Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	203×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	18×	body	1280	valid
2.0ms	9×	body	5120	valid
0.0ms	4×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	24	8
2	30	8
3	35	8
4	35	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

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)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
27.2b	(sqrt (+ (* re re) (* im im)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 54

Calls

4 calls:

9.0ms	(+ (* re re) (* im im))
26.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* re re) (* im im))
165.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	258	459
1	938	422
2	3098	412
3	5001	410

prune174.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.6b	(exp (log (sqrt (+ (* re re) (* im im)))))
12.4b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
27.2b	(sqrt (+ (* re re) (* im im)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-cube-cbrt` `log-prod` `exp-sum` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3-+` `log-pow` `flip-+` `difference-of-squares`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `diff-log` `sum-log` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

9.0ms	(+ (* re re) (* im im))
10.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
61.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* re re) (* im im))
36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
49.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	223	519
1	737	467
2	2078	451
3	5001	442

prune197.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize18.0ms

Local error

Found 4 expressions with local error:

5.0b	(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.6b	(exp (log (sqrt (+ (* re re) (* im im)))))
12.4b	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
27.2b	(sqrt (+ (* re re) (* im im)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`log-prod` `exp-sum`
14×	`*-un-lft-identity`
10×	`add-cube-cbrt` `exp-prod`
8×	`pow1` `sqrt-prod`
6×	`add-log-exp` `difference-of-squares`
4×	`add-exp-log` `log-div` `exp-diff` `sqrt-div` `log-pow` `add-cbrt-cube`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `flip--` `flip-+` `rem-exp-log` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `diff-log`

Counts

4 → 74

Calls

4 calls:

43.0ms	(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
10.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
60.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
36.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
50.0ms	(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 4 (83.0ms)

Iter	Nodes	Cost
0	227	700
1	468	624
2	1022	589
3	2844	575
4	5002	567

prune251.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
3.9b	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
19.2b	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
27.2b	(sqrt (+ (* re re) (* im im)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
15×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1` `associate-/l*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r*` `sqrt-prod`
3×	`sqrt-pow1` `flip3-+` `sqrt-div` `div-exp` `flip-+`
2×	`pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

29.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
24.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
44.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
8.0ms	(sqrt (+ (* re re) (* im im)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
191.0ms	(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
68.0ms	(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	417	1078
1	1461	985
2	5001	978

prune258.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes391.0ms

Accuracy

47.8% (16.5b remaining)

Error of 23.2b against oracle of 6.6b and baseline of 38.3b

bsearch140.0ms

Steps

Iters	Range	Point
8	1.948551490735315e+125	2.5938763934072053e+128	2.4888310110528145e+128
8	-4.077449333417644e-292	-7.37072569108761e-295	-9.566365453995885e-295
9	-1.3998839575152276e+110	-2.8431280732769518e+104	-1.9802675205288276e+108

Iters

Range

Point

1.948551490735315e+125

2.5938763934072053e+128

2.4888310110528145e+128

-4.077449333417644e-292

-7.37072569108761e-295

-9.566365453995885e-295

-1.3998839575152276e+110

-2.8431280732769518e+104

-1.9802675205288276e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	29
1	52	29

end0.0ms

sample721.0ms

Algorithm

intervals

Results

208.0ms	6026×	body	80	valid
129.0ms	683×	body	2560	valid
80.0ms	516×	body	1280	valid
66.0ms	289×	body	5120	valid
33.0ms	273×	body	640	valid
12.0ms	141×	body	320	valid
4.0ms	72×	body	160	valid