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.1b

regimes85.0ms

Accuracy

74.9% (2.5b remaining)

Error of 6.4b against oracle of 3.8b and baseline of 13.9b

bsearch56.0ms

Steps

Iters	Range		Point
8	-3.3536907579395365e-135	-4.586080391798997e-138	-7.09276973381737e-138

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	33	15
2	33	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

543.0ms	5965×	body	80	valid
298.0ms	712×	body	2560	valid
181.0ms	529×	body	1280	valid
136.0ms	266×	body	5120	valid
81.0ms	290×	body	640	valid
33.0ms	160×	body	320	valid
12.0ms	78×	body	160	valid